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Date May 2014 Marks available 2 Reference code 14M.3.SL.TZ2.6
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term Show that Question number 6 Adapted from N/A

Question

This question is about radioactive decay.

Define the decay constant of a radioactive isotope.

[1]
a.

Show that the decay constant λ is related to the half-life T12 by the expression

λT12=ln2.

[2]
b.

Strontium-90 is a radioactive isotope with a half-life of 28 years. Calculate the time taken for 65% of the strontium-90 nuclei in a sample of the isotope to decay.

[3]
c.

Markscheme

probability of decay (of a nucleus) per unit time;

Accept AN with symbols defined.

a.

N=N0eλt and N=N02 when t=T12orN02=N0eλT12;

12=eλT12or2=eλT12;

(so ln2=λT12)

Answer given, award marks for correct working only.

b.

λ=ln228or0.025(y1];

0.35=e0.025t;

t=42 (years);

Award [3] for a bald correct answer.

Award [2 max] for an answer of 17 years (using 0.65 instead of 0.35).

or

0.35=[12]x where x=tT12;

tT12=1.5;

t=42 (years);

Award [3] for a bald correct answer.

Award [2 max] for an answer of 17 years (using 0.65 instead of 0.35).

c.

Examiners report

(a) was an easy mark.

a.

In (b) about half of the candidates could derive the relationship between half-life and decay constant, but many were completely lost.

b.

The half-life calculation in (c) was generally well done, but a common mistake was to use 0.65 as the fraction remaining.

c.

Syllabus sections

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics » 12.2 – Nuclear physics
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