AQA A-Level Physics: Nuclear physics (7408) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover section 3.8 Nuclear physics (3.8.1.1 to 3.8.1.8) of the AQA AS and A-level Physics (7407/7408) specification, version 1.4 (AS and A-level exams June 2016 onwards). The section is A-level only and is assessed in Paper 2. Sections 3.9-3.13 are options (you study one, assessed in Paper 3 Section B); this section is compulsory.

Learn the content first with the study guide and the revision notes. Course pages: AQA A-level Physics hub, printable checklist and the free diagnostics.

Use: e = 1.60 × 10⁻¹⁹ C, ε₀ = 8.85 × 10⁻¹² F m⁻¹, Nᴀ = 6.02 × 10²³ mol⁻¹, h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, 1 u = 931.5 MeV, proton mass 1.007276 u, neutron mass 1.008665 u, electron mass 0.000549 u, nucleon mass 1.67 × 10⁻²⁷ kg, 1 year = 3.16 × 10⁷ s.

Questions

1. Describe the main observations of the α-particle scattering experiment with thin gold foil, and state what each tells you about the structure of the atom. [4]

2. A student tests a source with a GM tube. The background count rate is 25 min⁻¹. Count rates with different absorbers between source and tube are: none 1240 min⁻¹; paper 530 min⁻¹; 5 mm aluminium 26 min⁻¹; 25 mm lead 25 min⁻¹. Deduce which radiations the source emits. Explain your answer. [4]

3. A γ source gives a measured count rate of 1650 min⁻¹ at 0.15 m from a GM tube. The background count rate is 30 min⁻¹.

(a) Calculate the measured count rate expected at 0.45 m. [3] (b) A graph of corrected count rate against 1/d², where d is the measured distance, is not quite a straight line through the origin. Suggest why. [1]

4. A sample contains 5.0 mg of a radioactive isotope of molar mass 60.0 g mol⁻¹ and half-life 5.3 years.

(a) Calculate the number of nuclei in the sample. [2] (b) Calculate the decay constant in s⁻¹. [1] (c) Calculate the activity of the sample. [1] (d) Calculate the time, in years, for the activity to fall to 10% of its starting value. [2]

5. A best-fit line of ln(A/Bq) against time t passes through (0, 13.60) and (10.0 h, 11.29).

(a) Determine the decay constant. [2] (b) Calculate the half-life. [1] (c) Calculate the initial activity. [1] (d) State one advantage of a log graph over a decay curve for finding half-life. [1]

6. The nuclide ¹⁸₉X lies below the line of stable nuclei on a graph of N against Z.

(a) State what this tells you about its neutron-to-proton balance, and name a decay mode it could undergo. [1] (b) Write the equation for β⁺ decay of ¹⁸₉X to a daughter Y. [2] (c) Write the equation for electron capture by ¹⁸₉X. [1] (d) State the change in N and in Z for both decays. [1]

7. After β⁻ decay, a daughter nucleus can be left in excited states 0.35 MeV and 0.90 MeV above its ground state.

(a) State all the possible γ-photon energies as the nucleus returns to its ground state. [2] (b) Calculate the shortest wavelength emitted. [2]

8. An α particle of kinetic energy 6.0 MeV is aimed head-on at a nucleus with Z = 50 and A = 120.

(a) Calculate the distance of closest approach. [3] (b) Calculate the radius of the nucleus using R = R₀A^(1/3) with R₀ = 1.2 fm. [1] (c) Explain why your answers to (a) and (b) differ, and why electron diffraction gives a better value of the radius. [2]

9.

(a) Use R = R₀A^(1/3) to show that the density of nuclear material does not depend on A. [2] (b) Calculate this density for R₀ = 1.3 fm. [2]

10. The atomic mass of carbon-12 is 12.000000 u. Calculate the binding energy per nucleon of the carbon-12 nucleus in MeV. [5]

11. In a fusion reaction ²₁H + ³₁H → ⁴₂He + ¹₀n. Atomic masses: ²₁H 2.014102 u, ³₁H 3.016049 u, ⁴₂He 4.002603 u. Neutron mass 1.008665 u.

