Space Gravity

Universal Gravitation The Law of Universal Gravitation states that for two masses separated in space, there is a force of attraction

between them due to the interaction of their gravitational fields.

This formula can be used to derive

Variation in the Earth’s gravitational acceleration can be caused by:

Altitude: the changes in the formula

Crust density: denser crust results in slightly higher mass of Earth

Rotation of Earth: the Earth is spinning and trying to throw us off so that reduces slightly

Shape of the Earth: Earth bulges at the equator so d is slightly greater there

Gravitational Potential Energy Gravitational potential energy is the energy stored in a body due to its position in a gravitational field. A change in

GPE is related to work done because work makes the object move.

Ep = mgh <- because it doesn’t account for decrease in g by increase in height.

<- Better formula but remember that the d isn’t squared

Why is GPE negative?

Assume an object is at a point infinitely far away from the Earth. Its GPE is 0 because Earth’s gravitational field is 0. If

it were to move towards the Earth, its GPE would decrease whilst it gains KE. If GPE decreases below 0, it becomes

negative.

Although Ep is negative, ΔEp can be positive. For two places in a gravitational field where distances are r1 and r2,

formula is:

, where r1 is greater than r2.

Pendulum Motion Prac

√

Angle of pendulum should be less than 10o for simple harmonic motion; otherwise it will become a conical

pendulum. Time for 10 oscillations is used to reduce human error. Sources of error are reaction times, air friction

and non-linear swinging. Graph T2 vs l instead of T vs l for a linear graph.

Space Exploration

Projectile Motion Projectile motion is motion that is only influenced by weight force. It has two main rules:

Horizontal and vertical motion are independent and can be calculated separately

Horizontal velocity is constant whilst vertical velocity has downwards gravitational acceleration.

To do projectile motion problems, use trig to resolve the vector and use the kinematic equations for calculations:

s=ut, v=u+at, v2=u2+2as, s=ut+1/2 at2.

Galileo’s analysis of projectile motion:

He deduced that the trajectory of projectiles is parabolic

Horizontal motion is independent from vertical motion

He realised math is important for analysing projectile motion

Circular motion and Satellites Satellites orbiting around earth have two velocity components: the gravity pulling it towards the earth and its linear,

tangential speed. These two components combine to create its circular motion.

Orbital Velocity: The linear velocity a satellite must have to remain in orbit around an object.

Geosynchronous satellites have a period of 24 hours, whilst Geostationary have 24 hour period and go above

equator.

Launch To escape the gravitational field of a planet:

√

As the rocket ascends, its acceleration increases because mass decreases (use of fuel and stages fall off), velocity

changes from vertical to horizontal so it’s less affected by gravity, and g decreases as altitude increases. Earth rotates

from west to east at 465 ms-1, so rocket is launched eastward from equator (where rotational velocity is greatest) to

get additional velocity.

g-force: measure of acceleration as a multiple of 9.8

Positive g-force goes upwards (drains blood from brain causing blackout), negative g-force goes downwards (too

much blood in head, redout).

Slingshot Effect The slingshot effect is when a planet’s gravitational field and orbital field are used to help a space probe flying past it

gain extra speed.

When a probe flies past a planet, it speeds up, and then slows back to original due to the planet’s g field. However,

the planet is orbiting around the sun, so the probe will add on the planet’s velocity. The extra velocity is not free,

and the conservation of angular momentum means that the planet will slow down slightly.

Geostationary Satellites Low Earth Orbit Satellites

Description Stay at a fixed position above equator Orbit with earth, so period is 24 hours Very high altitude (35,900 km)

No fixed position Periods lower than 24 hours Lower orbital altitude (200-2000 km) Can pass over any point on Earth

Advantages Do not have orbital decay Easy to track due to constant position

Can scan different areas of Earth many times a day Low altitudes allow:

closer view of Earth

rapid information transmission

cheaper launchings

Disadvantages Delay in information transmission Limited view of Earth’s surface Expensive launch due to high altitude

Difficult to track Experiences atmospheric drag and orbital decay Control of orbital paths is needed to avoid hitting other satellites

Uses Information Relay Communications Weather monitoring

Geoscanning and geomapping Study weather patterns Remote scanning

Re-entry Rockets must re-enter the Earth’s atmosphere at an angle between 5.2O and 7.2O. If angle is too big, there will be too

much resistance from the atmosphere and the spacecraft will have too much deceleration, causing redout, and it will

burn up. If angle is too small, spacecraft will bounce off atmosphere and fly into the sun.

Von Braun German rocket engineer, made V2 rockets for Germany, later helped US make missiles for military and rockets for

high altitude studies and space exploration, led the development of Saturn rockets which put Armstrong on the

moon.

