ATOMIC STRUCTURE AND PERIODICITY

Electromagnetic Radiation

1. One of the ways that energy travels through space is by _________________________.

Examples are:

2. Waves have three primary characteristics.

3. ____________________ is the distance between two consecutive peaks or troughs in a wave.

4. ____________________ is defined as the number of waves (cycles) per second that pass a given point in space.

5. All types of electromagnetic radiation travel at the speed of light.

6. Mathematically, the relationship is:

***** An FM radio station broadcasts at 99.5 MHz. Calculate the wavelength of the corresponding radio waves.

***** Calculate the frequency of light having a wavelength of 589 nm.

***** Calculate the wavelength, in nm, of a laser used in eye surgery if the frequency is 4.688 x 1014 s-1.

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The Nature of Matter

1. The radiation profiles of solid bodies heated to incandescence could not be explained using classical physics. So, Max Planck postulated that energy can be gained or lost only in integer multiples of _______.

2. _______ is a constant called ______________________________. Its value is:

3. The change in energy can be determined by:

4. The transfer of energy is not continuous. It is instead, ____________________, and can occur only in discrete units of size hυ.

5. Each of these small “packets” of energy is called a ____________________.

6. Since a system can transfer energy only in whole quanta, it seems energy has particulate properties.

7. Einstein proposed that electromagnetic radiation could be viewed as a stream of particles called____________________.

8. The energy of each photon is given by the expression:

***** A laser emits light with a frequency of 4.69 x 1014 s-1.

(a) What is the energy of one photon of the radiation from this laser?

(b) If the laser emits a pulse containing 5.00 x 1017 photons of this radiation, what is the total energy of the pulse?

(c) If the laser emits 1.30 x 10-2J of energy during a pulse, how many photons are emitted during the pulse?

***** A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon and a mole of UV photons having a wavelength of 25.0 nm?

9. From Planck and Einstein we have:

(a) Energy is quantized. It can occur only in discrete units called quanta.

(b) Electromagnetic radiation, which was previously thought to exhibit only wave properties, seems to show certain characteristics of particulate matter as well.

10. This is referred to as the ___________________________________.

11. Lois de Broglie studied this question and proposed one could calculate the wavelength of particulate matter. De Broglie’s equation is:

***** Neutron diffraction is used in determining the structure of molecules.

(a) Calculate the de Broglie wavelength of a neutron moving at 1.00% of the speed of light. The mass of neutron is 1.67 x 10-24g.

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(b) Calculate the velocity of a neutron with a wavelength of 75.0 pm.

12. Diffraction patterns of x-rays passed through the lattice structures of various compounds and proved that particles have wavelike properties.

13. All matter exhibits both particle and wave properties.

14. Large pieces of matter exhibit particulate properties. Very small particles exhibit predominately wave properties. Intermediate particles, such as electrons, display both the particulate and wave properties of matter.

The Atomic Spectrum of Hydrogen

1. Visible light passed through a prism produces a ______________________________.

2. The emission spectrum of excited atoms is called a ______________________________.

3. A line spectrum indicates that only certain energies are allowed in the hydrogen atom. In other words, the energy of the electron in the hydrogen atom is ____________________.

4. The discrete line spectrum of hydrogen shows that only certain energy levels are possible.

The Bohr Model

1. Bohr developed the quantum model for the hydrogen atom.

2. He proposed that the electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.

3. Bohr accounted for a circular motion by saying the attraction for the nucleus kept the electron from flying off the atom.

4. A charged particle in motion should radiate energy. This means the electron should lose energy and spiral into the nucleus.

5. The experimental evidence showed that only certain electron energies were allowed.

6. Bohr found his model would work if he assumed the angular momentum of the electron could only occur in certain increments.

7. This assumption enabled Bohr’s model of the hydrogen atom to have energy levels consistent with the hydrogen emission spectrum.

8. The energy can be calculated by:

9. (-) means the energy of the electron bound to the nucleus is lower than it would be if the electron were at an infinite distance from the nucleus where there is no interaction and the energy is zero.