(a) Calculate the energy released in MeV. [3] (b) Convert this energy to joules. [1] (c) Explain why the nuclei must be at a very high temperature for fusion to happen. [1]

12. A thermal reactor uses uranium fuel enriched in U-235, with heavy water as moderator.

(a) Explain why a moderator is needed, and why a chain reaction needs at least the critical mass of fuel. [2] (b) A neutron (mass 1 u) collides head-on and elastically with a stationary deuterium nucleus (mass 2 u). Show that the neutron keeps 1/9 of its kinetic energy. [3] (c) Name a suitable material for the control rods and explain how the rods control the reaction. [2] (d) State one property a good coolant needs. [1] (e) Describe two safety features that protect workers from spent fuel and from an accident in the core. [2]

Answers

1. Most α particles pass straight through, so most of the atom is empty space. [1] Some are deflected through large angles, so there is a small, concentrated region of positive charge. [1] A very few rebound (deflected by more than 90°), so this nucleus is very small [1] and contains most of the atom’s mass. [1] [4] Examiner insight: Pair each observation with its conclusion; a list of observations alone is likely to earn little.

2. Corrected rates: 1215, 505, 1 and 0 min⁻¹. [1] The large fall with paper shows α is emitted. [1] The fall to background with aluminium shows β is emitted. [1] The aluminium reading is already at background, so no γ. [1] [4] Examiner insight: Claiming γ because the raw lead reading is non-zero ignores background and loses the final mark.

3. (a) Corrected rate = 1650 − 30 = 1620 min⁻¹ [1] Distance × 3, so corrected rate ÷ 9 = 180 min⁻¹ [1] Measured = 180 + 30 = 210 min⁻¹ [1] (b) The true distance differs from d by an unknown offset (source inside holder, detection inside tube). [1] [4] Examiner insight: Dividing 1650 by 9 without removing background gives 183 min⁻¹ and loses the method mark for the correction.

4. (a) Moles = 5.0 × 10⁻³ g / 60.0 g mol⁻¹ = 8.33 × 10⁻⁵ mol [1] N = 8.33 × 10⁻⁵ × 6.02 × 10²³ = 5.0 × 10¹⁹ [1] (b) λ = ln2 / (5.3 × 3.16 × 10⁷) = 4.1 × 10⁻⁹ s⁻¹ [1] (c) A = λN = 2.1 × 10¹¹ Bq [1] (d) 0.10 = e^(−λt), so t = ln10 / λ [1] t = 3.32 × 5.3 = 17.6 years [1] [6] Examiner insight: An error carried from (a) or (b) is usually allowed through (c) and (d) if your equation is shown.

5. (a) Gradient = (11.29 − 13.60) / 10.0 = −0.231 h⁻¹ [1] λ = −gradient = 0.231 h⁻¹ [1] (b) T½ = ln2 / 0.231 = 3.00 h [1] (c) A₀ = e^13.60 = 8.1 × 10⁵ Bq [1] (d) Uses all the data in one best-fit line, so random scatter is averaged (and λ comes straight from the gradient). [1] [5] Examiner insight: A negative decay constant is a physics error; state λ as the magnitude of the gradient, with units.

6. (a) Too many protons for stability (too few neutrons); it can decay by β⁺ or electron capture. [1] (b) ¹⁸₉X → ¹⁸₈Y + ⁰₊₁e [1] + νₑ [1] (c) ¹⁸₉X + ⁰₋₁e → ¹⁸₈Y + νₑ [1] (d) N increases by 1 and Z decreases by 1. [1] [5] Examiner insight: The neutrino in β⁺ decay and electron capture is an electron neutrino, not an antineutrino; the wrong one loses the mark.

7. (a) 0.90 MeV and 0.35 MeV [1] and 0.55 MeV (0.90 − 0.35) [1] (b) E = 0.90 × 10⁶ × 1.60 × 10⁻¹⁹ = 1.44 × 10⁻¹³ J; λ = hc/E [1] λ = 1.4 × 10⁻¹² m [1] [4] Examiner insight: Shortest wavelength means largest energy; using 0.35 MeV gives the longest wavelength.

