| Date | May 2015 | Marks available | 3 | Reference code | 15M.3.SL.TZ2.7 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Determine | Question number | 7 | Adapted from | N/A |
Question
This question is about radioactive decay.
Nuclide X has a half-life that is estimated to be in the thousands of years.
Outline how the half-life of X can be determined experimentally.
A pure sample of X has a mass of 1.8 kg. The half-life of X is 9000 years. Determine the mass of X remaining after 25000 years.
Markscheme
measurement of mass of sample / determination of molar mass;
determination of number of nuclei N;
measurement of activity A;
determination of decay constant from \(\lambda = \frac{A}{N}\);
half-life from \({T_{\frac{1}{2}}} = \frac{{1{\rm{n}}2}}{\lambda }\);
\(m = \left( {{m_0}{e^{ - \lambda t}} = } \right)1.8 \times {e^{ - 7.70 \times {{10}^{ - 5}} \times 25000}}\);
m=0.26 (kg);
or
\(\frac{{25000}}{{9000}} = 2.77\) half-lives;
fractional mass left = \({\left( {\frac{1}{2}} \right)^{2.77}} = 0.15\);
mass left=1.8×0.15=0.26 (kg);
Award [3] for a bald correct answer.
Examiners report
Most candidates were very uncertain about determining a very long half-life. Part marks were often obtained for stating how half-life was obtained from the decay constant, but determination of activity and number of sample atoms was not usually mentioned. Most candidates described how the half-life of a nuclide with a short half-life can be found.
In (b) surprisingly few candidates know the easy way to calculate fraction remaining. Find the number of half-lives passed (n). Fraction remaining = 0.5n. This works even when n is non-integer. Most obtained at least 1 mark for finding the decay constant or the number of half-lives. Quite a few candidates assumed a proportional relationship for the non-integer part of n.