10. The energy of the electron in any orbit is negative relative to this reference state.

11. The above equation can be used to calculate the change in the energy of an electron when the electron changes orbits.

12. The lowest possible energy state is called the _________________________.

***** Calculate the wavelength of light emitted when an electron transitions from n=5 to n=4 in the hydrogen atom.

13. The calculation of ∆E can be made simpler by using:

14. A simpler equation involving wavelength is known as the Rydberg equation:

15. There are two important points about the Bohr model:

(1) The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain allowed circular orbits for the electron.

(2) As the electron becomes more tightly bound, its energy becomes more negative relative to the zero-energy reference state (corresponding to the electron being at an infinite distance from the nucleus). As the electron is brought closer to the nucleus, energy is released from the system.

16. When Bohr’s model was applied to atoms other than hydrogen it did not work.

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17. Bohr’s model is fundamentally incorrect. Electrons do not move around the nucleus in circular orbits.

The Quantum Mechanical Model of the Atom

1. The approach taken by the physicists following Bohr became known as ____________ mechanics or ____________ mechanics.

2. Schrodinger and de Broglie said the electron bound to the nucleus seemed similar to a standing wave.

3. Only certain circular orbits have a circumference into which a whole number of wavelengths of the standing electron wave will fit.

4. Schrodinger’s equation looks like:

_____ called the wave function is a function of coordinates (x,y,z) of the electron’s position in three-dimensional space.

_____ is a set of mathematical instructions called operator.

_____ is the total energy of the atom

5. Each solution of the consists of a wave function that is characterized by a particular value of E.

6. A specific wave function is called an __________.

7. An orbital is not the same as a Bohr orbit.

8. The wave function gives us no information about the detailed pathway of the electron we cannot predict the motion of the electron.

9. The Heisenberg uncertainty principle states there is a fundamental limitation to just how precisely we can know both the position and the momentum of a particle at a given time.

10. Mathematically it looks like:

Thus, the minimum uncertainty is ____________________.

11. What this really says is that the more accurately we know a particle’s position, the less accurately we can know its momentum, and vice versa.

The Physical Meaning of a Wave Function

1. The square of the wave function indicates the probability of finding an electron near a particular point in space.

2. The model still gives no information concerning when the electron will be at a certain position or how it moves between positions.

3. The square of the wave function is most conveniently represented as a probability distribution.

4. The diagram that results from plotting the probabilities is known as an electron density map; electron density; or electron probability.

5. Most chemists refer to an atomic orbital, meaning an electron density map.

6. The definition most often used by chemists to describe the size of the hydrogen 1s orbital is the radius of the sphere that encloses 90% of the total electron probability.

Quantum Numbers

1. When we solve the Schrodinger equation for the hydrogen atom, we find many wave functions (orbitals) that satisfy it.

2. Each of these orbitals is characterized by a series of numbers, called ______________________________, which describe various properties of the orbital.

3. The ____________________ quantum number _______ has integral values: 1, 2, 3, … It is related to the size and energy of the orbital. As n increases, the orbital becomes larger and the electron spends more time further from the nucleus.

4. An increase in n also means higher energy, because the electron is less tightly bound to the nucleus and the energy is less negative.

5. The ________________________________________ quantum number _______ has integral values

from _________________ for each value of n. The quantum number is related to the shape of the atomic

orbitals.

6. The value of l for a particular orbital is commonly assigned a letter:

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7. The ___________________________________ quantum number _______ has integral values between

_________________, including zero. The value of ml is related to the orientation of the orbital in space

relative to the other orbitals in the atom.

***** Which of the following sets of quantum numbers are not allowed in the hydrogen atom?

(a) n = 3, l = 2, ml = 2

(b) n = 4, l = 3, ml = 4

© n = 0, l = 0, ml = 0

(d) n = 2, l = -1, ml = 1

(e) n = 3, l = 1, ml = -1

Orbital Shapes and Energies

1. Using the unique probability distribution for each orbital and using a surface that surrounds 90% of the total electron probability one can predict a shape for each orbital.

