Nuclear Physics

Question 1

Describe the experimental setup of the Rutherford scattering experiment.

Answer 1

Collimated beam of alpha particles.
Fire at a thin metal (gold) foil.
Fluorescent screen surrounding the whole apparatus

Question 2

State the three observations of the scattering experiment.

Answer 2

Most alpha particles passed straight through.
Some alpha particles deflected by small angles.
Tiny number of alpha particles deflected by large angles (> 90 degrees)

Question 3

State the three conclusions made from these observations of the scattering experiment.

Answer 3

The atom is mostly empty space (Nuclear radius &laquo_space;atomic radius).
Nucleus must be positively charged to repel positive alpha particles.
Nearly all of atom’s mass concentrated in a very tiny nucleus.

Question 4

What fundamental force is responsible for alpha particle scattering?

Answer 4

ElectroMAGNETIC force

Question 5

What are the two methods used for determining the nuclear radius?

Answer 5

Distance of closest approach of alpha particles.
Electron scattering patterns.

Question 6

Describe the energy changes of an alpha particle backscattering (180 degree deflection)

Answer 6

Alpha particle initially has kinetic energy.
As positive alpha particle approaches positive nucleus, kinetic energy is transferred into a store of electrical potential energy.

Question 7

Why is the distance of closest approach only an estimate for the maximum nuclear radius?

Answer 7

Alpha particle never actually reaches the nucleus, only travels very close to it
Therefore, nuclear radius must be lower than closest approach distance.

Question 8

Describe the experimental setup of electron scattering.

Answer 8

Collimated beam of electrons accelerated to relativistic speeds (energies of MeV).
Fired towards nuclei of thin film of material, onto a screen behind.

Question 9

What is the adapted de Broglie wavelength equation for these high energy electrons?

Answer 9

λ ≃ hc / E

Question 10

Describe the intensity-scattering angle interference pattern produced by electron scattering.

Answer 10

Bright central maximum.
Decreasing intensity as scattering angle increases.
Non-zero minima.

Question 11

State the advantages of using the distance of closest approach for determining nuclear radius.

Answer 11

Uses simple calculations for a good estimate of maximum nuclear radius.
Only requires alpha particles to be accelerated to low speeds, compared to acceleration for relativistic electrons.

Question 12

State the advantages of using the electron scattering method for determining nuclear radius.

Answer 12

Much more accurate value for nuclear radius, measured directly.
Electrons have a very small mass, so no recoil on nucleus compared to relatively larger alpha particles.

Question 13

Derive the general expression for nuclear density. What does it show?

Answer 13

Mass of nucleus = A x mnucleon
V = 4/3 πR³ = 4/3 π (R₀A^1/3)³ = 4/3 πR₀³A
Density = mass / volume = 3m_nucleon / 4πR₀³
Nuclear density is independent of mass number.

Question 14

List the assumptions made when deriving the nuclear density.

Answer 14

Assumed protons have the same mass as neutrons – (protons have slightly lower mass).
Assumed nucleus is a perfect sphere – (shape is not perfectly spherical).
Density within a nucleus is uniform – (density is non-uniform).

Question 15

Which nuclear instability causes radioactive decay of alpha, beta-minus, beta-plus and gamma?

Answer 15

Alpha – Heavy nuclei
Beta-minus – Too many neutrons (neutron-rich)
Beta-plus – Too many protons (proton-rich)
Gamma – Too much energy (highly energetic)

Question 16

Describe the ionising effect, range in air, penetrating power and behaviour in magnetic/electric fields for alpha radiation.

Answer 16

Strongly ionising
Travels several cm in air
Stopped by paper or skin
Positive charge and relatively high mass, deflected by a small amount in fields

Question 17

Describe the ionising effect, range in air, penetrating power and behaviour in magnetic/electric fields for beta radiation.

Answer 17

Weakly ionising
Travels a few m in air
Stopped by few mm of metal
Negative charge and relatively low mass, deflected by a large amount.

Question 18

Describe the ionising effect, range in air, penetrating power and behaviour in magnetic/electric fields for gamma radiation.

Answer 18

Very weakly ionising
Travels tens to hundreds of m in air
Stopped by few cm of concrete or lead
No charge, so unaffected by fields.

Question 19

Define the term background radiation and list 3 possible sources.

Answer 19

Radioactivity/nuclear radiation that is always present and cannot be eliminated.
Radon gas in the air.
Radioactive isotopes in rocks/ground/buildings.
Cosmic rays.
Medical application/waste.

Question 20

Describe the process of calculating a corrected count rate.

Answer 20

Take multiple (at least three) readings of background radiation.
Average these readings, and subtract the average from the measured count rate from a radioactive source.

Question 21

Describe the inverse-square law for gamma radiation.

Answer 21

Gamma radiation emitted in all directions.
Radiation spreads out as distance increases.
Less radiation per unit area = lower intensity of radiation.
Intensity decreases by the square of the distance from the source.

Question 22

Describe the activity of a sample and give the unit. What is activity proportional to?

Answer 22

• The number of nuclei that decay per second - (Becquerels, Bq) - Activity is directly proportional to the number of nuclei in the sample (N)

Question 23

What is the probability of a nucleus decaying per second called and why is a probability needed?

