DP Physics (last assessment 2024)

Question 18M.2.SL.TZ1.6

Date	May 2018	Marks available	[Maximum mark: 14]	Reference code	18M.2.SL.TZ1.6
Level	SL	Paper	2	Time zone	TZ1
Command term	Calculate, Derive, Discuss, Identify, Show that, Sketch, State	Question number	6	Adapted from	N/A

[Maximum mark: 14]

18M.2.SL.TZ1.6

The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (β–) decay to form a stable boron (B) nuclide.

(a)

Identify the missing information for this decay.

[1]

Markscheme

$_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}} \to _{{\mkern 1mu} {\mkern 1mu} 5}^{10}{\text{B}} + \beta + {\overline {\text{V}} _{\text{e}}}$

conservation of mass number AND charge $_{\,\,5}^{10}{\text{B}}$ , $_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}}$

Correct identification of both missing values required for [1].

[1 mark]

The initial number of nuclei in a pure sample of beryllium-10 is N₀. The graph shows how the number of remaining beryllium nuclei in the sample varies with time.

(b.i)

On the graph, sketch how the number of boron nuclei in the sample varies with time.

[2]

Markscheme

correct shape ie increasing from 0 to about 0.80 N₀

crosses given line at 0.50 N₀

M18/4/PHYSI/SP2/ENG/TZ1/06.b.i/M

[2 marks]

(b.ii)

After 4.3 × 10⁶ years,

$\frac{{{\text{number of produced boron nuclei}}}}{{{\text{number of remaining beryllium nuclei}}}} = 7.$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

[3]

Markscheme

ALTERNATIVE 1

fraction of Be = $\frac{1}{8}$ , 12.5%, or 0.125

therefore 3 half lives have elapsed

${t_{\frac{1}{2}}} = \frac{{4.3 \times {{10}^6}}}{3} = 1.43 \times {10^6}$ «≈ 1.4 × 10⁶» «y»

ALTERNATIVE 2

fraction of Be = $\frac{1}{8}$ , 12.5%, or 0.125

$\frac{1}{8} = {{\text{e}}^{ - \lambda }}(4.3 \times {10^6})$ leading to λ = 4.836 × 10^–7 «y»^–1

$\frac{{\ln 2}}{\lambda }$ = 1.43 × 10⁶ «y»

Must see at least one extra sig fig in final answer.

[3 marks]

(b.iii)

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 10⁶ years.

[1]

Markscheme

1.9 × 10¹¹

[1 mark]