2. The s orbitals are spherical in shape.

3. The p orbitals each have two lobes separated by a node at the nucleus; they are labeled according to how they lie along the x, y, and z axes.

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4. The d orbitals have five shapes.

5. The f orbitals have seven shapes.

6. The energy of a particular orbital is determined by its value of n.

7. All orbitals with the same value of n have the same energy, they are said to be ________________.

Electron Spin and the Pauli Exclusion Principle

1. A fourth quantum number, _________________________, is necessary to account for the details of the emission spectra of atoms.

2. The spectral data indicate that the electron has a magnetic moment with two possible orientations when the atom is placed in an external magnetic field.

3. The new quantum number is called the __________ quantum number _______ and has values of _____ and _____.

4. The main significance of electron spin is connected with the ______________________________.

5. It states: in a given atom no two electrons can have the same set of four quantum numbers.

6. An orbital can only hold two electrons and they must have opposite spins.

Polyelectronic Atoms

1. The Schrodinger equation for polyelectronic atoms cannot be solved exactly.

2. The difficulty arises in dealing with repulsions between electrons.

3. Since the electron pathways are unknown, the electron repulsions cannot be calculated exactly. This is known as the electron correlation problem.

4. The approximation most commonly used is to treat each electron as if it were moving in a field of charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons.

5. The outer electrons are screened or shielded from the nuclear charge by the repulsions of other electrons.

6. For polyelectronic atoms, the orbitals of a given quantum number are not degenerate. The energy levels are different.

7. This is because the penetration effect causes an electron in an s orbital to be attracted more strongly than an electron in a p orbital.

8. The more effectively an orbital allows its electrons to penetrate the shielding electrons to be close to the nuclear charge, the lower is the energy of that orbital.

History of the Periodic Table

1. It was originally constructed to represent the patterns observed in the chemical properties of the elements.

2. Johann Dobereimer found several groups of three elements that have similar properties, i.e., chlorine, bromine, and iodine. He developed a model of triads. As the number of known elements expanded, his model became very limited.

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3. John Newlands attempted to organize the elements in _______________ based on the idea that certain properties seemed to repeat every eighth element. While a little useful, it was not successful.

4. Dimitri Mendeleev is credited with coming up with the periodic table. His table allowed rows to expand and repeat patterns naturally. He left blank spaces where necessary and correctly predicted the properties of the missing elements.

5. Mendeleev’s table was organized by increasing atomic mass. It is now organized by increasing atomic number.

The Aufbau Principle and the Periodic Table

1. The aufbau principle states that as protons are added one by one to the nucleus to build up the elements, electrons are similarly added to these hydrogen like orbitals.

2. In addition to following the aufbau principle, the electrons fill orbitals of similar energy levels according to Hund’s Rule.

3. Hund’s rule states that the lowest energy configuration for an atom is one having the maximum number of unpaired electrons allowed by the Pauli exclusion principle in a particular set of degenerate orbitals.

Electron Configurations

1. The way in which electrons are distributed among the various orbitals of an atom is called the electron configuration of the atom.

2. The most stable electron configuration of an atom – the ground state – is that in which the electrons are in their lowest possible energy states.

3. If there were no restrictions, all the electrons would crowd into the 1s orbital. But the electron configuration seems best explained and organized according to the Pauli exclusion principle, the aufbau principle, and Hund’s rule.

4. ____________________ are the electrons in the outermost principal quantum level of an atom.

5. Valence electrons are the most important electrons to chemists because they are involved in bonding.

6. The inner electrons are known as _________________________.

7. The elements in the same group have the same valence electron configuration.

8. The __________ orbital fills before the _______ orbitals.

9. Lanthanides are elements in which the _______ orbitals are being filled.

10. Actinides are elements in which the _______ orbitals are being filled.

11. The group label tells the total number of valence electrons for that group.

12. The groups labeled ______________________________ or ______________________________ are

often called the _______________ or _______________ elements.