Special Relativity – Aether model Aether: an undetectable, extremely thin, elastic material that surrounded all matter and is thought to be the

medium for light propagation, as well as an absolute frame of reference for all motion.

Since every other wave requires a medium for propagation, scientists thought light would require a medium too, so

they thought up the idea of aether.

The Michelson-Morley experiment, named after Norman Experiment, attempted to determine the speed of the

Earth’s rotation relative to the aether.

Spoiler: there was no change in speed of light detected, so the experiment could not prove the existence of aether.

As a result, scientists were baffled and failed to theorize an explanation. Until one man had the idea of making time

and space relative, whilst saying that the measured speed of light is always constant, regardless of its relative

velocity. This not only throws out the idea of aether, but explains the results of the Michelson-Morley experiment.

That man’s name? Albert Einstein. However, if not for the Michelson-Morley experimental results, Einstein’s theory

of special relativity would not have been accepted and we would be harkling back to the caves with our aether

model.

Special Relativity – Galileo and Einstein Inertial frames of reference are either stationary or moving with constant velocity.

Most frames of reference are non-inertial.

Principles of special relativity (which only applies to inertial frames of reference):

1. Vlight is constant c (explains the non-existent change of interference pattern in MM experiment and makes space

and time relative)

2. All inertial frames of reference are equal and no inertial frame of reference is truer than others (resolves need

for an absolute frame of reference which the

aether fulfilled)

Impacts of special relativity 1. Two events that are simultaneous to one

observer may not be simultaneous to another

observer in a different frame of reference.

Suppose an observer is in the middle a really

long non-moving train with fireworks at both

ends. When the fireworks are lit at the same

time, the lights travel to the observer over the

same distance so they appear simultaneous. If

the train is moving at a fast speed, the light

from one of the fireworks will have a longer distance (d+vt) to travel than the light from the other one (d-vt) so

they don’t appear simultaneous.

2. Time dilation is like a moving clock running slower. Since d’ > d, Observer B sees the light travelling for a longer

time than what observer A sees.

3. Length contraction is when the length of a moving object is shorter in the direction of movement.

4. Mass dilation is when the mass of a moving object seems greater compared to the object’s mass at rest.

5. Energy and mass are equivalent and convertible e=mc2

Standard of Length In 1793 the French government decided that a metre is one ten-millionth of the distance from the north pole to the

equator.

In 1960 it was changed to 1650763.73 wavelengths of krypton-86 emission.

In 1983 it was changed to a definition based on time, the length of a path travelled by light in a vacuum during the

time interval of 1/299792458th of a second.

Evidence One atomic clock was put on a plane while the other was left on Earth. The plane flew away at a high speed and

when it finished flight, the time in the clock on the plane was found to run slower.

Muons are a type of subatomic particle formed from the interaction of cosmic radiation with the upper atmosphere.

They have a short half-life of only 2 microseconds, meaning it should be impossible for it to reach the Earth.

However, the presence of muons on the Earth’s surface has been detected. This is due to the muons’ high velocity

causing time dilation.

Twin Paradox There are two identical twins, one goes on a spacecraft and flies away to a star then back to Earth whilst the other

twin stays on Earth. The Earth twin thinks he’s stationary whilst the space twin is moving, so the space twin should

be younger. The space twin thinks he’s stationary whilst the Earth twin is moving relative to him, so the Earth twin

should be younger. The two twins cannot be younger than each other though. This paradox is resolved by discussing

the non-inertial frame of reference that the space twin undergoes while accelerating and decelerating.

Why Special Relativity is Special Trains cannot travel at relativistic velocities.

Even if a train can travel this fast, it is impossible to observe anything.

In the time dilation experiment, it is impossible to see the single light beam moving and reflecting.

In the relative simultaneity experiment, the train needs to be infinitely long, and even if it was infinitely long then

the observer wouldn’t be able to see the light flashes because the train is infinitely long.

Implications on Space Travel Increase of mass makes it more difficult to accelerate.

Due to time dilation, extremely long space travel won’t seem so long.

Due to length dilation, the distance travelled won’t seem so long.

Motors and Generators The Motor Effect

Τ = torque

n = number of coil turns

B = magnetic field strength

I = current in coil

A = area of coil

θ = angle between coil and

magnetic field

Applying the right hand palm rule, side ab has a downward force and side cd has an upwards force, forming a net

torque. However, when the coil has turned 90 degrees, the coil is perpendicular to the magnetic field, so the torque

is 0.The inertia will still make the coil turn, but after crossing past the 90 degree line, the forces will become reversed

and the coil will move back towards its initial position.

