First Year Chemistry (honors)

Science Department Glenbrook NorthMarcel Grdinic

2019 - 2020

Contents

1 Fundamentals of chemistry 111 What is chemistry 112 Models in science 213 The 12 principles of green chemistry 214 Chemical safety and disposal 215 The states of matter 316 Substances compounds and mixtures 317 The periodic table 4

2 Matter energy and change 521 Kinetic molecular theory 622 Maxwell-Boltzmann distribution 623 System surrounding and the flow of energy 724 Heat capacity 725 Phase diagrams 8

3 The gas state of matter and a few ideas related to weather 931 Gas pressure 932 Gas laws 933 Gases and weather 10

4 Atomic structure and nuclear chemistry 1041 The properties of the subatomic particles 10

1

42 Isotopes 1043 Atoms and electromagnetic radiation 1244 The Rutherford-Bohr model of the atom 1345 The electron shell model 1446 Electron configurations 1547 Radioactivity 1648 Nuclear decay equations 1649 Half-life 17410 Health effects of radiation 17411 Fission and fusion 18

Introduction

These notes serve to summarize the key concepts and problems covered in the firstyear chemistry course taught at Glenbrook North They are meant to supplement thematerial in the assigned readings class activities experiments and lectures Whenreading these notes you should reference your other course materials

1 Fundamentals of chemistry

Chemistry is a physical science that relies upon experimental techniques In the firstunit we discuss some of these techniques and how the scientific process works

11 What is chemistry

Chemistry is often defined as the study of matter and its properties By matter wemean anything that has mass and takes up space Chemistry has developed modelsand explanations of what all of the stuff around us is made of and how it changeswhen combined It is often called the central science as it deals with systems inbetween the size and scope of physics and biology

2

12 Models in science

A model is a simplified representation of some object idea or process Humanscreate models to understand and explain all sorts of things In science models areused to explain the physical world

A key model in chemistry is the particulate nature of matter model that views allmatter being composed of fundamental particles called atoms Models are alwayssimplified and never fully represent their targets While they are limited they oftenare incredibly useful for understanding and predicting

13 The 12 principles of green chemistry

Green chemistry also called sustainable chemistry is a movement focused on de-signing products and processes that minimize or eliminate the use and generation ofhazardous materials Every chemical compound made has an impact on the health ofhumans animals and the environment Methods in green chemistry aim to minimizethese effects

We employ green chemistry by working with the minimum amount of chemicalsnecessary to carry out an experiment and choosing chemicals that can be easilydisposed of with little impact in the environment

14 Chemical safety and disposal

Chemistry experiments are often potentially hazardous The first step in conductingany experiment is to research the safety hazards in order to take the proper precau-tions and the disposal protocols to make sure that we donrsquot put hazardous substancesinto the environment

15 The states of matter

Matter can exist in distinct forms that we call states Four states are observable ineveryday life solid liquid gas and plasma The particulate nature of matter model

3

can be used to represent these states in what we refer to as particle diagrams Figure1 shows particle diagrams for a solid liquid and gas of a substance

Figure 1 Particle diagram of the three main states of matter

This model is limited in many ways First it is a static model not showing themovement that all particles (including solids) have Second it only portrays thestates of matter in two dimensions Many of these limitations can be overcome byusing computer simulations

16 Substances compounds and mixtures

A chemical substance is a form of matter having a constant chemical compositionand characteristic properties Water (H2O) is a chemical substance A glass of waterhas certain properties that we can observe and measure It is a clear liquid It meltsat 273 K and boils at 373 K A water molecule is always composed of two atoms ofhydrogen and one atom of oxygen

A chemical substance usually cannot be separated into its constituent elements byphysical processes Filtering water will not separate the oxygen atoms from thehydrogen atoms in water

4

A chemical compound is defined as a chemical substance composed of atoms of morethan one element