13. There are three ways to represent an electron configuration: (a) a complete electron configuration; (b) orbital diagrams; and (c) abbreviated, or noble gas, configurations.

14. A diagram, known as the diagonal rule, can be used to summarize the order in which the orbitals fill in polyelectronic atoms:

7s2 7p6 7d10 7f14

6s2 6p6 6d10 6f14

5s2 5p6 5d10 5f14

4s2 4p6 4d10 4f14

3s2 3p6 3d10

2s2 2p6

1s2

15. One can also make use of the following diagram to help determine an electron configuration:

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***** Write the complete electron configuration, orbital diagram, and noble gas configuration for the following:

(a) Cu

(b) As

(c) W

Periodic Trends in Atomic Properties

Atomic Radius

1. As one goes down a group, the size (radius) increases because successive principal quantum levels physically add to the size of the atom.

2. In addition, the effective nuclear charge felt by the new valence shell is less than that felt by the previous valence shell due to the ______________________________ of the inner core electrons.

3. Effective nuclear charge can be calculated:

4. As one goes across a period from left to right, the size of the atoms decrease because there is an increase in effective nuclear charge. Zeff decreases because Z increases while S remains constant.

***** Compare the effective nuclear charge experienced by a valence electron in strontium, barium, and radium.

***** Compare the effective nuclear charge experienced by a valence electron in magnesium, silicon, and sulfur.

Sizes of Atoms and Ions

1. The formation of a cation involves the loss of electrons from the valence shell which decreases the number of electron-electron repulsions.

2. As a consequence, a cation is smaller than its parent atom.

3. The formation of an anion involves the addition of electrons to the valence shell and increases the number of electron-electron repulsions.

4. Anions are larger than their parent atoms.

5. For ions carrying the same charge, size increases as one goes down a column in the periodic table.

6. An ___________________________________ is a group of ions all containing the same number of electrons. An example is:

Each has 10 electrons.

7. Because the number of electrons remains constant in an isoelectronic series, the radius of the ion decreases with increasing nuclear charge:

***** Arrange the following atoms in order of increasing size: P, S, As, Se.

***** Arrange these atoms and ions in order of decreasing size: Mg2+, Ca2+, Ca.

***** Arrange the ions K+, Cl-, Ca2+, and S2- in order of decreasing size.

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***** Write the electron configuration for:

(a) Co3+

(b) S2-

Ionization Energy

1. _________________________ is the energy required to remove an electron from a gaseous atom or ion:

Where the atom or ion is assumed to be in its ground state.

2. The first ionization energy is the energy required to remove the highest energy electron of an atom.

3. The second ionization energy is much higher than the first ionization energy. Subsequent ionization energies get higher because the increasing positive charge causes the ionic radius to shrink and bind the electrons more tightly to the nucleus.

4. The first ionization energy increases as one goes across a period from left to right. The first ionization energy decreases as one goes down a group.

***** Explain why the first ionization energy tends to increase as one proceeds from left to right across a period and decreases as one goes down a group in the periodic table.

***** Arrange the following atoms in order of increasing first ionization energy: Ne, Na, P, Ar, K.

Electron Affinity

1. Electron affinity is the energy change associated with the addition of an electron to a gaseous atom. It measures the attraction, or affinity, of the atom for the added electron.

2. For most atoms, energy is released when an electron is added:

Therefore, the numerical value for the energy is preceded by a negative sign just like an exothermic process in thermodynamics.

3. The more negative the number, the greater the energy release.

4. Electron affinity does not vary greatly going down a group. In general, electron affinity becomes more positive (less energy released) as one goes down a group.

5. Electron affinities generally become more negative as one goes across a period from left to right.

***** The electron affinity of lithium is a negative value, whereas the electron affinity for beryllium is a positive value. Use electron configurations to account for this observation.

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