This problem is solved by using a split ring commutator, which reverses the direction of the current at the vertical

positions by changing its contact with the carbon brushes.

Other parts of DC motor The stator is the stationary part whilst the rotor is the spinning part. The magnetic field can come from a permanent

magnet or an electromagnet. A radial magnet is a type of permamagnet used when a constant rotational speed is

needed, as the coil is always parallel to the curved magnetic field formed.

The armature is the coil of wire in the magnetic field.

Carbon brushes allow electrical contact between the split ring commutator and wires from the power source. They

are made of carbon or graphite because it is a lubricant, conducts electricity and can withstand high heat.

Galvanometer/Loudspeaker

Galvanometer: When an electrical current is passed through the coil, it rotates due

to the magnetic field.

Loudspeaker: The electrical currents going through the coil create a force in the magnetic field. The force pushes the

coil back and forth, creating vibrations which make sound

Electromagnetic Induction

Faraday

In the experiments, the galvanometer would register a small current, then drop to zero when the power source was

switched on. A greater current was registered when an iron ring was used. This phenomena is caused by the current

in the primary coil building up to its maximum value when the power is switched on, creating a changing magnetic

field, which induces EMF in the secondary coil.

This discovery was a major advance in scientific understanding because inducing a current using a changing magnetic

field proved that electricity and magnetism were related. The discovery was very valuable because it led to further

work on electromagnetism and the subsequent development of electrical generators.

Field lines, Flux and Density Magnetic flux is the number of magnetic field lines passing through an area.

= magnetic flux in Webers (Wb)

B = magnetic field strength in Teslas (T)

A = area

= angle between magnetic field lines and the normal of the area

Magnetic field strength (B) is the amount of magnetic flux per unit area, it is also called magnetic flux density.

Faraday’s law The size of an induced EMF is directly proportional to the rate of change in magnetic flux.

= induced EMF (V)

n = number of turns of coil

= rate of change in flux

Factors determining size of the induced EMF

1. Size of change in magnetic field

2. Speed of relative motion between magnetic

field and conductor

3. Number of turns of coil

4. Change in area that magnetic field passes

through

Lenz’s Law When an EMF is being induced in a conductor as a result of changing magnetic flux, the current it produces will make

a magnetic field that always opposes the change and hence opposes the cause of induction. This is to obey the law

of conservation of energy.

Lenz’s law affects motors, as the spinning coil in the magnetic field will induce a current which flows in the opposite

direction (back EMF). As the rotational speed of the coil increases, the back EMF increases.

Induction cooktops

AC current going through coil produces a changing magnetic field,

which induces eddy currents in metal

More efficient as there is less energy loss

Safer as only the metal pot is heated, no open flame

Ceramic cooktop is easier to clean

Eddy current brakes

Powerful magnets are lowered near train wheels

The rotating wheels in the presence of a magnetic field slow down

due to the induced eddy currents

This braking is smooth as the braking force is dependent on

rotation of wheels

No wear as there is no physical contact between wheels and brakes

Generators A generator uses electromagnetic induction to convert mechanical energy into electrical energy. Diagram is opposite

of motor.

Difference between AC and DC Generator DC generators use a split ring commutator, to allow each half of the commutator to contact a different at every half

rotation at the vertical positions. This ensures that the output current flows in one direction.

AC generators use a slip ring commutator, so the polarity of the current is reversed at every half cycle.

In power stations, three-way AC generators are used for their efficiency.

Transmission Wires The top wire is an overhead wire that carries no current, used to protect from lightning.

Transmission wires are bare, so if they contact the metal towers, the towers will short circuit and become live with

electricity. As a result, wires are suspended by stacks of ceramic disks.

There is energy loss through heat, P=I2R

Advantages and disadvantages of AC and DC generators AC generators DC generators

Advantages Disadvantages Advantages Disadvantages

Three-phase generation Frequencies must be synched

Some devices must use DC

Split ring commutators are expensive

Easily transformed More dangerous DC is more powerful Less efficient

Westinghouse and Edison competition Westinghouse and Tesla’s AC won because AC is more efficient, can be transformed and the split ring commutator of

DC posed a problem with high speed rotation.

Assess effects of AC generation on society and environment Advantages Disadvantages

Improvements in living Environmental pollution

Efficient, clean energy Disturbing natural habitats

Concentration in production of electricity Accidents

Development of industry Replacement of labour

Less energy loss through transmission Industrialisation

Transformers Transformers change the voltage of an electrical current. When AC current flows through the primary coil, it creates

a changing magnetic flux which is amplified by the soft iron core, and generates electricity in the secondary coil.

Since size of EMF depends on turns of coil, the ratio of coil turns determines the ratio of voltage transformation.