A mixture is a material made up of two or more different chemical substances whichare physically combined Sucrose (table sugar) mixed with water is a mixture Airis a mixture composed of nitrogen gas oxygen gas and other trace gases

Mixtures can usually be separated by physical means In the laboratory we separateda mixture of sand iron and sodium chloride by using the differences in variousphysical characteristics

Example 1 Classify each of the following as a(n) element compound or mixturea) CO2 b) ocean water c) Ar d) CO

a) CO2 is a compound composed of two elements carbon and oxygen

b) Ocean water is a mixture composed of water molecules dissolved salts and gasesand a whole list of other compounds

c) Ar is the element argon

d) CO is the compound carbon monoxide composed of one atom of the elementcarbon and one atom of the element oxygen

17 The periodic table

The periodic table (Figure 2) is a list of all the known elements in the universe Itis arranged in order of increasing atomic number beginning from the top left andmoving across what are called periods The elements in the same column all have anumber of similar properties and are referred to as families

The families that we will be most concerned with are the alkali metals alkaline earthmetals transition metals inner transition metals halogens and noble gases The

5

Figure 2 The periodic table of elements

distinction between metals and non-metals will also be very important when we beginour discussion of bonding

2 Matter energy and change

Energy is the currency of change In physics it is defined as the quantitative propertythat must be transferred to an object in order to perform work on or to heat anobject Energy is needed for an object to move from one place to another Energy isinvolved when chemical substances change from one state of matter to another TheSI unit of energy is the joule J It takes 1 J of energy to life a medium-sized tomatoup 1 meter A tennis ball thrown at 6 msec also takes about 1 J of energy

While energy is a unifying concept it is often described in different forms such askinetic potential and thermal

21 Kinetic molecular theory

Since molecules move it is useful to describe the energy of their motion kineticenergy As molecules move around faster they have more kinetic energy On averagemolecules in the gas state have more kinetic energy than those in the liquid state

6

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

42 Isotopes 1043 Atoms and electromagnetic radiation 1244 The Rutherford-Bohr model of the atom 1345 The electron shell model 1446 Electron configurations 1547 Radioactivity 1648 Nuclear decay equations 1649 Half-life 17410 Health effects of radiation 17411 Fission and fusion 18

Introduction

These notes serve to summarize the key concepts and problems covered in the firstyear chemistry course taught at Glenbrook North They are meant to supplement thematerial in the assigned readings class activities experiments and lectures Whenreading these notes you should reference your other course materials

1 Fundamentals of chemistry

Chemistry is a physical science that relies upon experimental techniques In the firstunit we discuss some of these techniques and how the scientific process works

11 What is chemistry

Chemistry is often defined as the study of matter and its properties By matter wemean anything that has mass and takes up space Chemistry has developed modelsand explanations of what all of the stuff around us is made of and how it changeswhen combined It is often called the central science as it deals with systems inbetween the size and scope of physics and biology

2

12 Models in science

A model is a simplified representation of some object idea or process Humanscreate models to understand and explain all sorts of things In science models areused to explain the physical world

A key model in chemistry is the particulate nature of matter model that views allmatter being composed of fundamental particles called atoms Models are alwayssimplified and never fully represent their targets While they are limited they oftenare incredibly useful for understanding and predicting

13 The 12 principles of green chemistry

Green chemistry also called sustainable chemistry is a movement focused on de-signing products and processes that minimize or eliminate the use and generation ofhazardous materials Every chemical compound made has an impact on the health ofhumans animals and the environment Methods in green chemistry aim to minimizethese effects

We employ green chemistry by working with the minimum amount of chemicalsnecessary to carry out an experiment and choosing chemicals that can be easilydisposed of with little impact in the environment

14 Chemical safety and disposal

Chemistry experiments are often potentially hazardous The first step in conductingany experiment is to research the safety hazards in order to take the proper precau-tions and the disposal protocols to make sure that we donrsquot put hazardous substancesinto the environment

