Nuclear Physics

Question 1

Describe the Rutherford scattering experiment.

Answer 1

• Fired a beam of alpha particles at thin gold foil.
• Circular fluorescent screen used to detect deflected alpha particles: glowed wherever an alpha particle hit it.
• Angle of deflection of each alpha particle recorded.

Question 2

Describe the results of the Rutherford scattering experiment and their implications.

Answer 2

• Most of the alpha particles passed straight through therefore most of the atom must be empty space.
• The nucleus must have a large positive charge, as some positively-charged alpha particles were repelled and deflected by a large angle.
• Most of the mass must be in the nucleus, since the fast (high mtm.) alpha particles are deflected by the nucleus instead of the nucleus moving as well.

Question 3

What was different about Rutherford’s proposed structure to all the other models before it?

Answer 3

First model to include a nucleus i.e. the mass and charge not being uniformly distributed.

Question 4

What can cause a nucleus to become unstable?

Answer 4

Too many neutrons. Not enough neutrons.

Question 5

What is ionising radiation?

Answer 5

Radiation made up of radioactive particles which can knock off electrons when they hits atoms, forming ions.

Question 6

Give the ionising strength, speed, penetrating power and susceptibility to magnetic fields of: Alpha particles Beta-minus particles Beta-plus particles Gamma radiation

Answer 6

Alpha: Strongly, slow, absorbed by a sheet of paper or a few cm of air, yes. Beta-minus: Weakly, fast, absorbed by ~3mm of aluminium, yes. Beta-plus: annihilated by electron so virtually zero range. Gamma: V. weakly, speed of light, intensity greatly reduced by many cm of lead or m of concrete but infinite range, no.

Question 7

Why are alpha particles used in smoke detectors?

Answer 7

They ionise many atoms quickly, allowing current to flow but they have a short range.

Question 8

Why are alpha emitters much more dangerous if ingested?

Answer 8

They can’t penetrate your skin if they are outside your body but when ingested they will quickly ionise body tissue in a small area, causing lots of damage.

Question 9

Why are beta particles less ionising that alpha particles?

Answer 9

They have a lower mass and charge therefore they are not able to knock as many electrons off of atoms that they meet, therefore fewer ionising interactions.

Question 10

How do radioactive tracers work?

Answer 10

Radioactive source with a short half-life (to prevent prolonged exposure to radiation) is either eaten or injected into patient. Detector eg PET scanner used to detect emitted gamma rays and locate tumours without need for surgery.

Question 11

How is ionising radiation used to treat tumours?

Answer 11

Multiple rays rotate around patient, with focal point on the tumour. This ensures the dosage to the tumour is high and the damage to the surrounding healthy cells is as low as possible.

Question 12

What can cause a nucleus to become unstable?

Answer 12

Too many neutrons. Not enough neutrons.

Question 13

What is ionising radiation?

Answer 13

Radiation made up of radioactive particles which can knock off electrons when they hits atoms, forming ions.

Question 14

Give the ionising strength, speed, penetrating power and susceptibility to magnetic fields of: Alpha particles Beta-minus particles Beta-plus particles Gamma radiation

Answer 14

Alpha: Strongly, slow, absorbed by a sheet of paper or a few cm of air, yes. Beta-minus: Weakly, fast, absorbed by ~3mm of aluminium, yes. Beta-plus: annihilated by electron so virtually zero range. Gamma: V. weakly, speed of light, intensity greatly reduced by many cm of lead or m of concrete but infinite range, no.

Question 15

Why are alpha particles used in smoke detectors?

Answer 15

They ionise many atoms quickly, allowing current to flow but they have a short range.

Question 16

Why are alpha emitters much more dangerous if ingested?

Answer 16

They can’t penetrate your skin if they are outside your body but when ingested they will quickly ionise body tissue in a small area, causing lots of damage.

Question 17

Why are beta particles less ionising that alpha particles?

Answer 17

They have a lower mass and charge therefore they are not able to knock as many electrons off of atoms that they meet, therefore fewer ionising interactions.