There is energy loss through heat, as eddy currents are induced in the iron core. This can be reduced through

lamination, where stacks of iron with insulation in between are used to create the core.

Voltage changes Electricity generated by three-phase AC generator has 23000V and 10000A

For long distance transmissions, the voltage is stepped up to 330000 V

After the electricity is transmitted over a long distance, it is stepped down at regional sub-stations for safety

Eventually it is stepped down to 240 V for households.

Energy loss is related to current, not voltage, so electricity is stepped up to increase efficiency

Many home appliances require a transformer. A cathode ray TV requires thousands of volts, whilst small appliances

require low voltage electricity.

Impact of Transformers Encouraged shift from DC to AC

Increases efficiency in transmission of electricity

Allows distant location of power stations

Allows development of appliances running at different voltages

Ideas to Implementation From CRTs to CROs to TVs The inconsistent behaviour of cathode rays caused debate to whether they were particles or waves. German

scientists such as Hertz thought that they were waves because they could not be deflected by electric plates (small

amount of gas in his CRT and plates too weak), could cast shadows and diffract. British scientists thought they were

particles because they cause fluorescence and have momentum.

Charge to mass ratio experiment A cathode ray was deflected by both an electric and

magnetic field such that the forces balance out.

The electric field is turned off, and the deflection by

magnetic field is circular motion.

Conclusion and implications:

Proved cathode rays were negatively charged particles

Showed they had a large negative charge with low mass

Contributed to discovery of electrons and development of newer atom models

Allowed mass of electrons to be calculated (Milikan’s oil drop experiment)

Properties of Cathode Rays Emitted from cathode and travel in straight lines (Maltese cross)

Cause fluorescence

Can be deflected by magnetic and electric fields

Carry and transfer momentum (Paddle Wheel)

Implementation - CRO Electron Gun: Thermionic emission is heating cathode to release free electrons

Deflection System: Voltage to Y plates is

controlled by an external signal, whilst

voltage to X plates is time-based and

controlled by inbuilt circuitry.

Display Screen: Contains pixels made up of

fluorescent material.

Implementation – TV Electron Gun: Black and White TV has one

electron gun whilst colour has 3. There is a

grid in each electron gun to control

brightness.

Deflection System: Magnetic fields created

by current coils are used to ensure more

efficient and larger deflections.

Display Screen: Made of pixels. In BW, a

pixel ranges from white (max intensity) to

black (no intensity). In RBG, a shadow mask

is used to ensure the beam from each

colour gun only hits its spot. Each pixel has three sub-pixels: red, blue and green.

Prac – Striations High Pressure: Purple streamers between anode and cathode

Medium Pressure: Purple turns to pink, which breaks into alternate bright and dark regions. From cathode to anode,

they are named: Aston dark space, cathode glow, Crooke’s dark space, negative glow, Faraday’s dark space, positive

column, anode glow and anode dark space. A glowing region is a result of electrons colliding into gas molecules and

exciting them. A dark space is a result of electrons having insufficient energy (from past collisions) to excite the gas

molecules.

Low Pressure: Whole tube is dark (Crooke’s dark space) except green fluorescence on glass wall at anode region.

From the Photoelectric Effect to Photo Cells

Hertz Experiment Before Hertz’s experiment, we only had James Maxwell’s

v=fλ equation for EMR, which implied the existence of other

forms of EMR.

Once Hertz had identified radio waves, which behaved as

Maxwell’s equations predicted, other forms of EMR were

sought. Radio waves were soon used for communications.

Hertz noticed that when the coil was placed in a dark box,

the spark’s intensity decreased, and when a light source was

placed near it, the intensity increased. He recorded these

observations but did not further investigate them.

Photoelectric Effect and Black Body Radiation The photoelectric effect is the phenomena that a metal

surface emits electrons when struck by EMR with a frequency

above a certain value. It is a subset of quantum physics, just like

black body radiation.

A black body is an object that can absorb and/or emit energy

perfectly. Scientists thought that black body radiation gets

exponentially larger at small wavelengths, but it actually

peaks at a certain wavelength. In response, Planck theorised that

black body radiation is quantised – emitted in quanta

(photons). Their energy is related to their frequencies: E=hf

Although Planck first proposed the quantisation of energy, no one

believed it until Einstein picked it up and provided convincing

evidence to back it up.

Einstein came from a Jewish family, and was very pacifist and

politically active, openly criticizing German militarism during

WWI and wrote to Franklin Roosevelt convincing him to

make nuclear weapons because he thought Germany was going to make them.

Planck was not as politically active as Einstein and focused on physics research during the war. However, he did go to

Hitler to try and stop his racial policies.

