State what the decay constant of a radioactive isotope means.
Show that the decay constant $\lambda$ and the half-life $t_{\frac{1}{2}}$ of an isotope are related by the expression $\lambda t_{\frac{1}{2}} = 0.693$.
To determine 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 measured count rate is 538 per minute. After 8.0 hours, the measured count rate is 228 per minute. Use these data to estimate the half-life of the isotope.
The accepted value of the half-life of the isotope in (b) is 5.8 hours. The difference between this half-life and the value found in (b) cannot be accounted for by faulty equipment. Suggest two possible reasons for this difference.