Cambridge International AS & A Level · 23 · structured

Compute a reaction's energy release from masses

Compute a reaction's energy release from masses · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand: demanding
Marks: 5
Topics: 1
Answer: Complete

structured5 marks

For a deuterium–tritium fusion reaction, use these consistent particle/atomic masses: deuterium 2.01410 u, tritium 3.01605 u, helium-4 product 4.00260 u, neutron 1.00866 u. The atomic electron counts balance between the reactants and products. Use 1 u=1.66×10⁻²⁷ kg, c=3.00×10⁸ m s⁻¹ and 1 MeV=1.60×10⁻¹³ J.

(a)
Calculate the sum of reactant masses, sum of product masses and the positive mass loss per reaction.
2 marks
(b)
Calculate the energy released per reaction in joules and MeV. Explain the physical meaning of its positive sign.
3 marks

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Answer overview(a) Reactants 5.03015 u; products 5.01126 u; mass loss 0.01889 u. (b) 2.82×10⁻¹² J ≈17.6 MeV; product rest mass is smaller and the energy appears mainly as product kinetic energy.

(a)

2 marks

Calculate the sum of reactant masses, sum of product masses and the positive mass loss per reaction.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

1
Add reactants: 2.01410+3.01605=5.03015 u.
2
Add products: 4.00260+1.00866=5.01126 u; subtract final from initial to get 0.01889 u.

(b)

3 marks

Calculate the energy released per reaction in joules and MeV. Explain the physical meaning of its positive sign.

How to approach it

1
Δm=0.01889×1.66×10⁻²⁷=3.14×10⁻²⁹ kg.
2
E=Δmc²=2.82×10⁻¹² J; dividing by 1.60×10⁻¹³ gives 17.6 MeV.
3
Initial rest mass exceeds final rest mass, so this amount is released as other energy, mainly kinetic energy of the reaction products.

Complete marking guidance

Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.

(a) Add reactants: 2.01410+3.01605=5.03015 u.
(a) Add products: 4.00260+1.00866=5.01126 u; subtract final from initial to get 0.01889 u.
(b) Δm=0.01889×1.66×10⁻²⁷=3.14×10⁻²⁹ kg.
(b) E=Δmc²=2.82×10⁻¹² J; dividing by 1.60×10⁻¹³ gives 17.6 MeV.
(b) Initial rest mass exceeds final rest mass, so this amount is released as other energy, mainly kinetic energy of the reaction products.

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