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Y2: Nuclear Physics Flashcards

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1
Q

What is the Rutherford scattering experiment

A
  • A stream of (+) α-particles from a radioactive source are fired at a thin gold foil
  • Alpha particles passed through the foil and struck a curved fluorescent screen (small, visible flash of light)
  • The number of α-particles scattered at different angles was recorded
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2
Q

What would have been seen in the α scattering experiment if J.J.Thompson’s plum pudding model was correct

A

αparticles would have been deflected by small angles, as they were repelled by the electrons.

However, the experiment instead showed that most α-particles passed straight through, but some occasionally deflected at angles greater than 90 degrees, which can’t be explained by the plum pudding model.

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3
Q

What were the conclusions from Rutherford’s α-scattering experiment

A
  • Most of the α-particles passed straight through the foil
    ∴ Most of the atom is empty space
  • Some α-particles are deflected at large angles
    ∴ Nucleus must have a large positive charge (to repel +α)
  • Only a few α-particles were deflected by large angles
    ∴ Nucleus must be tiny compared to the size of the atom
  • Fast moving α-particles (∴ high mv) are deflected
    ∴ Most of the mass of the atom must be in the nucleus
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4
Q

How were protons and neutrons discovered

A
  • In 1919, protons were discovered by firing high-energy α-particles at different gasses
  • ∴ It was though that the nucleus was made up of only protons, however, this theory didn’t work as the mass didn’t have the relationship with the charge that this would suggest (1:1)
  • In 1920, Rutherford proposed a ‘proton-electron’ couplet to correct this error, but it was James Chadwick in 1932 that provided experimental evidence for the neutron to solve the issue.
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5
Q

How would you calculate the distance of closest approach to the nucleus of a scattered α-particle

A

Initial Ek = Qq/(4πεor)
(r: distance of closest approach)

  • If an α-particle is deflected through 180 degrees by a nucleus, it will have stopped a short distance from the nucleus before rebounding
  • At this point, all of the initial Ek will have been converted to electric potential energy
    ∴ Initial Ek = Final Ep = Qq/(4πεor)
    ∴ Initial Ek = Qq/(4πεor)
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6
Q

How can the distance of closest approach to the nucleus of a scattered α-particle be used to estimate the nuclear radius

A

Nuclear radius ≤ Distance of closest approach
(∴ r ≈ closest approach)

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7
Q

How can electron diffraction be used to determine an accurate value for the nuclear radius (R)

A
  • Electrons are leptons, so don’t interact with the strong nuclear force
    ∴ They will get closer to the nucleus before they are diffracted, giving a more accurate value for R
  • The (De Broglie) wavelength of these electrons can be calculated: λ = hc/E
  • To investigate nuclear radius, λ must be tiny (10^-15m)
    ∴ electrons must have high energy
  • If these electrons are directed at a thin film of material, a circular diffraction pattern will occur, the size of which can be used to determine R
    (Sinθ = 1.22λ/2R)
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8
Q

What is the equation to calculate the nuclear radius by electron diffraction

A

Sinθ = 1.22λ/2R
(θ: Angle of the first minimum)

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9
Q

What is the radius of an atom

A

~0.05nm

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10
Q

What is the radius of the (smallest) nucleus

A

~1fm

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11
Q

What is the relationship between Radius of a nucleus and the number of nucleons within it

A

R = (Ro)A^1/3

R: nuclear radius
A: Nucleon number
Ro: Constant ≈ 1.4fm

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12
Q

What is the equation for nuclear density

A

p = 3m(nucleons) / 4π(Ro^3) = 1.45 x 10^17

The mass of all nucleons is roughly the same, given as: m(nucleon)
∴ Mass of nucleus = (A)m(nucleon)
Assuming the nucleus is spherical, V=(4/3)πR^3
p = m/V
∴ p = (A)m(nucleon) / (4/3)πR^3
R = (Ro)A^1/3
∴ p = (A)m(nucleon) / (4/3)π((Ro)A^1/3)^3
∴ p = 3m(nucleons) / 4π(Ro^3)