Question 18

How do radioactive tracers work?

Answer 18

Radioactive source with a short half-life (to prevent prolonged exposure to radiation) is either eaten or injected into patient. Detector eg PET scanner used to detect emitted gamma rays and locate tumours without need for surgery.

Question 19

How is ionising radiation used to treat tumours?

Answer 19

Multiple rays rotate around patient, with focal point on the tumour. This ensures the dosage to the tumour is high and the damage to the surrounding healthy cells is as low as possible.

Question 20

How do you find the distance of closest approach of a scattered alpha particle and what does this value correlate to?

Answer 20

Consv. of energy & Coulomb’s Law gives:

E_k = E_{elec. pot.} = Q_{gold nucleus} Q_{alpha particle}/4πε₀r

Rough extimate of nuclear radius (maximum the nuclear radius could be).

Question 21

Why is electron diffraction more accurate than distance of closest approach when measuring nuclear radius?

Answer 21

Electrons are leptons and so don’t interact with the strong force (whereas neutrons and alpha particles do).

Question 22

Why do electrons used to measure nuclear radius have to have lots of energy?

Answer 22

Their de Broglie wavelength must be v. small so that they behave like waves when interacting with the v. small nucleus. At high speeds:

λ = hc/E

Therefore, if their wavelength is very small their energy must be very high.

Question 23

What is the equation for the radius of a nucleus from a diffraction pattern?

Answer 23

sinθ = 1.22λ/2R

where θ is the angle between the normal to the screen and the first minimum.

Question 24

Describe the graph of intensity against angle of diffraction for an electron beam scattered by a nucleus.

Answer 24

Central bright maximum surrounded by dimmer maximua on both sides.

Intensity of maxima decreases as angle increases.

Intensity never hits zero.

Question 25

What are typical values for the radius of:

1. a nucleus?
2. an atom?

Answer 25

1. 1 fm (1 x 10^-15 m)
2. 50 pm (5 x 10^-11 m)

Question 26

What is the relationship linking nuclear radius and nucleon number?

Answer 26

R = R₀A^1/3

where R₀ = 1.4 fm

Question 27

Prove that all nuclei have a similar density, and state an estimate of its value.

Answer 27

ρ = mass/V

= A x m_nucleon /4/3 π R³

= A x m_nucleon /4/3 π (R₀A^1/3)³

= 3m_nucleon/4πR₀³

ρ = 1.45 x 10¹⁷ kgm^-3

Question 28

Give the:

• ionising strength
• speed
• penetrating power
• susceptibility to magnetic fields

of:

1. alpha particles
2. beta-plus particles
3. beta-minus particles
4. gamma radiation

Answer 28

1. strong, slow, absrobed by a sheet of paper or a few cm of air, v. strongly affected by magnetic fields
2. weak, fast, absorbed by 3mm of aluminium, strongly affected by magnetic fields.
3. quickly annihilated by any electron so virtually zero range.
4. very weak, speed of light, intensity greatly reduced by mnay cm of lead or serveral m of concrete.

Question 29

How do you measure the penetrating power of radiation?

Answer 29

1. Record the background count rate (when no source is present).
2. Place unknown source near to a Geiger counter and record count rate.
3. Place sheet of paper between source and counter. Record new count rate.
4. Repeat step 3, replacing the paper with 3mm aluminium.
5. If paper absorbs → alpha. If paper doesn’t absorb but aluminium does → beta (+ possibly gamma). If neither absorb → gamma only.

Question 30

Why are alpha sources suitable for use in smoke detectors?

Answer 30

They quickly ionise many atoms, allowing current to flow, but they don’t travel far so they are safe to have prolonged exposure to.

Question 31

Why is beta radiation safer than alpha radiation?

Answer 31

Beta particles have a lower charge and mass than alpha particles (but a higher speed) so they knock off fewer electrons from atoms they collide with, meaning they are less strongly ionising. Lower number of interactions means less damage to body tissue.

