3.8 Nuclear physics (A-level only) — AQA 7408 spec coverage

3.8.1.1

Rutherford scattering

In Rutherford scattering, most alpha particles pass through a thin metal foil with little or no deflection, showing that atoms are mostly empty space.
A small proportion are deflected through large angles because the positive alpha particles experience electrostatic repulsion near a concentrated positive nucleus.
The very rare backward deflections show that nearly all the mass and positive charge occupy a region much smaller than the atom.
Exam answers must link each observation to an inference. A common error is merely to list the observations without explaining how they contradict a diffuse-charge model.

Tier 1 · Easy

1 mark

ORIGINAL

State what is inferred from the observation that most alpha particles cross a very thin gold foil without changing direction.

Tier 2 · Standard

3 marks

ORIGINAL

A small fraction of alpha particles directed at a thin platinum foil are deflected through angles greater than $90^\circ$ . Explain what this reveals about the atom.

Tier 3 · Hard

5 marks

ORIGINAL

In a scattering experiment, most alpha particles continue straight through a metal foil, some are deflected slightly, and about one in twelve thousand returns towards the source. Explain how these observations support the nuclear model rather than a model with positive charge spread throughout the atom.

3.8.1.2

Alpha, beta and gamma radiation

Alpha radiation is strongly ionising and has a short range; beta radiation is moderately ionising and is absorbed by a few millimetres of aluminium; gamma radiation is weakly ionising and needs thick, dense shielding.
For a point gamma source, intensity or background-corrected count rate follows $I=k/x^2$ when distance $x$ is measured from the source.
Subtract the background count rate before testing an inverse-square relationship, then add it back only if a predicted detector reading is required.
Absorption measurements can identify radiation and enable thickness monitoring: beta can monitor thin aluminium or paper, whereas gamma is used for thicker steel.
A common error is to apply the inverse-square law to a raw count rate that still includes background radiation.

Tier 1 · Easy

2 marks

ORIGINAL

A radioactive source produces radiation that is stopped by a sheet of paper. Identify the radiation and state one relative hazard when it is inside the body.

Tier 2 · Standard

3 marks

ORIGINAL

A gamma detector records $920\,\text{s}^{-1}$ at $0.20\,\text{m}$ from a point source. The background rate is $20\,\text{s}^{-1}$ . Calculate the detector reading expected at $0.50\,\text{m}$ .

Tier 3 · Hard

5 marks

ORIGINAL

Describe an experiment to test the inverse-square law for a sealed gamma source. Your method must explain how background radiation is handled and how the data are analysed.

3.8.1.3

Radioactive decay

Radioactive decay is random for an individual nucleus, but each nucleus of a given isotope has the same constant decay probability per unit time, represented by $\lambda$ .
The number of undecayed nuclei follows $N=N_0e^{-\lambda t}$ and activity follows $A=\lambda N=A_0e^{-\lambda t}$ ; activity is measured in becquerels, where $1\,\text{Bq}=1\,\text{s}^{-1}$ .
Half-life and decay constant are related by $T_{1/2}=\ln 2/\lambda$ ; time and $\lambda$ must use reciprocal units.
On a graph of $\ln A$ or $\ln N$ against $t$ , the gradient is $-\lambda$ . A common error is to treat a decay curve as linear or to omit the minus sign.
When activity is used to find a number of nuclei, rearrange $A=\lambda N$ only after converting the half-life into seconds if activity is in Bq.

Tier 1 · Easy

2 marks

ORIGINAL

An isotope has a half-life of $6.0\,\text{h}$ . Calculate its decay constant in $\text{s}^{-1}$ .

Tier 2 · Standard

3 marks

ORIGINAL

A source initially has activity $480\,\text{Bq}$ and decay constant $1.8\times10^{-4}\,\text{s}^{-1}$ . Determine its activity after $2.40\times10^3\,\text{s}$ .

Tier 3 · Hard

5 marks

ORIGINAL

A pure sample has activity $860\,\text{Bq}$ at a time $5.0\,\text{h}$ after it was prepared. Its half-life is $3.0\,\text{h}$ . Calculate the number of radioactive nuclei present when the sample was prepared.