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13
Q

Why is the density of all nuclear matter constant

A

R = (Ro)A^1/3
∴ R^3 ∝ A
V = (4/3)πR^3
∴ R^3 ∝ V
∴ A ∝ V
∴ The volume of each nucleon is roughly the same
The mass of each nucleon is roughly the same
p = m/V
m = constant
V = constant
∴ p = constant

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14
Q

What is the value for nuclear density

A

p = 1.45 x 10^17 (kgm^-3)

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15
Q

What can be concluded from the difference between nuclear density and atomic density

A

Nuclear density (1.45 x 10^17)&raquo_space; Atomic density (10^3-10^5)

∴ Most of the mass of an atom is in it’s nucleus
∴ Nucleus is small compared to the size of the atom
∴ Atom is mostly empty space

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16
Q

What is radioactive decay

A

The release of energy and/or particle from an unstable atomic nucleus until it becomes stable
(Individual decay is random and can’t be predicted)

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17
Q

What is Alpha radiation (α)

A
  • Constituents: Helium nucleus (2p &2n)
  • Relative charge: +2
  • Relative mass: 4u
  • Penetrating power: Stopped by Paper, skin, few cm of air
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18
Q

What is Beta-minus radiation (ꞵ-/ꞵ)

A
  • Constituents: 1 Electron
  • Relative charge: -1
  • Relative mass: Negligible
  • Penetrating power: Stopped by ~3mm of alluminium
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19
Q

What is Beta-plus radiation (ꞵ+)

A
  • Constituents: 1 Positron
  • Relative charge: +1
  • Relative mass: Negligible
  • Penetrating power: Positron almost instantly annihilates with an electron, so range = 0
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20
Q

What is Gamma radiation (𝛾)

A
  • Constituents: Short wavelength, high energy EM wave
  • Relative charge: 0
  • Relative mass: 0
  • Penetrating power: Stopped by several cm of lead or several m of concrete
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21
Q

How can you investigate the types of radiation emitted by a source (based on penetrating power)

A
  • Using a Geiger-Müller tube and a Geiger counter, record the background count with no source present (to be subtracted from later counts)
  • Place an unknown source near the tube (record count)
  • Place a sheet of paper between tube and source (record count)
  • Place a sheet of aluminium between tube and source (record count)

Depending on when the count rate significantly decreases, the type of radiation emitted can be determined

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22
Q

How can you investigate the types of radiation emitted by a source (with a magnetic field)

A
  • Charged particles moving through a uniform, perpendicular magnetic field are deflected in circular paths
  • Direction of deflection depends on charge
  • Radius of circular path can show magnitude of charge and mass.
    ∴ Type of radiation can be determined based on it’s path in a magnetic field
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23
Q

What is an example of an application for α radiation

A

Smoke alarms:
- α-particles are strongly positive so can easily ionise atoms (Knock off electrons)
- This ionisation transfers energy from the α to the atoms
- In air, α-particles quickly ionise (~10000mm^-1), so quickly loose all their energy
∴ α-particles allow a current to flow, but don’t travel very far (won’t release radiation)
∴ If smoke is present, α-particles can’t pass through the air, stopping the current, setting off the alarm

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24
Q

What is an example of an application for ꞵ radiation

A

Material thickness controller:
- (ꞵ-)-particles have a lower mass and charge than α-particles, but have a higher speed
∴ (ꞵ-)-particles will ionise atoms in air (~100mm^-1)
- When a material is fed through rollers to be flattened, a ꞵ- source is placed on one side, with a detector on the other
- Radiation is absorbed by the material, so a thicker material causes the count to decrease more
∴ If too much is absorbed, rollers move closer together to make the material thinner
∴ If too little is absorbed, rollers move further apart to make the material thicker

