State the meaning of the decay constant of a radioactive isotope.
Show that the decay constant $\lambda$ and the half-life $t_{\frac{1}{2}}$ of an isotope are linked by $\lambda t_{\frac{1}{2}} = 0.693$.
To estimate the half-life of a radioactive isotope sample, a student measures the count rate close to the sample, as shown in Fig. 9.1. At the start, the count rate recorded is 538 per minute. After 8.0 hours, the measured count rate is 228 per minute. Use these data to estimate the isotope’s half-life. Give your answer in hours.
The accepted half-life for the isotope in part (b) is 5.8 hours. The gap between this half-life and the value found in part (b) cannot be accounted for by saying the equipment was faulty. Suggest two possible reasons for this gap.