From Semiconductors to Solid State Devices

Energy Bands The energy band is the range of energy electrons possess in a lattice.

The valence band is made up of the energy levels of valence electrons, and has higher energy levels than the

bands of the inner shells.

When valence electrons gain energy, they move up to the conduction band, where they are free to move

and conduct electricity.

In semiconductors and insulators, there is a forbidden energy gap between valence and conduction band.

As temperature increases, resistance of semiconductor decreases. In a semiconductor, when an electron jumps the

forbidden energy gap, there is an electron deficiency in the valence shell. This is a ‘positive hole’, where electrons

jump in and out without having to spend a lot of energy. When an electron jumps into a positive hole, its previous

location becomes a positive hole. This allows easier movement of electrons, therefore higher conductivity.

Extrinsic Semiconductors p-type semiconductor: Doped with group III elements, e.g. boron, they contain positive holes as boron only has 3

valence electrons.

n-type semiconductor: Doped with group V elements, contain free electrons as there are 5 valence electrons.

When p-type and n-type semiconductors are joined together,

the p-type becomes negative whilst n-type becomes positive.

During WWII, thermionic devices were used in

communications and radar. With more complex electronic

circuits, vacuum tubes needed to be replaced. Researchers

started using semiconductors, such as Germanium, and the

transistor was invented in 1947. Transistors are made by

alternating NPN or PNP semiconductors, and the flow of

electrons between the emitter and base alters the conductivity of the

middle semiconductor, therefore affecting the flow of current between

the emitter and collector. Thus, transistors allow current to be

moderated.

Advantages of Solid State over Thermionic

Smaller size

Durable and longer lasting

More rapid operational speed

More energy efficient

Cheaper

Scientists originally used Germanium because Silicon had not been discovered yet. Silicon is better because it is

easily extracted from sand, functions better in high temperatures and can form a silicon dioxide layer.

Impact on society The invention and development of integrated circuits has formed the foundation of modern

microelectronics, promoting the development of information technology.

Microchips are found in many electronic devices, such as biotechnology and telecommunications.

Their development has allowed more powerful computers to be made, which are essential in our daily lives

as well as in industries and businesses.

Leads to invention of intelligent terminals and robots, which could do labour in dangerous situations.

Overall, from semiconductors, diodes and transistors are made. These are integrated to make microchips

and microprocessors, which have had a significantly positive impact on society.

From Superconductors to Maglev Trains

Braggs X-ray Diffraction experiment

nλ=2dsinθ where n is an integer

Superconductivity Superconductivity is the phenomenon exhibited by certain metals where they have 0 electrical resistance when they

are cooled below a critical temperature.

Types of Semiconductors Metal Semiconductors Oxides and Ceramics

Examples Aluminium – 1.2K Mercury – 4.2K

YBa2Cu3O7 – 90 K HgBa2Ca2Cu3O8 – 133 K

Advantages Malleable, tough and ductile Easily produced

Only needs liquid nitrogen to cool Cheaper to cool

Disadvantages Very low critical temperatures Require liquid helium to cool

Difficult to produce Brittle and fragile

BCS Theory

A quantum theory that only applies to

metal semiconductors.

1. First electron attracts the lattice, which

responds slowly (low temperature),

distorting after the electron passes

through.

2. This creates a positive region (phonon)

behind the first electron, which attracts

the next electron and helps it move

through the lattice

3. This process repeats as electrons move through the lattice in Cooper pairs.

Meissner effect A superconductor is able to exclude external magnetic fields, so it has no internal magnetic field.

When an external magnetic field

attempts to enter a superconductor, it

induces a perfect eddy current to

circulate in the superconductor. It is

perfect and has a high current due to the

zero resistance, so it flows in such a

direction that it totally opposes the

external magnetic field.

Applications – Maglev Train Advantages

Minimises friction

Energy efficient

Less wear and tear

Disadvantages

Expensive

Applications – Computers, Motors, Power Grids Superconductors have 0 resistance, therefore 0 heat production so they

can be integrated much more closely in supercomputers, making them extremely fast.

They can be used in Motors because 0 resistance makes them much more powerful and efficient.

If Transmission Wires can be made from superconductors, there will be no energy loss. However, the entire

transmission system must be cooled and Cooper Pairs don’t form from AC electricity.

Quanta to Quarks Thomson After his cathode ray experiment, Thomson proposed the

plum pudding model of the atom, which was electrons in a

positive jelly. To prove this, Rutherford bombarded gold

foil with alpha particles, but one in eight thousand particles

deflected, implying a dense positively charged mass in the

atoms, which he named the nucleus.