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25
Q

What are some examples of applications for 𝛾 radiation

A

Radioactive tracers:
- 𝛾 is less ionising than ꞵ-, so does less damage to body tissue
∴ Radioactive source can be ingested/injected into a patient and traced within the body
(eg. PET scanner: Positron emission tomograph - positrons emitted by source annihilate with e- to produce detectable 𝛾)

Cancer treatment:
- Radiation damages cells, so can destroy cancerous tissue
- May damage healthy cells, so risks of use must be evaluated
(Shielding/rotating beams may be used to reduce damage to healthy cells)

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26
Q

What is background radiation

A

Nuclear radiation from sources other than the one being measured (In the ‘background’)
This background count must be measured and subtracted from any recorded values

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27
Q

What are some potential sources of background radiation

A
  • Geological (in the air)
    • Radioactive radon gas is released by rocks (α)
    • Conc. varies, usually the largest source of background
  • The ground/buildings
    • Nearly all rocks contain radioactive material
  • Cosmic radiation
    • High energy photons from space
    • Collide with particle in atmosphere to release radiation
  • Living things
    • All plants/animals contain carbon (some C-14)
  • Man-made radiation
    • Medical or industrial sources
    • In most places, this is a tiny proportion of background
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28
Q

What is the equation for the intensity of radiation, and what does it show about the relationship between intensity and distance

A

I = k/(x^2)
∴ I ∝ 1/x^2 (inverse square law)

  • Intensity is the amount of radiation per unit area
  • A 𝛾 source will emit radiation in all directions, spreading out further from the source
    ∴ Radiation will spread out as a sphere
    ∴ SA = 4πr^2, (r=x)
    ∴ SA ∝ x^2
    Intensity will decrease as this area increases,
    ∴ I ∝ 1/SA
    ∴ I ∝ 1/x^2
    ∴ I = k/(x^2)
    (k: constant)
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29
Q

How would you investigate the relationship between the intensity of radiation and the distance from the source

A
  • Set up a Geiger-Müller tube at the start of a measuring scape
  • Record background count
  • Place a radioactive source a distance d from the tube
  • Take at least 3 count rate readings and record an average (subtract background)
  • Move the source to distances 2d, 3d, 4d, etc… and record the average count rate at each
  • Plot a graph of count against distance
  • This will show an inverse-square relationship between count and distance (count ∝ 1/x^2)
  • The area of the Geiger-Müller tube is constant, so count ∝ Intensity
    ∴ I ∝ 1/x^2
    ∴ I = k/(x^2)
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30
Q

What are the main safety measures when working with radioactive sources

A
  • Keep as far away from the source as possible
    • I ∝ 1/x^2, so intensity and ∴ exposure decreases with distance
    • Hold source away from body (+ long handle tongs), and stand back when possible
  • Keep source in lead box when no in use
    • Lead will absorb the radiation
    • Only remove from the box for as short a time as possible
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31
Q

How is the rate of radioactive decay measured

A
  • Decay is completely random, so can’t be predicted for an individual nucleus, but a pattern occurs with a large number of nuclei
  • Any sample of a particular isotope will decay at the same rate, with a constant decay probability that can be used to determine the activity
32
Q

What is Activity (A)

A

The number of nuclei that decay each second
- Measured in Becquerels (1Bq = 1 decay per second)
- Proportional to the number of unstable nuclei (A ∝ N)

33
Q

What is the decay constant (λ)

A

The probability that a specific nuclei will decay, per unit time
- Measure of how quickly an isotope will decay (Unit: s^-1)
- Constant of proportionality for A and N
- Can be determined from a graph of N-t

34
Q

What is the relationship between the activity of an isotope and the number of nuclei within it

