Answer
See answers.
Work Step by Step
Use equations 30–5 and 30–3b to relate the activity and the half-life.
$$R=\lambda N=\frac{ln 2}{T_{1/2}}N$$
$$ T_{1/2}=\frac{ln 2}{R }N$$
Find the number of Gd atoms by using the sample mass and gadolinium’s atomic weight. Evaluate to find the half-life.
$$T_{1/2}=\frac{ln 2}{1\;decay/s}(1.5\times10^7 g)\frac{6.02\times10^{23}nuclei}{152g}\frac{1\;y}{3.156\times10^7 s}$$
$$=1.3\times10^{21}y$$