8. (a) Eₖ = 6.0 × 10⁶ × 1.60 × 10⁻¹⁹ = 9.6 × 10⁻¹³ J [1] Eₖ = (2e)(50e) / (4πε₀r) [1] r = 2.4 × 10⁻¹⁴ m [1] (b) R = 1.2 × 10⁻¹⁵ × 120^(1/3) = 5.9 × 10⁻¹⁵ m [1] (c) The α stops and turns back before touching the nucleus, so (a) is only an upper limit. [1] Electrons are leptons and do not feel the strong force, and diffraction measures the radius directly. [1] [6] Examiner insight: Forgetting the α’s charge is 2e halves the answer; check both charges in Qq.

9. (a) Mass ≈ A × nucleon mass and volume = (4/3)πR₀³A [1] so ρ = m/((4/3)πR₀³), with A cancelling. [1] (b) ρ = 1.67 × 10⁻²⁷ / ((4/3)π(1.3 × 10⁻¹⁵)³) [1] = 1.8 × 10¹⁷ kg m⁻³ [1] [4] Examiner insight: A “show that” needs the cancellation of A written out; stating “density is constant” alone does not earn credit.

10. Nuclear mass = 12.000000 − 6(0.000549) = 11.996706 u [1] Nucleons: 6(1.007276) + 6(1.008665) = 12.095646 u [1] Mass difference = 0.098940 u [1] Binding energy = 0.098940 × 931.5 = 92.2 MeV [1] Per nucleon = 92.2 / 12 = 7.68 MeV [1] [5] Examiner insight: Skipping the electron-mass correction gives 7.42 MeV per nucleon and loses the first mark.

11. (a) Mass before = 5.030151 u; mass after = 5.011268 u [1] Mass lost = 0.018883 u [1] Energy = 0.018883 × 931.5 = 17.6 MeV [1] (b) 17.6 × 10⁶ × 1.60 × 10⁻¹⁹ = 2.8 × 10⁻¹² J [1] (c) The nuclei need enough kinetic energy to overcome their electrostatic repulsion and get close enough for the strong force to act. [1] [5] Examiner insight: Atomic masses work here because each side has two electrons; say so if asked to justify the method.

12. (a) Fission neutrons are fast; U-235 is far more likely to absorb thermal neutrons. [1] Below the critical mass too many neutrons escape, so on average fewer than one fission follows each fission. [1] (b) Momentum: u = v₁ + 2v₂; kinetic energy: u² = v₁² + 2v₂² [1] Solving: v₁ = −u/3 (and v₂ = 2u/3) [1] Fraction kept = (v₁/u)² = (1/3)² = 1/9 [1] (c) Boron (or cadmium) [1] absorbs neutrons; inserting the rods further leaves fewer neutrons, so the fission rate falls. [1] (d) High specific heat capacity (or flows easily, or low neutron absorption). [1] (e) Spent fuel is moved by remote handling (or stored behind shielding); [1] in an emergency the control rods drop fully into the core and stop the chain reaction. [1] [10] Examiner insight: In (c), “control rods slow neutrons down” earns no credit; slowing is the moderator’s job.

Where marks are usually lost

• Using raw count rates without correcting for background.
• Mixing units for λ: activity in Bq needs λ in s⁻¹.
• Quoting the ln A gradient as λ with its minus sign.
• Taking atomic mass as nuclear mass in binding-energy calculations.
• Using charge e instead of 2e for the α particle in closest-approach work.
• Calling the closest-approach distance the radius.
• Writing an antineutrino in β⁺ or electron-capture equations.
• Confusing moderator, control rods and coolant roles.
• Swapping the fission and fusion regions of the binding energy per nucleon graph.

Next steps

• Nuclear physics revision notes
• Nuclear physics study guide
• AQA A-level Physics hub
• Printable checklist
• All free 10-minute diagnostics
• Book a free trial class

Official syllabus

AQA AS and A-level Physics (7407/7408) specification, version 1.4, July 2026 (AS and A-level exams June 2016 onwards), published by AQA. Section 3.8 Nuclear physics (A-level only).