A

A = λN = -ΔN/Δt

Activity is the number of nuclei that decay per second, so can be considered as the rate of change of N
∴ A = -ΔN/Δt (negative as N decreases)
λ is the probability that a specific nuclei will decay, so is the constant of proportionality for A and N
∴ A = λN
∴ A = λN = -ΔN/Δt

35
Q

What is the decay equation

A

N = Noe^(-λt)

N: Number of remaining nuclei at time t
No: Initial number of nuclei
λ: Decay constant

Nuclear decay occurs exponentially as it is an iterative process (The number that decay in one time period controls the number available to decay in the next)

Can be used to calculate the change in the number of moles, as N=nNA

36
Q

What is the equation for the Activity of an isotope as it decays

A

A = Aoe^(-λt)

A: activity at time t
Ao: Initial activity
λ: Decay constant

N = Noe^(-λt)
A ∝ N (A = λN)
∴ A = Aoe^(-λt)

37
Q

What is the half-life of an isotope (T(1/2))

A

The average time taken for the number of unstable nuclei to halve

38
Q

How is half-life measured

A

Measured as the time taken for the activity (count rate) to halve, as N∝A, and N is more difficult to accurately determine

39
Q

What is the half-life equation

A

T(1/2) = ln(2)/λ

T(1/2) = t, when N = (1/2)No
N = Noe^(-λt)
∴ (1/2)No = Noe^(-λ(T(1/2)))
∴ 1/2 = e^(-λ(T(1/2)))
∴ ln(1/2) = -λ(T(1/2))
∴ ln (2) = λ(T(1/2))
∴ T(1/2) = ln(2)/λ

40
Q

How are radioactive isotopes used for radioactive dating

A

Radioactive Carbon-14 used for carbon dating
- Living plants take up CO2, some of which contains C-14
- When plants die, activity of C-14 starts to fall (half-life ≈ 5730 years)
- Archaeological finds containing once living material (eg. wood) can be tested to find the number of C-14
∴ Can be dated based on No and T(1/2)

41
Q

What are some issues with the reliability of radioactive dating with radioactive isotopes

A
  • For man-made objects, process can only find age of material, not when item was made
  • The objects may have been contaminated by other sources
  • May be a high background count that will obscure findings
  • There may be uncertainty in the amount of C-14 that was present thousands of years ago (No)
  • Sample size/count rate may be too small so results are statistically unreliable
42
Q

How are radioactive isotopes used in medical diagnosis

A

Radioactive tracers ingested/injected and traced around the body, to give an image of internal structures

43
Q

What isotope is commonly used as a radioactive tracer

A

Technetium-99m
- Emits 𝛾 radiation, so escapes the body with least damage
- T(1/2) = 6hrs, which s long enough to record data, but short enough to reduce risk
- Decays into much more stable isotopes

44
Q

What factors effect the stability of a nucleus

A

Nuclear stability is influenced by the strong nuclear force holding the nucleons together, and the electrostatic force pushing protons apart
∴ Nucleus will be unstable if:
- Too many/few neutrons (changes the average distance between protons, altering the electrostatic repulsion)
- Too many nucleons (Too heavy, effecting the strong nuclear force)
- Too much energy

45
Q

Where is the valley of stability located on an N-Z graph

A

Line curving up, just above the line N=Z (starts at origin, and is linear until Z≈20)

46
Q

How does the position of an isotope on an N-Z graph determine the mode of decay

A
  • Just above the line of stability, nuclei have too many neutrons, so undergo ꞵ- decay (n→p)
  • Just below the line of stability, nuclei have too many protons, so undergo ꞵ+ decay (p→n)
  • Heavier nuclei have too many nucleons so undergo α decay
47
Q

When does α emission occur

A

In very heavy atoms
- α-particle emitted (2p & 2n)
- eg. Uranium-238 decays into Thorium-234

48
Q

When does ꞵ- emission occur

A

In neuron-rich atoms (N»Z)
- Electron, and antineutrino emitted (n→p)
- eg. Rhenium-188 decays into Osmium-188

