DP Chemistry (last assessment 2024)

Question 20N.3.sl.TZ0.10b

Date	November 2020	Marks available	[Maximum mark: 2]	Reference code	20N.3.sl.TZ0.10b
Level	sl	Paper	3	Time zone	TZ0
Command term	Calculate	Question number	b	Adapted from	N/A

[Maximum mark: 2]

20N.3.sl.TZ0.10b

$1.57 %$ of the mass of a rock weighing $46.5 kg$ is uranium(IV) oxide, ${UO}_{2}$ . $99.28 %$ of the uranium atoms in the rock are uranium-238, ${}^{238}U$ .

(b)

The half-life of ²³⁸U is $4.46 \times 10^{9}$ years. Calculate the mass of ²³⁸U that remains after $0.639 kg$ has decayed for $2.23 \times 10^{10}$ years.

[2]

Markscheme

Alternative 1
$« \frac{2.23 \times 10^{10} year}{4.46 \times 10^{9} year} = » 5.00 « half - lives »$ ✔

$« m = 0.639 kg \times (0.5)^{5} = » 0.0200 « kg »$ ✔

Alternative 2
$« 𝜆 = \frac{\ln 2}{4.46 \times 10^{9} year} = » 1.554 \times 10^{- 10} « {year}^{- 1} »$ ✔

$« m = 0.639 kg \times 𝑒^{- 1.554 \times 10^{- 10 {year}^{- 1}} \times 2.23 \times 10^{10 year}} = » 0.0200 « kg »$ ✔

Award [2] for correct final answer.

Examiners report

This continues to be a topic that students understand well, and probably more used alternative 1 to calculate the half-life. Students should always clearly show their calculations so examiners can award marks throughout the question and potentially award ECF if possible. It is very difficult to do this when students do not show work clearly.

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Options » C: Energy » C.3 Nuclear fusion and fission

Options » C: Energy

Question 20N.3.sl.TZ0.10b

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