15 The states of matter

Matter can exist in distinct forms that we call states Four states are observable ineveryday life solid liquid gas and plasma The particulate nature of matter model

3

can be used to represent these states in what we refer to as particle diagrams Figure1 shows particle diagrams for a solid liquid and gas of a substance

Figure 1 Particle diagram of the three main states of matter

This model is limited in many ways First it is a static model not showing themovement that all particles (including solids) have Second it only portrays thestates of matter in two dimensions Many of these limitations can be overcome byusing computer simulations

16 Substances compounds and mixtures

A chemical substance is a form of matter having a constant chemical compositionand characteristic properties Water (H2O) is a chemical substance A glass of waterhas certain properties that we can observe and measure It is a clear liquid It meltsat 273 K and boils at 373 K A water molecule is always composed of two atoms ofhydrogen and one atom of oxygen

A chemical substance usually cannot be separated into its constituent elements byphysical processes Filtering water will not separate the oxygen atoms from thehydrogen atoms in water

4

A chemical compound is defined as a chemical substance composed of atoms of morethan one element

A mixture is a material made up of two or more different chemical substances whichare physically combined Sucrose (table sugar) mixed with water is a mixture Airis a mixture composed of nitrogen gas oxygen gas and other trace gases

Mixtures can usually be separated by physical means In the laboratory we separateda mixture of sand iron and sodium chloride by using the differences in variousphysical characteristics

Example 1 Classify each of the following as a(n) element compound or mixturea) CO2 b) ocean water c) Ar d) CO

a) CO2 is a compound composed of two elements carbon and oxygen

b) Ocean water is a mixture composed of water molecules dissolved salts and gasesand a whole list of other compounds

c) Ar is the element argon

d) CO is the compound carbon monoxide composed of one atom of the elementcarbon and one atom of the element oxygen

17 The periodic table

The periodic table (Figure 2) is a list of all the known elements in the universe Itis arranged in order of increasing atomic number beginning from the top left andmoving across what are called periods The elements in the same column all have anumber of similar properties and are referred to as families

The families that we will be most concerned with are the alkali metals alkaline earthmetals transition metals inner transition metals halogens and noble gases The

5

Figure 2 The periodic table of elements

distinction between metals and non-metals will also be very important when we beginour discussion of bonding

2 Matter energy and change

Energy is the currency of change In physics it is defined as the quantitative propertythat must be transferred to an object in order to perform work on or to heat anobject Energy is needed for an object to move from one place to another Energy isinvolved when chemical substances change from one state of matter to another TheSI unit of energy is the joule J It takes 1 J of energy to life a medium-sized tomatoup 1 meter A tennis ball thrown at 6 msec also takes about 1 J of energy

While energy is a unifying concept it is often described in different forms such askinetic potential and thermal

21 Kinetic molecular theory

Since molecules move it is useful to describe the energy of their motion kineticenergy As molecules move around faster they have more kinetic energy On averagemolecules in the gas state have more kinetic energy than those in the liquid state

6

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

12 Models in science

A model is a simplified representation of some object idea or process Humanscreate models to understand and explain all sorts of things In science models areused to explain the physical world

A key model in chemistry is the particulate nature of matter model that views allmatter being composed of fundamental particles called atoms Models are alwayssimplified and never fully represent their targets While they are limited they oftenare incredibly useful for understanding and predicting

13 The 12 principles of green chemistry

Green chemistry also called sustainable chemistry is a movement focused on de-signing products and processes that minimize or eliminate the use and generation ofhazardous materials Every chemical compound made has an impact on the health ofhumans animals and the environment Methods in green chemistry aim to minimizethese effects

We employ green chemistry by working with the minimum amount of chemicalsnecessary to carry out an experiment and choosing chemicals that can be easilydisposed of with little impact in the environment

