Answer
See answers.
Work Step by Step
a. Calculate the decay constant using equation 30–6.
$$\lambda=\frac{ln 2}{T_{1/2}}=\frac{ln2}{(1.59\times10^5y)(3.156\times10^7s/y)}=1.38\times10^{-13}s^{-1}$$
b. The activity is the decay constant multiplied by the number of nuclei, equation 30-3b.
$$|\frac{\Delta N}{\Delta t}|=\lambda N$$
$$=(1.381\times10^{-13}s^{-1}) (4.50\times 10^{18}nuclei)$$
$$=6.216\times10^5 \frac{decay}{s}\left(\frac{60s}{1min}\right)$$
$$=3.73\times10^7 decays/min$$