Dalton’s proposal of an indivisible atom in 1800s was

overthrown when Thomson discovered electrons in 1897

and Goldstein discovered that atoms have positive charges

in 1886, implying atoms may be divisible. However,

Thomson had the idea of a plum pudding model, which was proven wrong by Rutherford’s work. It was the first to

propose a nucleus with electrons around it, enabling advances in chemistry and leading to the development of

quantum physics by Bohr and other scientists. There were problems with his atom model though:

Could not explain composition of the nucleus and electrons

Failed to explain how electrons could stay away from nucleus without collapsing into it, and when electrons

orbit, they produce EMR, releasing energy, violating conservation of energy

Bohr Proposed a model based on Planck’s hypothesis and hydrogen emission spectrum:

1. All electrons around the nucleus are only allowed to occupy certain fixed positions and energy levels outward

from the nucleus, thus the electron orbits are quantized and are known as the principle energy shells. While in a

particular orbit, electrons are in a stationary state and do not radiate energy.

2. When an electron moves from a lower orbit to a higher orbit, or falls down from a higher orbit to a lower orbit, it

will absorb or release a quantum of energy (EMR). The energy of the quantum is related to the frequency of the

EMR by the formula, E=hf.

3. The electrons’ angular momentum is quantized as mvr=nh/2π

The wavelength of EMR made by

falling electrons is calculated using:

(

)

The type of radiation emitted is mostly

determined by where the electron

falls to, as lower orbits have larger

energy gaps.

Limitations:

Mixed classical and quantum

physics – angular momentum and

quantisation of energy

Could not explain the relative intensity between spectral lines

Did not work for multi-electron atoms, only hydrogen worked

Couldn’t explain hyperfine spectral lines, thin faint lines that cluster around a main spectral line

Could not explain Zeeman effect – spectral lines split when powerful magnetic field applied

Matter Waves

De Broglie proposed that any kind of particle has wave-particle duality

Diffraction is the bending of waves when the pass around a corner or through a slit. Davisson and Germer fired

electrons towards a nickel crystal and noticed that some of the returning electrons would pass through the gaps

between the nickel atoms, with maxima and minima points consistent with diffracted waves, proving that electrons

can act like waves.

De Broglie stated that electrons in atoms are electron waves, which are like standing waves wrapping around the

nucleus in an integral number of wavelengths. They don’t propagate but vibrate between two boundaries.

Pauli and exclusion principle The exclusion principle states that no two electrons in the same atom can have all four quantum numbers the same.

1. Principal quantum number (n) related to the principal energy shells

2. Orbit quantum number (l) related to the angular momentum and therefore the orbital shape of the electrons,

takes the values of 0, 1, 2… (n-1), 0 is spherical 1 is pear shaped and so on.

3. Magnetic quantum number (ml) related to magnetic orientation, takes values of …-2, -1, 0, 1, 2…

4. Magnetic spin quantum number (ms) assigned to spin on their axis, ½ or - ½

Heisenberg and uncertainty principle The uncertainty principle states that the product of the uncertainty in measuring the position and uncertainty in

measuring the momentum of an object has to be always equal to or larger than a constant.

Neutrons When beryllium was bombarded with alpha particles, a neutral but highly penetrative radiation could be obtained,

but its nature could not be explained. Chadwick proposed that it was a neutral particle with a similar mass to

protons, found in the nucleus. His experiment is shown.

The detector measured the energy and velocity of

the ejected protons, and Chadwick used the laws of

conservation of momentum and energy to

determine that the mass of the neutron was

approximately the same as a proton.

Strong Nuclear Force The gravitational attraction between protons is minute compared to the

electrostatic repulsion, so a new force must be holding the nucleons

together. Strong nuclear force acts equally between all nucleons,

explaining the role of neutrons in stabilizing the nucleus as they separate

protons. When nucleons get too close, it becomes a repulsive force and

otherwise, it attracts over a very small distance.

Neutrinos Ejected alpha particles either have identical or predictable energies, but

beta particles have a wide range. The beta particles with a sub-maximal energy level should have had some energy

loss, which is explained by Pauli’s proposal that another small particle called the neutrino was emitted.

Neutrinos are electrically neutral, have almost no mass, carry energy + momentum, and travel at light speed.

β- decay:

Anti-neutrino

β+ decay:

Neutrino

Nuclear Fission Fermi realized that neutrons have 0 charge so they easily reach the nucleus of atoms to cause reactions, so he

bombarded many elements with neutrons to make isotopes which underwent beta decay, transmuting into new

elements. He decided that he could make a new element by getting the largest natural atom, U-238, and

bombarding it with a neutron to make U-239, which undergoes beta decay to make Np-239, which undergoes beta

decay to make Pu-239. However, he found that other than the anticipated transuranic elements, there were other

isotopes formed. This was explained by stating that U-235, when bombarded with neutrons, undergoes nuclear

fission and breaks into two smaller nuclei.