14 Chemical safety and disposal

Chemistry experiments are often potentially hazardous The first step in conductingany experiment is to research the safety hazards in order to take the proper precau-tions and the disposal protocols to make sure that we donrsquot put hazardous substancesinto the environment

15 The states of matter

Matter can exist in distinct forms that we call states Four states are observable ineveryday life solid liquid gas and plasma The particulate nature of matter model

3

can be used to represent these states in what we refer to as particle diagrams Figure1 shows particle diagrams for a solid liquid and gas of a substance

Figure 1 Particle diagram of the three main states of matter

This model is limited in many ways First it is a static model not showing themovement that all particles (including solids) have Second it only portrays thestates of matter in two dimensions Many of these limitations can be overcome byusing computer simulations

16 Substances compounds and mixtures

A chemical substance is a form of matter having a constant chemical compositionand characteristic properties Water (H2O) is a chemical substance A glass of waterhas certain properties that we can observe and measure It is a clear liquid It meltsat 273 K and boils at 373 K A water molecule is always composed of two atoms ofhydrogen and one atom of oxygen

A chemical substance usually cannot be separated into its constituent elements byphysical processes Filtering water will not separate the oxygen atoms from thehydrogen atoms in water

4

A chemical compound is defined as a chemical substance composed of atoms of morethan one element

A mixture is a material made up of two or more different chemical substances whichare physically combined Sucrose (table sugar) mixed with water is a mixture Airis a mixture composed of nitrogen gas oxygen gas and other trace gases

Mixtures can usually be separated by physical means In the laboratory we separateda mixture of sand iron and sodium chloride by using the differences in variousphysical characteristics

Example 1 Classify each of the following as a(n) element compound or mixturea) CO2 b) ocean water c) Ar d) CO

a) CO2 is a compound composed of two elements carbon and oxygen

b) Ocean water is a mixture composed of water molecules dissolved salts and gasesand a whole list of other compounds

c) Ar is the element argon

d) CO is the compound carbon monoxide composed of one atom of the elementcarbon and one atom of the element oxygen

17 The periodic table

The periodic table (Figure 2) is a list of all the known elements in the universe Itis arranged in order of increasing atomic number beginning from the top left andmoving across what are called periods The elements in the same column all have anumber of similar properties and are referred to as families

The families that we will be most concerned with are the alkali metals alkaline earthmetals transition metals inner transition metals halogens and noble gases The

5

Figure 2 The periodic table of elements

distinction between metals and non-metals will also be very important when we beginour discussion of bonding

2 Matter energy and change

Energy is the currency of change In physics it is defined as the quantitative propertythat must be transferred to an object in order to perform work on or to heat anobject Energy is needed for an object to move from one place to another Energy isinvolved when chemical substances change from one state of matter to another TheSI unit of energy is the joule J It takes 1 J of energy to life a medium-sized tomatoup 1 meter A tennis ball thrown at 6 msec also takes about 1 J of energy

While energy is a unifying concept it is often described in different forms such askinetic potential and thermal

21 Kinetic molecular theory

Since molecules move it is useful to describe the energy of their motion kineticenergy As molecules move around faster they have more kinetic energy On averagemolecules in the gas state have more kinetic energy than those in the liquid state

6

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

can be used to represent these states in what we refer to as particle diagrams Figure1 shows particle diagrams for a solid liquid and gas of a substance

Figure 1 Particle diagram of the three main states of matter

This model is limited in many ways First it is a static model not showing themovement that all particles (including solids) have Second it only portrays thestates of matter in two dimensions Many of these limitations can be overcome byusing computer simulations

16 Substances compounds and mixtures

A chemical substance is a form of matter having a constant chemical compositionand characteristic properties Water (H2O) is a chemical substance A glass of waterhas certain properties that we can observe and measure It is a clear liquid It meltsat 273 K and boils at 373 K A water molecule is always composed of two atoms ofhydrogen and one atom of oxygen

A chemical substance usually cannot be separated into its constituent elements byphysical processes Filtering water will not separate the oxygen atoms from thehydrogen atoms in water