3.8.1.4

Nuclear instability

The $N$ - $Z$ graph has a band of stable nuclei: light stable nuclei have approximately $N=Z$ , while heavier stable nuclei require $N>Z$ .
A neutron-rich nucleus tends to undergo beta-minus decay, changing a neutron into a proton so that $N$ decreases by $1$ and $Z$ increases by $1$ .
A proton-rich nucleus can undergo beta-plus decay or electron capture; in either case $Z$ decreases by $1$ and $N$ increases by $1$ .
Alpha decay changes $A$ by $-4$ and $Z$ by $-2$ . Gamma emission changes neither $A$ nor $Z$ because it de-excites the nucleus.
In nuclear equations, conserve nucleon number and charge separately. A common error is to change $A$ during beta decay.

Tier 1 · Easy

2 marks

ORIGINAL

A nucleus lies above the band of stability on an $N$ - $Z$ graph. State its likely beta decay mode and the changes in $N$ and $Z$ .

Tier 2 · Standard

3 marks

ORIGINAL

Fluorine-18 is proton-rich and decays to oxygen-18. State the decay mode and complete the equation $^{18}_{9}\mathrm{F}\rightarrow{}^{18}_{8}\mathrm{O}+\ldots$

Tier 3 · Hard

5 marks

ORIGINAL

Strontium-90 undergoes two successive beta-minus decays, first to yttrium and then to zirconium. Complete the equations $^{90}_{38}\mathrm{Sr}\rightarrow\ldots$ and $^{90}_{39}\mathrm{Y}\rightarrow\ldots$ and explain the movement of each nucleus on an $N$ - $Z$ graph.

3.8.1.5

Nuclear radius

Nuclear radii are typically of order $10^{-15}\,\text{m}$ and follow $R=r_0A^{1/3}$ , where the value of $r_0$ must be taken from the question or experimental data.
The closest approach of an alpha particle can estimate an upper limit for nuclear radius by equating its kinetic energy to electrostatic potential energy.
Electron diffraction gives nuclear size from the angular positions of intensity minima; electrons are suitable because their de Broglie wavelength can be comparable with a nuclear diameter.
Because $R^3\propto A$ , nuclear volume is proportional to nucleon number, providing evidence that nuclear matter has approximately constant density.
Convert femtometres using $1\,\text{fm}=10^{-15}\,\text{m}$ . A common error is to use $A$ rather than $A^{1/3}$ in the radius equation.

Tier 1 · Easy

2 marks

ORIGINAL

Use $R=r_0A^{1/3}$ with $r_0=1.05\,\text{fm}$ to calculate the radius of an aluminium-27 nucleus.

Tier 2 · Standard

3 marks

ORIGINAL

A nucleus has radius $4.20\,\text{fm}$ . Using $R=r_0A^{1/3}$ and $r_0=1.05\,\text{fm}$ , determine its nucleon number.

Tier 3 · Hard

5 marks

ORIGINAL

Model a nucleus as a sphere with $R=r_0A^{1/3}$ , where $r_0=1.05\,\text{fm}$ . Taking each nucleon to have mass $1.67\times10^{-27}\,\text{kg}$ , calculate the nuclear density and show why your result is independent of $A$ .

3.8.1.6

Mass and energy

Any energy change has an equivalent mass change through $E=mc^2$ ; a decrease in total rest mass appears as released energy.
For nuclear mass differences quoted in atomic mass units, use $1\,\text{u}=931.5\,\text{MeV}$ and show the reactant mass, product mass and mass defect before conversion.
Binding energy is the energy required to separate a nucleus into free nucleons; a larger average binding energy per nucleon means a more tightly bound nucleus.
Fusion of light nuclei and fission of heavy nuclei release energy because the products have a higher average binding energy per nucleon.
Use atomic masses consistently so that electron masses cancel where appropriate. A common error is to multiply a mass defect in kilograms by $931.5$ instead of using $E=mc^2$ .