Question 32

How do radioactive tracers work?

Answer 32

Radioactive source either ingested or injected into patient. A detector e.g. PET scanner tracks location of tracer to locate blockages indicating tumours. Source with a short half-life is chosen to prevent prolonged exposure to radiation. Eliminates need for diagnostic surgery.

Question 33

How are gamma rays used to remove tumours?

Answer 33

Beam of gamma rays has its focal point centred on the tumour. Rays rotate so that dosage to tumour is high but dosage to healthy tissue is low, limiting damage to healthy tissue.

Question 34

What are the main sources of background radiation?

Answer 34

• The air: radon gas released from rocks emits alpha radiation.
• The ground and buildings: all rocks contain radioactive isotopes.
• Cosmic radiation: Cosmic rays (high energy protons from space) collide with particles in the upper atmosphere, producing nuclear radiation.
• Carbon-based life: contains small amounts of ¹⁴C
• Man made radiation from industrial and medical sources.

Question 35

What implications does the inverse square law have on safe handling of radioactive sources?

Answer 35

• Using a radioactive source becomes significantly more dangerous the closer it is to your body. Should hold source away from body when transporting & use long handling tongs to minimise radiation absorbed by body.

Question 36

Describe the procedure for experimental verification of the inverse square law.

Answer 36

1. Set up equipment (Geiger counter with window positioned at the end of a meter rule).
2. Turn on counter and take a reading of the background count rate. Repeat 2 times and average 3 readings.
3. Place the radioactive source a distance d from the window. Record count rate and repeat 2 time to average over 3 readings.
4. Move the source to a distance of 2d and repeat step 3. Repeat for 3d and 4d etc.
5. Correct averages by subtracting background count rate.
6. Plot corrected count rate against 1/distance² . Should get a straight line, verifying inverse square relationship.

Question 37

What are the defining features of nuclear decay>

Answer 37

• Random - can’t predict which nucleus will decay at a specific time.
• Any sample of a particluar isotope with have the same rate of decay i.e. the same proportion of the sample will decay in a given time.

Question 38

What is the equation for activity?

Answer 38

A = dN/dt = -λN

where λ is the decay constant, or the probability of a given nucleus decaying over 1 second.

Question 39

Define the term ‘half-life’.

Answer 39

The half-life of an isotope is the average time taken for the number of unstable nuclei in a sample to halve.

Question 40

Give the equations for:

1. half-life in terms of decay constant
2. number of unstable nuclei as a function of time
3. activity as a function of time

Answer 40

1. t_½ = ln(2)/λ
2. N = N₀e^-λt
3. A = A₀e^-λt

Question 41

Describe the how common isotopes with specific half-lives can be useful (C-14 & Ar-40).

Answer 41

• C-14 has a half-life of about 5730 yrs so measuring activity of fossils and comparing to activity of modern living tissue can help date objects.
• Ar-40 has a half-life of 1.3 billion years and so can be used to date igneous rocks.

Question 42

Describe and explain the shape of the N-Z graph.

Answer 42

• Line of stability curving upwards:
  
  • For small Z, N ≈ 2Z (i.e. no. of protons = no. of neutrons). As proton number increases, the number of neutrons becomes higher than the number protons. This is because the electrostatic repulsion between protons becomes more significant as the nucleus grows, so more neutrons are needed to provide the strong force needed to balance the extra repulsive force.
• Left of line of stability, beta-minus decay occurs, as nuclei don’t have enough protons to be stable, so they convert a neutron into a proton and a beta particle.
• Right of line of stability and close to the top, alpha decay occurs, as nuclei have too many protons.
• Right of line of stability and at bottom, beta-plus/K-capture occur, as nuclei have too many protons.
• The line of stability ends at Z=82 (Pb-82) as this is the heaviest stable element.

Question 43

Write general equations for:

1. alpha emission
2. beta-minus emission
3. beta-plus (positron) emission
4. K-capture

Answer 43

Question 44

Describe how isotopes with excited nuclear states are used in medicine.