Uncontrolled fission reactions are fission reactions where all neutrons produced are allowed to strike more

fissionable material, causing an exponentially increasing fission.

Controlled fission reactions allow the extra neutrons produced to be absorbed, so that approximately the same

amount of neutrons are present for each subsequent reaction, causing steady fission.

Similarities between controlled and uncontrolled

Both require either fissionable U-235 or Pu-239 as fuels, which need a mass over their critical mass (smallest

amount of material that would sustain a chain reaction).

Both use a moderator to slow down the neutrons, as fast neutrons go through the nuclei without being

captured.

Differences between controlled and uncontrolled

Controlled reactions have moveable control rods that absorb neutrons, slowing the reaction

Controlled reactions have a coolant to carry heat (energy) away from the core

Controlled reactions have a radiation shield – inner layer made of lead, reflecting neutrons back into the core to

stop them from reaching the outer environment, and ensuring there are enough neutrons to sustain the reaction

– outer layer made of thick concrete, acting as a biological shield to further block radiation from exiting the core.

Assess the impacts of nuclear fission on society and environment Applications: nuclear weapons, electricity generation, nuclear powered satellites, radioactive isotopes.

Society: Significant and major.

Nuclear weapons blew up Japan, which is good because they surrendered, ending WWII and preventing deaths

that would have happened during an invasion, but it’s bad because people died. They also led to the worldwide

paranoia during the Cold War, but prevented a hot war between NATO and the USSR due to mutually assured

destruction.

It is a reliable and affordable method of producing electricity in many countries, but it’s bad because Chernobyl.

It also successfully powers satellites and space probes.

Nuclear fission is used to produce radioactive isotopes, which aid industry and medicine.

Environment: Significant and mostly negative

Hiroshima and Nagasaki got completely destroyed, and there is still very minor radioactive fallout (although the

cities are now rebuilt and inhabitable)

Radioactive contamination surrounds many nuclear test sites, rendering them uninhabitable

Radioactive waste remains dangerous for thousands of years and in the past, some countries simply dumped the

waste at sea in metal drums, which rusted and leaked.

On the positive side, they do not produce carbon dioxide to generate heat, unlike coal and oil.

Assessment: The applications of nuclear fission have had significant and major impacts on the society and

environment; the impacts on society have been mostly positive whilst there has been mostly negative impacts on

the environment.

Fermi’s first controlled chain reaction In 1942, a team of scientists led by Fermi built a nuclear pile, consisting of graphite blocks surrounding a 60 ton

uranium core. Cadmium control rods were inserted between the uranium blocks. Radioactivity monitors detected

the reaction, which continued as the cadmium control rods were withdrawn.

Mass defect and binding energy The total mass of the neutrons, protons and electrons that

make up an atom is greater than the mass of the same atom

as a whole. This is due to mass defect and binding energy.

Mass defect is the loss in mass when the mass of an atom as a

whole is compared to the mass of its components individually.

If mass is lost energy must be liberated E=mc2 and similarly,

energy must be put back in to separate the atom. Binding

energy is the energy needed to separate an atom into its

separate parts.

This explains the release of energy from nuclear fission.

Fission reactor

Reactor core: where

the fission reaction of U-235 or Po-239 takes place. It contains fuel rods and control rods embedded in the

moderator. Since a fission reaction involves bombarding neutrons into the nucleus of the fissionable atoms, creating

heat and more neutrons which cause more reactions, the reactions grow at an exponential rate. To prevent all the

fuel from reacting at once, control rods are used to absorb neutrons, controlling the rate of reactions.

Heat exchanger: The primary coolant (normally molten sodium or molten sodium chloride) carries the heat out of

the reactor core to a heat exchanger to form steam, which drives a turbine, producing electricity. The primary

coolant circulates back to the nuclear core to carry more energy.

Generator and secondary coolant: After the steam turns the turbine, it is condensed to warm water through the

secondary coolant, usually cool water from a river, before it is recirculated back into the heat exchanger.

Radiation shield: The inner lead layer reflects most of the neutrons produced back into the reaction core, resulting

in fewer neutrons causing damage outside and ensuring there are enough neutrons to cause reactions. The outer

concrete layer blocks the radiation from coming out of the core.

Radioisotopes Medicine: Tc-99m has a half-life of 6 hours, and is formed from the radioactive decay of Mo-99, which has a half-life

of 66 hours and is a fission product of U-235. Tc-99m is a gamma emitter, the m means metastable (too much

energy). It is used for diagnosis, as when it is injected into the bloodstream, the gamma emission can be detected,

showing blood clots, constrictions and other circulation disorders.

