Answer
See answers.
Work Step by Step
a. Calculate the number of nuclei, N. We are given the mass of the sample, and the atomic mass.
$$N=\frac{1.0g}{130.91g/mol}(6.02\times 10^{23}nuclei/mol)=4.599\times10^{21}nuclei$$
Find the activity from the half-life (8.02 days = 693000 s) and the number of nuclei. Use equations 30–3b and 30–5.
$$R=\lambda N=\frac{ln 2}{(6.93\times10^5 s)}( 4.599\times10^{21})=4.6\times10^{15}decays/s$$
b. Calculate the number of nuclei, N. We are given the mass of the sample, and the atomic mass.
$$N=\frac{1.0g}{238.05g/mol}(6.02\times 10^{23}nuclei/mol)=2.529\times10^{21}nuclei$$
Find the activity from the half-life ($4.47\times10^9 y = 1.41\times10^{17} s$) and the number of nuclei. Use equations 30–3b and 30–5.
$$R=\lambda N=\frac{ln 2}{(1.41\times10^{17} s)}(2.529\times10^{21})=1.2\times10^{4}decays/s$$