Answer 23

Probability of a given nucleus decay per second is called the decay constant (λ).
Probability is required as the decay of an individual nucleus is completely random – it cannot be exactly predicted.

Question 24

Define the half-life of an isotope.

Answer 24

The average time it takes for the number of unstable nuclei to halve.
The longer the half-life, the longer an isotope stays radioactive.
T_1/2 = ln2 / λ

Question 25

Describe the shape of a graph of ln(N) against time.

Answer 25

Straight line graph. Gradient = -λ

Question 26

Describe a suitable radioactive isotope for a medical tracer.

Answer 26

Isotope should emit either beta or gamma radiation – able to pass through the human body. Half-life should be long enough to take measurements, but short enough to limit radiation exposure.

Question 27

Describe the line of stability curve and what causes each decay mode.

Answer 27

Graph of N (nucleon number) against Z (proton number), where the line of stability is found by plotting N against Z for stable nuclei Above line of stability, nuclei have too many nuetrons - undergo beta minus decay Below line of stability, nuclei have too many protons - undergo beta plus decay Very heavy nuclei have too many nucleons - undergo alpha decay

Question 28

Explain why electron capture may result in the emission of gamma radiation.

Answer 28

Electron capture causes a proton to change into a neutron, emitting a neutrino. This leaves the nucleus in an excited state with excess energy, requiring the emission of gamma radiation to make the nucleus stable.

Question 29

State the quantities that must be conserved in a nuclear decay

Answer 29

Energy and momentum Charge Nucleon number Lepton number

Question 30

Describe the key features of an energy level diagram for nuclear decay.

Answer 30

Vertical energy axis. Elements written in nuclide notation. Arrows between energy levels. Arrows labelled with the type of decay and energy change (ΔE).

Question 31

Define mass defect.

Answer 31

The difference in the mass of a nucleus, and the mass of its individual constituents (nucleons).

Question 32

Define binding energy.

Answer 32

The energy required to completely separate a nucleus into its constituent nucleons.

Question 33

Describe what is meant by average binding energy per nucleon.

Answer 33

Each nucleus has a unique amount of binding energy. By dividing the binding energy of a nucleus by the number of nucleons, you can determine how much each nucleon is “worth” in terms of binding energy.

Question 34

Describe the graph of average binding energy per nucleon against nucleon number. Which nucleus is the most stable?

Answer 34

Graph of average nuclear binding energy per nucleon in Mev (from 0 to 10) against nucleon number (0 to 50) Average binding energy per nucleon decreases gently for heavier nuclei Average binding energy per nucleon increases rapidly for light nuclei Iron is the most stable nucleus

Question 35

Describe nuclear fission and explain why fission releases energy.

Answer 35

Large nucleus is unstable and randomly splits into smaller nuclei. The new, smaller nuclei produced have a higher than average binding energy per nucleon than the original nucleus.

Question 36

Describe nuclear fusion and explain why fusion releases energy.

Answer 36

Two light nuclei combine to create a larger nucleus. The new, heavier nucleus has a higher than average binding energy per nucleon than the two original nuclei.

Question 37

Which nuclei undergo fission? Which undergo fusion?

Answer 37

Nuclei smaller than iron-56 undergo fusion. Nuclei larger than iron-56 undergo fission.

Question 38

Explain why fusion typically releases more energy than fusion.

Answer 38

Graph of average binding energy per nucleon against nucleon number is steeper for smaller nuclei. For fusion, greater change in average binding energy per nucleon than for fission.

Question 39

Explain what is meant by enriched uranium.

Answer 39

Only a certain isotope of uranium (U-235) can undergo fission. Enriched uranium contains a greater proportion of fissionable isotopes (i.e. greater proportion of U-235).

Question 40

Describe a chain reaction and what is meant by a steady rate of reaction.

Answer 40

A neutron is required to induce fission (in U-235 for example). This fission process also releases further neutrons which can go on to induce further fission processes. A steady rate of reaction only releases one neutron per fission.

Question 41

Describe the role of the moderator in a nuclear reactor and state two examples.

Answer 41

To slow down neutrons via elastic collisions, transferring kinetic energy and momentum (becoming thermal neutrons). For example: water and graphite.

Question 42

Describe what is meant by critical and supercritical mass.

Answer 42

Critical mass is the amount of fuel required to sustain a steady rate of fusion. Supercritical mass is an amount of fuel greater than this, with the reaction rate controlled by the control rods.

Question 43

Describe the role of control rods in a nuclear reactor and state one example.

Answer 43

Control rods absorb excess neutrons produced by fission, in order to control the rate of fission reactions in a reactor. For example: boron.

Question 44

Describe the role of coolant in a nuclear reactor and state one example.

Answer 44

Remove heat produced by fission (coolant should be efficient at transferring heat). Heat from the reactor turns coolant into steam which is used to power turbines and generate electricity. For example: water.

Question 45

State two safety precautions used for nuclear reactors.

Answer 45

Reactor shielding: Nuclear reactor surrounded in thick concrete case to limit radiation exposure for factory workers. Emergency shut-down: Reaction rate slowed down as quickly as possible by fully lowering all control rods.

Question 46

What is the most dangerous product of nuclear fission? What safety precautions are taken?

Answer 46

Used/spent fuel rods which emit beta and gamma radiation and are extremely hot. Used fuel rods should be cooled down in a cooling pond and safely stored in lead containers deep underground.