| Date | May 2015 | Marks available | 2 | Reference code | 15M.3.SL.TZ1.7 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate | Question number | 7 | Adapted from | N/A |
Question
This question is about radioactive decay.
A nucleus of magnesium-23 decays forming a nucleus of sodium-23 with the emission of an electron neutrino and a β+ particle.
Outline why the existence of neutrinos was hypothesized to account for the energy spectrum of beta decay.
The decay constant for magnesium-23 is 0.061 s−1. Calculate the time taken for the number of magnesium-23 nuclei to fall to 12.5% of its initial value.
Markscheme
spectrum of beta decay is continuous;
with a maximum value of energy;
the resulting energy difference between energy of any β(+) and maximum β(+) energy is accounted for by the energy of the neutrino / reference to energy difference between parent energy level and excited energy level of daughter;
\({{\text{T}}_{\frac{1}{2}}} = \frac{{{\text{In}}2}}{{0.061}} = 11.4\left( {\text{s}} \right)\);
\(\left( {N = \frac{1}{8}{N_0}{\text{ so}}} \right)t = \left( {3{T_{\frac{1}{2}}} = } \right)34\left( {\text{s}} \right)\)
or
\(t = - \frac{{{\text{In}}0.125}}{{0.061}}\);
t=34(s);