4

A chemical compound is defined as a chemical substance composed of atoms of morethan one element

A mixture is a material made up of two or more different chemical substances whichare physically combined Sucrose (table sugar) mixed with water is a mixture Airis a mixture composed of nitrogen gas oxygen gas and other trace gases

Mixtures can usually be separated by physical means In the laboratory we separateda mixture of sand iron and sodium chloride by using the differences in variousphysical characteristics

Example 1 Classify each of the following as a(n) element compound or mixturea) CO2 b) ocean water c) Ar d) CO

a) CO2 is a compound composed of two elements carbon and oxygen

b) Ocean water is a mixture composed of water molecules dissolved salts and gasesand a whole list of other compounds

c) Ar is the element argon

d) CO is the compound carbon monoxide composed of one atom of the elementcarbon and one atom of the element oxygen

17 The periodic table

The periodic table (Figure 2) is a list of all the known elements in the universe Itis arranged in order of increasing atomic number beginning from the top left andmoving across what are called periods The elements in the same column all have anumber of similar properties and are referred to as families

The families that we will be most concerned with are the alkali metals alkaline earthmetals transition metals inner transition metals halogens and noble gases The

5

Figure 2 The periodic table of elements

distinction between metals and non-metals will also be very important when we beginour discussion of bonding

2 Matter energy and change

Energy is the currency of change In physics it is defined as the quantitative propertythat must be transferred to an object in order to perform work on or to heat anobject Energy is needed for an object to move from one place to another Energy isinvolved when chemical substances change from one state of matter to another TheSI unit of energy is the joule J It takes 1 J of energy to life a medium-sized tomatoup 1 meter A tennis ball thrown at 6 msec also takes about 1 J of energy

While energy is a unifying concept it is often described in different forms such askinetic potential and thermal

21 Kinetic molecular theory

Since molecules move it is useful to describe the energy of their motion kineticenergy As molecules move around faster they have more kinetic energy On averagemolecules in the gas state have more kinetic energy than those in the liquid state

6

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

A chemical compound is defined as a chemical substance composed of atoms of morethan one element

A mixture is a material made up of two or more different chemical substances whichare physically combined Sucrose (table sugar) mixed with water is a mixture Airis a mixture composed of nitrogen gas oxygen gas and other trace gases

Mixtures can usually be separated by physical means In the laboratory we separateda mixture of sand iron and sodium chloride by using the differences in variousphysical characteristics

Example 1 Classify each of the following as a(n) element compound or mixturea) CO2 b) ocean water c) Ar d) CO

a) CO2 is a compound composed of two elements carbon and oxygen

b) Ocean water is a mixture composed of water molecules dissolved salts and gasesand a whole list of other compounds

c) Ar is the element argon

d) CO is the compound carbon monoxide composed of one atom of the elementcarbon and one atom of the element oxygen

17 The periodic table

The periodic table (Figure 2) is a list of all the known elements in the universe Itis arranged in order of increasing atomic number beginning from the top left andmoving across what are called periods The elements in the same column all have anumber of similar properties and are referred to as families

The families that we will be most concerned with are the alkali metals alkaline earthmetals transition metals inner transition metals halogens and noble gases The

5

Figure 2 The periodic table of elements

distinction between metals and non-metals will also be very important when we beginour discussion of bonding

2 Matter energy and change

Energy is the currency of change In physics it is defined as the quantitative propertythat must be transferred to an object in order to perform work on or to heat anobject Energy is needed for an object to move from one place to another Energy isinvolved when chemical substances change from one state of matter to another TheSI unit of energy is the joule J It takes 1 J of energy to life a medium-sized tomatoup 1 meter A tennis ball thrown at 6 msec also takes about 1 J of energy

While energy is a unifying concept it is often described in different forms such askinetic potential and thermal