Tier 1 · Easy

2 marks

ORIGINAL

A nuclear reaction has a mass defect of $0.00320\,\text{u}$ . Use $1\,\text{u}=931.5\,\text{MeV}$ to calculate the energy released.

Tier 2 · Standard

4 marks

ORIGINAL

In one fission event, uranium-235 absorbs a neutron and produces barium-141, krypton-92 and three neutrons. The relevant masses are $235.0439\,\text{u}$ , $140.9144\,\text{u}$ , $91.9262\,\text{u}$ and $1.0087\,\text{u}$ for a neutron. Use $1\,\text{u}=931.5\,\text{MeV}$ to calculate the energy released.

Tier 3 · Hard

6 marks

ORIGINAL

A deuterium nucleus and a tritium nucleus fuse to form helium-4 and a neutron. The corresponding atomic masses of deuterium, tritium and helium-4 are $2.01410\,\text{u}$ , $3.01605\,\text{u}$ and $4.00260\,\text{u}$ ; the neutron mass is $1.00867\,\text{u}$ . Use $1\,\text{u}=931.5\,\text{MeV}$ and $1\,\text{MeV}=1.602\times10^{-13}\,\text{J}$ . Calculate the energy released in both MeV and joules, and explain the release using binding energy per nucleon.

3.8.1.7

Induced fission

A slow, thermal neutron can be absorbed by a fissile nucleus, making it unstable so that it splits into two smaller nuclei, releases energy and emits further neutrons.
A chain reaction is critical when, on average, one neutron from each fission induces another fission; below this it dies away and above this it grows.
A moderator slows neutrons by elastic collisions and should contain light nuclei while absorbing few neutrons; water and graphite are examples.
Control rods absorb neutrons and are inserted or withdrawn to regulate the reaction; boron and cadmium are suitable because of their high neutron absorption.
A coolant transfers thermal energy from the core and should have suitable thermal properties and chemical stability. A common error is to say the moderator absorbs neutrons rather than slows them.

Tier 1 · Easy

2 marks

ORIGINAL

State the function of the moderator and the function of the control rods in a thermal nuclear reactor.

Tier 2 · Standard

3 marks

ORIGINAL

Each fission in a reactor releases an average of $2.5$ neutrons. If $40\%$ of these neutrons induce another fission, calculate the multiplication factor and state whether the reactor is subcritical, critical or supercritical.

Tier 3 · Hard

5 marks

ORIGINAL

Explain how induced fission becomes a controlled chain reaction in a thermal reactor. Include the roles and suitable material properties of the moderator, control rods and coolant.

3.8.1.8

Safety aspects

Reactor fuel and radioactive waste are handled remotely to increase distance and reduce the time for which workers are exposed; dense shielding absorbs ionising radiation.
Emergency shutdown inserts neutron-absorbing control rods rapidly, but radioactive decay continues to produce heat, so cooling must continue after fission stops.
Waste is classified and contained according to its activity and half-life; high-activity material requires remote handling, shielding and secure long-term storage.
Inverse-square reasoning can reduce exposure from a compact source, but it does not replace shielding, contamination control or controlled access.
Risk-benefit discussions should compare specific hazards with benefits such as reliable low-carbon electricity. A common error is to state that shutdown immediately removes all heat production.

Tier 1 · Easy

2 marks

ORIGINAL

State two ways in which worker exposure is reduced while spent reactor fuel is moved.

Tier 2 · Standard

3 marks

ORIGINAL

Explain why a reactor still needs coolant circulation immediately after an emergency shutdown has fully inserted the control rods.

Tier 3 · Hard

5 marks

ORIGINAL

During remote handling, a detector reads $365\,\text{s}^{-1}$ at $1.5\,\text{m}$ from a compact gamma source. Background is $40\,\text{s}^{-1}$ . Assuming inverse-square behaviour, determine the distance at which the source contribution is $13\,\text{s}^{-1}$ and state the detector reading there. Explain why this distance alone is not a complete safety measure.