A-LevelPhysicsNuclear physics9702/43 · Oct/Nov 2019 · Q1210 Marks

One possible nuclear reaction that takes place is ²³⁵U + ¹n → ⁹⁵Mo + ¹³⁹La + 2¹n + 7⁰e ⁹² ₀ ⁴² ⁵⁷ ₀ ⁻¹ Data for nuclei in this reaction are given in Fig. 12.1. [Figure 12.1]

(a)Show that the energy equivalent to a mass of 1.00 u is 934 MeV.[2]
(b)(i)Use data from Fig. 12.1 to calculate the binding energy per nucleon of a nucleus of uranium-235 (²³⁵U). Complete Fig. 12.1.[2]
(b)(ii)The nucleon number of an isotope of the element rutherfordium is 267. State whether the binding energy per nucleon of this isotope will be greater than, equal to or less than the binding energy per nucleon of uranium-235.[1]
(c)Calculate the total energy, in MeV, released in this nuclear reaction.[2]
(d)The nuclei in 1.2 × 10⁻⁷ mol of uranium-235 all undergo this reaction in a time of 25 ms. Calculate the average power release during the time of 25 ms.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] (a) E = (3.0 × 10⁸)² × 1.66 × 10⁻²⁷ (= 1.49 × 10⁻¹⁰ J)
[A1] (a) = (1.49 × 10⁻¹⁰) / (1.60 × 10⁻¹⁹) = 9.34 × 10⁸ = 934 MeV
[C1] (b)(i) binding energy = 1.865 × 934 (= 1741.91 MeV)
[A1] (b)(i) = 7.41 (MeV)
[B1] (b)(ii) less (than)
[C1] (c) energy = {(1.219 +0.859) – 1.865)} × 934
[A1] (c) = 199 MeV
[C1] (d) number of reactions = 1.2 x 10⁻⁷ x 6.02 x 10²³
[C1] (d) energy release (for one reaction) = 199 × 1.60 × 10⁻¹³ (= 3.18 × 10⁻¹¹ J)
[A1] (d) = 9.2 x 10⁷ W

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