49
Q

When does ꞵ+ emission occur

A

In proton-rich atoms (Z»N)
- Positron, and neutrino emitted (p→n)
- eg. Sodium-22 decays into Neon-22

50
Q

When does 𝛾 emission occur

A

Nuclei with excess energy after α/ꞵ decay
- Energy emitted as 𝛾 rays
- 𝛾 (+neutrino) released during electron capture
- eg. Beryllium-7 decays into Lithium-7

51
Q

What properties are always conserved in nuclear reactions

A
  • Energy
  • Momentum
  • Charge
  • Nucleon number
  • Lepton number
52
Q

How are nuclear reactions shown on energy level diagrams

A

Vertical axis show relative energy, with the energy levels of the different isotopes shown as horizontal lines
The size of the emitted particle determines the distance moved to the right
(ꞵ moves to the right less than α, and 𝛾 only moves down)

53
Q

What is the mass defect of a nucleus

A

The difference between the mass of the nucleus and the total mass of it’s constituent nucleons
- As the nucleons join together, their total mass decreases, as the mass is ‘lost’ and converted to energy, holding the nucleus together

54
Q

What is the binding energy of a nucleus

A

The energy required to completely separate all the nucleons within a nucleus
…or…
The total energy released when the nucleons bind together to form the nucleus (as some of the mass is converted to energy and released)

55
Q

What is the equation for the binding energy of a nucleus

A

E = mc^2

E: binding energy
m: mass defect
c: speed of light (~3x10^8)

56
Q

What is the value for the binding energy per atomic mass unit for all nuclei

A

1u: E ≈ 931.15MeV

57
Q

What is the average binging energy per nucleon

A

Binding energy / Nucleon number

  • Allows you to compere the binding energies of different nuclei
  • The greater the average binding energy per nucleon, the more stable the nucleus (as more energy is required to separate the nucleons)
58
Q

What is shown on a graph of ‘average binding energy per nucleon’ against ‘nucleon number’

A

Gives a curve to show the relative stability of atoms
- Average binding energy per nucleon rapidly increases for lighter nuclei
- Average binding energy per nucleon gradually decreases for heavier nuclei
- Most stable at max of curve (Fe-52, average binding energy per nucleon = 8.8MeV)

59
Q

What is nuclear fission

A

When a large nucleus (unstable), randomly splits into two smaller nuclei, releasing energy as the new smaller nuclei have a higher average binding energy per nucleon (are more stable)
The process will also release several neutrons

60
Q

Why will nuclear fission occur spontaneously

A

As the large nucleus is unstable, so splits into two. After this, the smaller nuclei are more stable, so random fission is reduced.

61
Q

How can nuclear fission be induced

A

Collision of the nucleus with a Thermal neutron

62
Q

What is a thermal neutron and what are it’s properties

A

Particle that collides with a large nucleus to induce nuclear fission (makes the nucleus unstable)
- No charge (neutron), so no electrostatic repulsion during collision with nucleus
- Low energy (speed ≈ 2000ms^-1), as to not move straight through the nucleus during the collision

63
Q

What is nuclear fusion

A

When two light nuclei (unstable) combine to create a larger nucleus, releasing a lot of energy as the new heavier nuclei has a higher average binding energy per nucleon (is more stable).
Eg. hydrogen nuclei fusing in the sun to produce helium, releasing energy

64
Q

What conditions are needed for nuclear fusion to occur and why

A

Very high temperature and pressure:
All nuclei are positively charged, so the electrostatic repulsion must be overcome so they can get close enough for the strong nuclear force to hold them together.