21 Kinetic molecular theory

Since molecules move it is useful to describe the energy of their motion kineticenergy As molecules move around faster they have more kinetic energy On averagemolecules in the gas state have more kinetic energy than those in the liquid state

6

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

Figure 2 The periodic table of elements

distinction between metals and non-metals will also be very important when we beginour discussion of bonding

2 Matter energy and change

Energy is the currency of change In physics it is defined as the quantitative propertythat must be transferred to an object in order to perform work on or to heat anobject Energy is needed for an object to move from one place to another Energy isinvolved when chemical substances change from one state of matter to another TheSI unit of energy is the joule J It takes 1 J of energy to life a medium-sized tomatoup 1 meter A tennis ball thrown at 6 msec also takes about 1 J of energy

While energy is a unifying concept it is often described in different forms such askinetic potential and thermal

21 Kinetic molecular theory

Since molecules move it is useful to describe the energy of their motion kineticenergy As molecules move around faster they have more kinetic energy On averagemolecules in the gas state have more kinetic energy than those in the liquid state

6

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

than those in the solid state Kinetic molecular theory is a helpful model to describethe movement of molecules

22 Maxwell-Boltzmann distribution

Consider a beaker filled with H2O at room temperature Not all of the molecules havethe same kinetic energy Some are moving relatively fast and some are moving rela-tively slow The distribution of kinetic energies of a collection of particles is describedby the Maxwell-Boltzmann distribution (Figure 3) Changing the temperature of thesample will change the distribution of speeds

Figure 3 Distribution of molecules at three different temperatures

The average kinetic energy of a sample of particles is what we commonly refer toas temperature When an object at a high temperature comes in contact with anobject at a low temperature energy is transferred in the form of heat Heat alwaysflows from the hotter object to the cooler object There has never been an observedexception to this rule

7

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

23 System surrounding and the flow of energy

In order to clearly communicate the movement of energy scientists will divide theuniverse into the system and surroundings (Figure 4) When energy flows from thesystem to the surroundings the process is referred to as exothermic and when energyflows from the surroundings into the system it is referred to as endothermic

Figure 4 Boundaries for indicating endothermic and exothermic processes

24 Heat capacity

Every chemical substance will have a specific amount of energy needed to change itstemperature by a given amount This property is called heat capacity Water hasan experimentally measured heat capacity of 4184 Jg C This value tells us that toraise the temperature of 1 gram of water by 1 degree C requires the input of 4184J

The information found in a heat capacity can be written into a useful equation

q = mC(Tf minus Ti) (1)

Example 2 How much energy is needed to raise the temperature of 125 g of waterfrom 22 C to 87 C

Using equation 1

8

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

q = (125 g)(4184 Jg C)(87C minus 22C)

q = + 33 995 J

25 Phase diagrams

The simplest phase diagrams are the pressure-temperature diagrams for a single sub-stance such as water shown in Figure 5 The y-axis shows the pressure on the sub-stance and the -axis the temperature Reading the graph gives the state of matterthat the substance will be found at the given pressure and temperature

Figure 5 The states of matter of water

Example 3 A sample of water at a pressure of 025 atm is heated from -25 C to 125C

The only way to answer a question such as this is to have the phase diagram Thepressure exerted on the water is not changing The sample of water begins as a solidand as it is heated it sublimates and becomes a gas

9

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

3 The gas state of matter and a few ideas related

to weather

We breath a mixture of nitrogen gas and oxygen gas each day

The key distinguishing feature between gases and liquids and solids is the vast relativeseparation of particles from one another This distance usually renders gases invisibleto the human eye

31 Gas pressure

Pressure is defined as the force applied to the surface of an object Gases exertpressure by their collisions with the surface of a container Anything that increasesthe number of collisions gas particles undergo will increase the pressure

Gas pressure is additive Daltonrsquos law of partial pressures can be used to calculatethe pressure of a mixture of a gas or determine the partial pressure of one gas giventhe total pressure

