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Question 18M.2.HL.TZ1.b.ii

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Date May 2018 Marks available [Maximum mark: 3] Reference code 18M.2.HL.TZ1.b.ii
Level HL Paper 2 Time zone TZ1
Command term Show that Question number b.ii Adapted from N/A
b.ii.
[Maximum mark: 3]
18M.2.HL.TZ1.b.ii

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

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.

After 4.3 × 106 years,

number of produced boron nuclei 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 = 1 8 , 12.5%, or 0.125

therefore 3 half lives have elapsed

t 1 2 = 4.3 × 10 6 3 = 1.43 × 10 6  «≈ 1.4 × 106» «y»

 

ALTERNATIVE 2

fraction of Be = 1 8 , 12.5%, or 0.125

1 8 = e − λ ( 4.3 × 10 6 ) leading to λ = 4.836 × 10–7 «y»–1

ln ⁡ 2 λ = 1.43 × 106 «y»

 

 

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

[3 marks]

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