65
Q

How do fission and fusion change the position of nuclei on a graph of ‘average binding energy per nucleon’ against ‘nucleon number’

A
  • Element larger then Fe-52 can release energy through fission, producing smaller, more stable nuclei
  • Elements smaller then Fe-52 can release energy through fusion, producing a larger, more stable nuclei
66
Q

How can the energy released during fission/fusion be determined by the change in ‘average binding energy per nucleon’

A

ΔE=Δmc^2

ΔE: Energy released (change in binding energy)
Δm: Change in mass, taking neutrons into account
c: speed of light (~3x10^8)

The binding energy is the total energy released as a nucleus forms, so the change in binding energy is equal to the energy released.
Binding energy is calculated through E=mc^2
∴ Change in binding energy (energy released)
is calculated through ΔE=Δmc^2

67
Q

How do the fuel rods work inside a nuclear fission reactor

A

Rods contain Uranium-235, or sometimes Plutonium-239, which undergoes fission (+ some other isotopes that don’t undergo fission)
These fission reactions produce neutrons which can induce other nuclei to undergo fission (if thermal neutrons)

68
Q

What is the moderator within a nuclear fission reactor, and what is it’s function

A

A liquid (usually water), surrounding the fuel rods to slow down the neutrons in order to indue more fission reactions

69
Q

How does the moderator slow down the neutrons within a nuclear fission reactor

A
  • Particles in the moderator collide with the neutrons
  • If the collisions are perfectly elastic, Ek is conserved
  • If the moderator particle has the same mass as the neutron, and is initially at rest, all of the Ek is transferred to the moderator particle (in order for momentum and energy to be conserved).
  • However, neutrons only need to be slowed rather than stopped
    ∴ Water is used as a moderator, as H atoms have a similar mass to the neutrons (not identical), so neutrons aren’t stopped
70
Q

Why are control rods required in nuclear fission reactors

A
  • For the reactors to work, a chain reaction must occur , with one fission followed by another
  • The amount of fuel required for this is called the critical mass (any less and the reactions would eventually stop
  • ∴ The reactors use a supercritical mass of fuel ( >critical mass), where multiple reactions would follow each other, to ensure the reactor continues to release energy
  • In order to control these chain reactions, control rods are used between the fuel rods
71
Q

How do control rods control the reaction within a nuclear fission reactor

A

The fuel rods are made of a material such as boron, which will absorb neutron, ∴ stopping them from inducing further fission reactions.
These control rods can be inserted by varying amounts between the fuel rods to control the amount of fuel exposed to each other to cause a chain reaction, ∴ controlling the rate at which the reactions occur

72
Q

What is the coolant in a nuclear fission reactor, and what is it’s function

A

Liquid/gas (at room temp), sent around the reactor to remove excess heat produced by fission
Often the same water used as the moderator, as steam released from heated water will turn a turbine to generate electricity

73
Q

What are the main safety features/procedures for nuclear fission reactors

A
  • Reactor shielding:
    Thick concrete shield surrounding the reactor to prevent radiation escaping
  • Emergency shutdown:
    Control rods can automatically be fully lowered in the case of an emergency, to slow the reaction as soon as possible
74
Q

How do you deal with the waste products of nuclear fission reactors

A
  • Unused fuel rods only emit α (easily contained), but nuclei in spent fuel rods have a larger proportion of neutrons than nuclei with a similar mass, so are unstable and emit ꞵ/𝛾
  • ∴ Highly reactive, hot waste material must be placed in a continuously regulated cooling pond until cool
  • Waste should then be stored in a sealed contained until activity has fallen sufficiently
75
Q

What are the main benefits of nuclear fission reactors that justify their use

A
  • Enough fuel to last centuries (unlike fossil fuels)
  • No greenhouse gas emissions (although some parts of the process does, such as petrol generators to regulate cooling ponds)
  • More efficient that fossil fuel power (1000x more energy per kg of fuel)
76
Q

What are the main risks of nuclear fission reactors that must be considered

A
  • Waste poses risks, as can damage the environment/people
  • Although the reactors are built to minimise danger, accidents can occur (eg. Chernobyl)

It is important that society understand the science and analyse the risks before use

Physics (14 decks)

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