Ptotal = P1 + P2 + (2)

32 Gas laws

Mathematical relationships have been established to estimate the measured values ofa gas sample These are collectively known as the gas laws We only concerned ourtime with two of the gas laws Boylersquos law (Equation 3) and Charlesrsquo law (Equation4)

pV = k (3)

P

T= k (4)

10

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

33 Gases and weather

Weather is the term used to describe the current state of our atmosphere in termssuch as wet or dry hot or cold clear or stormy Weather is determined by theinterplay of gas pressure temperature and moisture in one area of the planet toanother

The gas laws we have studied can help explain the reasons for cold fronts and warmfronts as well as the types of clouds present in the sky Weather is complicated andis determined by a multitude of variables

4 Atomic structure and nuclear chemistry

The discovery that everything in the world around us is composed of tiny discreteunits is one of the greatest accomplishments of humanity This discovery has lead tocountless technologies that have improved our lives

41 The properties of the subatomic particles

Each atom of an element is composed of three primary particles protons neutronsand electrons There are more fundamental particles but they usually are not neededto understand chemistry The fundamental properties are shown in Figure 6

Experiments beginning in the late 1800s established that atoms were mostly emptyspace with an incredibly dense nucleus containing almost all of the mass Electronswere initially thought to be orbiting the nucleus

42 Isotopes

The elements found in nature were formed from the death of starts in our universeLighter elements fused together to form larger elements Each element has a char-acteristic number of protons (what we call the atomic number but the number ofneutrons can vary This leads to an average atomic mass for each element that is the

11

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

Figure 6 The particles of most concern in chemistry

weighted average of all the known isotopes Figure 7 below shows the models of thethree known isotopes of the element hydrogen

Scientists use an instrument called a mass spectrometer to analyze elements anddetermine the number and mass of isotopes When this information is known theaverage mass found on the periodic table can be calculated using a weighted averageequations as shown

Avg Mass =983131

(mass I 1) (abundance) + (mass I 2) (abundance) + middot middot (5)

The symbol on the right side of the equals sign in the equation is the Greek lettersigma It stands for sum and means that you add up all of the values calculated foreach isotope

When a scientist writes out a chemical symbol for an element as shown in (6) itrepresents a single isotope

22790Th (6)

A single atom of an element will always have an integer number of subatomic parti-cles The above atom of thorium has an atomic number (number of protons) equal

12

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

Figure 7 The three known isotopes of the element hydrogen

to 90 and a mass number of 227 Since the mass is calculated only from the num-ber of protons and neutrons the number of neutrons is equal to 227 - 90 which is137

43 Atoms and electromagnetic radiation

Atoms and light are clearly connected Ancient civilizations knew that metal glowedhot white when heated and fireworks can be made to give off different colors basedupon which substance was burned

What we call light is just one small fraction of the full electromagnetic spectrum(Figure 8) Energy of this type can be described as waves with a constant velocityknown commonly as the speed of light c = 200 x 108ms

Since the speed is constant there is an inverse relationship between the size of thewave (wavelength) and the frequency of the waves If one is known the other canbe calculated using Equation 7

c = λν (7)

13

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

Figure 8 The electromagnetic spectrum

The higher the frequency (and therefore shorter wavelength) the more energy thatparticular type of electromagnetic radiation has

44 The Rutherford-Bohr model of the atom

The early picture of atoms contradicted all of the known laws of physics of the timeThe electrons and protons should attract leading the electrons to accelerate intothe nucleus and the positively charged protons in the nucleus should all repel awayfrom each other To solve this conundrum scientists developed a theory known asquantum mechanics that had very different (and counterintuitive) explanations as tohow the subatomic particles behave

The new model of the atom viewed the atom not as a solar system but as a multi-story building The lobby was where the nucleus lived and the floors above werewhere the electrons lived When energy was absorbed by the atom electrons wouldmake instantaneous quantum jumps to higher floors When the electron returns tothe initial energy level it gives off the gained energy as light (Figure 9)

