A-LevelPhysicsNuclear physics9702/42 · Oct/Nov 2019 · Q128 Marks

Radon-222 (²²²₈₆Ra) is a radioactive gas that decays randomly with a decay constant of 7.55 × 10⁻³ hour⁻¹.

(a)(i)random decay[1]
(a)(ii)decay constant.[2]
(b)The activity of radon gas in a sample of 4.80 × 10⁻³ m³ of air taken from a building is 0.600 Bq. There are 2.52 × 10²⁵ air molecules in a volume of 1.00 m³ of air. Calculate, for 1.00 m³ of the air, the ratio number of air molecules ────────────────────── number of radon atoms ratio = ..................................................... [5][5]

Mark scheme

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

[B1] (decay is) unpredictable/cannot be predicted
[M1] probability of decay (of a nucleus)
[A1] per unit time
[C1] A = λN
[C1] (for 1.00 m³) A = 0.600 / 4.80 × 10⁻³ (= 125 Bq)
[C1] N = 125 / ([7.55 × 10⁻³] / 3600) (= 5.96 × 10⁷)
[C1] so ratio = (2.52 × 10²⁵) / (5.96 × 10⁷)
[C1] or (for 4.80 × 10⁻³ m³) N for air = 2.52 × 10²⁵ × 4.80 × 10⁻³ (= 1.21 × 10²³)
[C1] N for radon = 0.600 / ([7.55 × 10⁻³] / 3600) (= 2.86 × 10⁵)
[C1] so ratio = (1.21 × 10²³) / (2.86 × 10⁵)
[A1] ratio = 4.2 x 10¹⁷

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