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Date May 2013 Marks available 1 Reference code 13M.3.SL.TZ1.6
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Define Question number 6 Adapted from N/A

Question

This question is about radioactive decay.

Sodium-22 undergoes β+ decay.

Identify the missing entries in the following nuclear reaction.

\[{}_{11}^{22}{\rm{Na}} \to {}_ \ldots ^{22}{\rm{Ne}} + {}_ \ldots ^0e + {}_0^0 \ldots \]

 

[3]
a.

Define half-life.

[1]
b.

Sodium-22 has a decay constant of 0.27 yr–1.

(i) Calculate, in years, the half-life of sodium-22.

(ii) A sample of sodium-22 has initially 5.0 × 1023 atoms. Calculate the number of sodium-22 atoms remaining in the sample after 5.0 years.

[4]
c.

Markscheme

\({}_{11}^{22}{\rm{Na}} \to {}_{10}^{22}{\rm{Ne}} + {}_{ + 1}^0e + {}_0^0v\)
\({}_{10}^{22}{\rm{Ne}}\);
\({}_{ + 1}^0e\) (accept \({}_ + ^0e\))
\({}_0^0v\); (award [0] for \({}_0^0\bar v\))

 

a.

time taken for half/50% of the nuclei to decay / activity to drop by half/50%;

b.

(i) \({T_{\frac{1}{2}}} = \frac{{\ln 2}}{\lambda }\);
\(\frac{{0.693}}{{0.27{\rm{y}}{{\rm{r}}^{ - 1}}}}\)=2.6 (years);
Award [2] for a bald correct answer.

(ii) N=5.0 x 1023 x e-0.27x5.0;
N=1.3 x 1023;
Award [2] for a bald correct answer.

c.

Examiners report

 This question was well done in general.

a.

Many candidates referred to mass halving rather than activity.

b.

 

c.

Syllabus sections

Core » Topic 7: Atomic, nuclear and particle physics » 7.1 – Discrete energy and radioactivity
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