Co-60 emits both beta and gamma radiation, half-life 5.3 years, produced by bombarding Co-59 with a neutron,

gamma radiation kills cancer cells.

Agriculture: Phoshorus-32 has a half-life of 14 days, produced by neutron bombardment of phosphorous-31, used as

a biological tracer to study natural processes e.g. nutritional uptake by plants.

Engineering: Na-24 emits both beta and gamma radiation, 15 hour half-life, produced by neutron bombardment of

Na-23, used to detect leakage from underground water pipes by being introduced into pipes as NaCl and monitoring

the radiation (mainly gamma) at ground level.

Industry: Sr-90 (a product of uranium fission) is a radioisotope used in thickness gauges, as it emits low energy beta

particles (significantly absorbed by the material and safety) and has a long half-life (infrequent replacement).

Neutron scattering and probing Neutron scattering or probing uses the same principle as Braggs’ X-ray diffraction. Many neutrons are used as they

do not have any charge so are hard to manipulate. They are made to pass through certain crystals such as sodium

chloride so they have the same kinetic energy, then are directed to collide with the nuclei of the material to be

analyzed and subsequently lose a specific amount of energy according to the nature of the collision. Head-on

collisions cause them to lose more energy than in side-on collisions. Collisions with neutrons or small elements result

in more energy loss than collisions with large elements, which cause the neutrons to bounce off without losing much

energy. Since particles are waves, the neutrons will be scattered and returned with different wavelengths, which

generate an interference pattern. By analyzing the interference pattern, the internal structure and composition of

the material can be deduced.

Advantages: not charged, so if they don’t hit the nucleus they pass through and move on to next layer, enabling

analysis of the entire depth of the sample material. It also allows them to probe the nucleus.

Useful for probing small elements and proton-rich materials, as electron microscope or X-ray scattering work on

electrons, which they have few of, whilst neutrons work on nuclei.

Applications: Structural faults in welds and metals, developing magnetic material for computer data storage,

developing new superconductors, identification and study of viruses

Manhattan Project The purpose of the US’ Manhattan project was to develop atomic bombs during WWII, and it was started during

1939 when Einstein wrote a letter to US president Roosevelt advocating the development of atomic bombs, as

Germany discovered nuclear fission in 1938 and had the potential to create nuclear weapons. In October 1939,

Roosevelt set up an advisory committee on uranium, marking the beginning of the Manhattan project.

During the 1940s – The project had an overall significantly positive impact on the 1940s society as despite it costing

the US $2 billion and leading to the deaths of hundreds of thousands of Japanese civilians, it had promptly ended

WWII, indirectly saving many other lives by avoiding invasion.

From 1950 to 1980s – Although it led to worldwide fear of nuclear war during the Cold War, the project prevented a

war between NATO and the USSR as both sides would be totally destroyed if any one side started to fire a weapon

(mutually assured destruction), so it has had a highly significant, positive impact on this society.

From 1980s to present time – The project has had a very significant impact on this time period, as it has accelerated

the development of nuclear technologies, giving us the ability to manipulate nuclear power. It facilitated the

development of technologies to produce fissionable fuels, leading to production of electricity in nuclear power

plants.

Particle Accelerators

Standard model of matter

Bosons

The four fundamental forces act through the

exchange of force particles, called bosons

Electromagnetic force –

photons

Strong nuclear force –

gluons

Weak nuclear force –

weakons

Gravity force – gravitons

Quarks

Particles with charges are sub-multiples of

electron charges, called quarks. There are six flavors of quarks. Anti-quarks exist.

Hadrons

Quarks do not exist by themselves as they are unstable, rather they combine with other quarks to make hadrons.

There are two types of hadrons: baryons (3-quark) and mesons (2-

quark).

Baryons form the nucleons – protons are 2 ups and 1 down

quarks, whilst neutrons are 1 up and 2 downs quarks.

Mesons consist of a quark and an anti-quark, they are unstable

and therefore short-lived.

Leptons

They have little or no mass. All leptons interact through weak nuclear force, and charged leptons interact through

EM force. Anti-leptons e.g. positrons exist.

Generation Quarks Symbols Charges

1 Up Down

u d

+2/3 -1/3

2 Charm Strange

c s

+2/3 -1/3

3 Top Bottom

t b

+2/3 -1/3

Generation Leptons Symbols Charges

1 Electron Electron-neutrino

e- ve

-1 0

2 Muon Muon-neutrino

μ-

vμ

-1 0

3 Tau Tau-neutrino

τ-

vt -1 0