This model was soon realized to be incorrect and only a primitive approximationas to what is now understood However its importance is in the introduction to

14

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

Figure 9 Two electron quantum jumps blue light and red light

quantum theory an idea that gets very complicated

45 The electron shell model

Further work in the early 1900s established more details about the structure of theatom The relatively simple floors of the Rutherford-Bohr model gave way to a seriesof atomic orbitals of various sizes and shapes (Figure 10)

Figure 10 Atomic orbitals maps of the most likely location of an electron in a givenenergy level

Electrons (and other atomic level particles) have properties of both particles and

15

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

waves The rules of quantum mechanics state that one cannot not know both theposition and velocity of an electron with absolute certainty The orbitals describethe area in space that one has a 95 chance of finding the electron

46 Electron configurations

Visualizing all of the electrons in a quantum mechanical model of the atom can bedifficult To simplify the notation scientists use two notations to account for all ofthe electrons in an atom a Aufbau diagrams and b electron configurations

An Aufbau diagram shows the electrons as arrows on lines (or sometimes boxes)increasing in energy going up the diagram (Figure 11) Electron configurationscondense the model into a line of text distinguishing between the levels and sub-levels

Figure 11

Example 4 Write the electron configuration for the element sodium

Sodium has 11 electrons Using the periodic table or an Aufbau digram follow therules for adding electrons

Na 1s22s22p63s1

16

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

47 Radioactivity

The nucleus of an atom involves the interaction of attractive forces between the pro-tons from the strong nuclear force and the repulsive forces between protons from theelectromagnetic force Observations made have found that certain ratios of protonsto neutrons are energetically unstable (Figure 12) Unstable atoms will undergoa process of radioactive decay in which the nucleus changes by emitting particlesandor electromagnetic radiation to become more stable

Figure 12 Summary of experimental observations of types of radioactive decay

48 Nuclear decay equations

Scientists can represent radioactive decay by writing nuclear decay equations to showthe changes that occur For example uranium-238 undergoes alpha decay

23892U rarr 234

90Th + 42α (8)

17

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

49 Half-life

Radioactive decay is a random process We cannot look at a single atom of a ra-dioactive element and know when it is going to undergo decay However over thelifetime of a sample the half-life is constant Half-life is the time required for half ofthe substance to decay (on average) Equation 9 can be used to model half life forradioactive substances

Nt = N0

9830611

2

983062 tt12

(9)

The simulation with pennies showed us that half-life is the time for half of a substanceto most likely decay We are modeling a random event that depends upon probabilityA better definition for half-life is therefore rdquothe time required for exactly half of theentities to decay on averagerdquo

410 Health effects of radiation

The field of radiobiology studies the effects of ionizing radiation on living systemsespecially the health effects The particles released during radioactive decay have alot of energy and the ability to knock electrons off of molecules

The removal of electrons from stable molecules can then lead to two broad categoriesof radiation damage deterministic and stochastic Deterministic damage is usuallydue to high doses that outright kill cells in our bodies Stochastic damage is due todamage to our DNA that leads to various types of cancers

Cancer is a group of diseases characterized by abnormal cell growth Despite radia-tion often causing cancer it can be used in directed ways as a treatment for cancerThe high energy radiation can be aimed directly at the cancer cells killing them andstopping tumor growth

18

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19

411 Fission and fusion

The course of humanity was radically changed when scientists learned how to splitmassive atoms like uranium into smaller pieces This process called nuclear fissionreleases massive amounts of energy Scientists have found ways to harness this energyin nuclear power plants as well as nuclear weapons

All nuclear fission currently involves the production of what is referred to as nuclearwaste Nuclear waste is a collection of compounds that are radioactive and harmfulto living systems Many have half-lives in the thousands of years making them amajor problem if we continue to use nuclear fuel for our power needs

19