Answer 44

• After a nucleus undergoes decay, its nucleons are left in an excited state. Normally they drop down from this state, releasing energy as gamma radiation, v. quickly. If they stay excited for seconds-years, they are called metastable.
• Mo-99 undergoes beta-minus decay to form Tc-99m, a process w/ a half life of 66 hrs. The Tc-99m then decays to Tc-99, releasing gamma rays, with a half-life of 6 hrs. This is useful as Mo-99 has a long enough half-life to be transported to hospitals and Tc-99m has a short enough half-life to be used as a medical tracer.

Question 45

What are:

1. mass difference?
2. mass defect?
3. binding energy?
4. binding energy per nucleon?

Answer 45

1. mass of reactant nuclei - mass of product nuclei
2. total mass of individual nucleons - mass of nucleus (in amu, converted total binding energy in MeV by multiplying by 931.5)
3. Energy needed to seperate all the nucleons in a nucleus.
4. binding energy (from mass defect) / no. of nucleons

Question 46

Draw and label the graph of binding energy against nucleon number.

Why is the most stable isotope at the maximum?

Answer 46

Because the higher the avg. binging energy per nucleon, the greater the energy needed to remove nucleons from the nucleus.

Question 47

Why does fusion release more energy than fission?

Answer 47

New, heavier nucleus formed in fusion has a much higher binding energy per nucleon than the orignal nuclei (graph to the left of maximum has much steeper gradient than to the right) so lots of energy is released.

Question 48

What is fission and how can it be induced?

Answer 48

• When a heavy and therefore unstable nucleus splits into two, releasing energy and (in the case of U-235) 2,3 or 4 neutrons.
• Can be induced by ensuring a slow moving (thermal) neutron is absorbed into a heavy nucleus e.g. U-235, making it v. unstable.

Question 49

Why does fission release energy?

Answer 49

The new, smaller nuclei have a higher binding energy per nucleon: the difference in total binding energy of products - parent is equal to the energy released.

Question 50

Why is there a limit to the number of nucleons a nucleus can contain?

Answer 50

Larger nucleus → more unstable → spontaneous fission more likely

Question 51

What is the critical mass?

Answer 51

Minimum mass of fuel needed to ensure the no. of nuclei (and therefore neutrons) involved in the reaction is constant or increasing.

This is to counteract the loss of neutrons from the surface of the fuel, therefore the shape of the sample affects the critical mass.

Question 52

What is the role of the moderator?

Answer 52

• Slows down the neutrons released in fission reactions as when released they are travelling too fast to be absorbed by a U-235 nucleus.
• Neutrons collide elastically w/ particles in the moderator, transferring their KE & therefore slowing down.
• Graphite and heavy water are used as moderators as they don’t absorb neutrons and the mass of their particles is relatively close to the mass of the neutron meaning KE is tranferred more efficiently.

Question 53

What is the role of control rods?

Answer 53

• Control the rate of fission reactions. Boron steel and cadmium are used to absorb neutrons w/o undergoing fission, thereby slowing down the rate of the nuclear reaction.
• The deeper the rods are lowered into the core, the more neutrons are absorbs so the slower the reaction.

Question 54

Describe how the coolant system in a nuclear reactor works.

Answer 54

• Primary loop contains pressurized water/CO₂, which runs through the reactor core, absorbing heat.
• Primary loop then passes through the heat exchanger/boiler.
• Heat tranferred to the secondary loop of water, which boils to high pressure steam.
• Steam drives turbine, generating electricity, before passing through a condensing unit (cooled by sea water) before returning as a liquid to heat exchanger.

Question 55

How are the waste products of nuclear fission processed?

Answer 55

• Material removed from a reactor will be v. hot so first placed in cooling pond until it reaches safe temps.
• Material handled remotely using robots to limit radiation exposure.
• Material then stored in containers until its activity has fallen sufficiently to be moved to long term storage: deserted areas away from life chosen.
• Some used as medical tracers.