AQA A-Level Physics Paper 1, June 2024: Question 4

4 marks · Medium difficulty · Short Answer

Show that the kinetic energy of the neutron in a deuterium-tritium fusion reaction is approximately 80% of the total energy transferred, and calculate its initial speed given the combined kinetic energy.

Practise this question

Question

An exam question about the deuterium-tritium nuclear reaction. Part 04.1 asks to show that the kinetic energy of the neutron represents approximately 80% of the total energy transferred (2 marks). Part 04.2 gives the combined kinetic energy of the helium nucleus and the neutron as 2.82 x 10^-12 J and asks to calculate the initial speed of the neutron (2 marks).
Question text

04 The deuterium–tritium (D–T) reaction is a nuclear reaction between two isotopes

of hydrogen.

The D–T reaction is

2Η + 3Η → 4 Ηe + n

11 2

The energy from this reaction is transferred to the kinetic energy of the helium nucleus

and the kinetic energy of the neutron.

Assume that the kinetic energies of the hydrogen nuclei are zero just before the

reaction occurs.

04.1 Show that the kinetic energy of the neutron represents approximately 80% of the

total energy transferred.

[2 marks]

04.2 The combined kinetic energy of the helium nucleus and the neutron is 2.82 × 10–12 J.

Calculate the initial speed of the neutron.

[2 marks]

initial speed = m s−1

Mark scheme

Show the mark scheme The mark scheme for question 04. Part 04.1 awards 2 marks for appreciating momentum conservation and mass relationships to derive that neutron KE is 4 times that of helium. Part 04.2 awards 2 marks for calculating the neutron KE and applying the kinetic energy formula to find the speed v = 5.2 x 10^7 m s^-1.

Question Answers Additional comments/Guidelines Mark AO

04.1 Either appreciation of mass of He = 4 × mass of neutron 2 AO3

OR idea that n and He have equal (and opposite) momenta

p

Combination of momentum and KE equations (to give idea Expect to see KE =

2m

that KE is inversely proportional to m with same p) and

therefore KE of neutron = 4 × KE of He

04.2 calculates KE of neutron 80% × 2.82 × 10–12 = 2.26 × 10–12 (J) 2 AO2

OR –12

uses mass of neutron from data booklet with their Do not allow use of 2.82 × 10 as their

calculated KE in a KE equation calculated KE.

7 –1 m =1.67(5) × 10–27 kg

v = 5.2 × 10 m s n

Accept answers of 5.18 × 107 or

5.19 × 107 m s-1

Calculator values:

5.1823878 × 107; (using 1.68)

5.1901169 × 107; (using 1.675)

5.1978807 × 107 (using 1.67)

Total 4

How to answer it

Deuterium-Tritium Fusion & Kinetic Energy Partition

What this question tests

This question assesses your ability to combine conservation laws—specifically conservation of momentum and conservation of energy—in a nuclear fusion context. You must link particle mass ratios to momentum and kinetic energy distribution ( KE = p² / (2m) ) before executing multi-step calculations involving data booklet constants and percentage scaling.

Question Part 04.1 (2 marks)

Proportion of Energy Transferred to the Neutron

💡 Key Knowledge

  • Momentum Conservation: Because the system starts with zero initial momentum (stationary reactants), the total final momentum must also be zero. Therefore, the helium nucleus and the neutron must move in opposite directions with equal magnitudes of momentum ( p_He = p_n ).
  • Mass Relationship: A helium-4 nucleus has a nucleon number of 4, meaning its mass is approximately 4 times that of a single neutron ( m_He ≈ 4m_n ).
  • Kinetic Energy & Momentum: Combining KE = 0.5mv² and p = mv gives KE = p² / (2m) . Since momentum p is constant, KE is inversely proportional to mass ( KE ∝ 1/m ).

🧠 Exam Technique & Mark Scheme

To secure both marks, you must explicitly link mass, momentum, and kinetic energy:

  • Mark 1: Awarded for stating/appreciating that mass(He) = 4 × mass(n) OR recognising that the neutron and helium nucleus have equal and opposite momenta.
  • Mark 2: Awarded for combining momentum and KE equations to deduce that KE_neutron = 4 × KE_helium , which mathematically proves the neutron takes 80% (or 4/5) of the total kinetic energy.

❌ Common Errors & Examiner Commentary

Many students lose marks here by merely stating a ratio without proof, or by confusing mass numbers with velocity ratios. Examiners noted that top-level responses cleanly set up p_He = p_n and substituted √(2m_He KE_He) = √(2m_n KE_n) to derive the final energy distribution statement effortlessly.

Question Part 04.2 (2 marks)

Calculating the Initial Speed of the Neutron

📐 Step-by-Step Calculation

  1. Find the neutron's kinetic energy:
    Calculate 80% of the combined kinetic energy.
    KE_n = 0.80 × 2.82 × 10⁻¹² J = 2.256 × 10⁻¹² J (retain extra sig figs for working).
  2. Identify the mass of a neutron:
    From the AQA Data Booklet: m_n = 1.67 × 10⁻²⁷ kg (or 1.675 × 10⁻²⁷ kg ).
  3. Rearrange the kinetic energy equation for velocity ( v ):
    KE = 0.5mv² ⇒ v = √(2KE / m)
  4. Substitute values and compute:
    v = √((2 × 2.256 × 10⁻¹² J) / (1.67 × 10⁻²⁷ kg))
    v = √(2.70059 × 10¹⁵) = 5.197 × 10⁷ m s⁻¹
Final Answer: 5.2 × 10⁷ m s⁻¹ (to 2 significant figures, matching data precision). Acceptable range: 5.18 × 10⁷ to 5.19 × 10⁷ m s⁻¹ depending on exact data booklet mass used.

🧠 Exam Technique & Guidance

  • Mark 1: Correctly calculating the neutron's kinetic energy ( 2.26 × 10⁻¹² J ) OR correctly substituting m_n into a kinetic energy formula with a derived energy.
  • Mark 2: Reaching the final velocity value with correct standard units ( m s⁻¹ ).
  • Sig Figs: The input data ( 2.82 × 10⁻¹² J ) is given to 3 significant figures, but standard AQA convention allows rounding final answers to 2 or 3 sig figs. Ensure you don't round intermediate steps too early!

❌ Common Calculation Traps

  • Trap 1: Using the total combined energy ( 2.82 × 10⁻¹² J ) directly in the velocity equation instead of scaling it down to the neutron's 80 share.
  • Trap 2: Forgetting the factor of 2 in KE = 0.5mv² when rearranging for velocity (a classic slip-up under exam pressure).

Topics

Physics · 3.4 Mechanics and materials · 3.8 Nuclear physics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.