Question 42.34: Calculate the mass of a sample of (initially pure) ^40K that......

Combining Eqs. 42-20 and 42-21, we obtain

R=\frac{N_{40} \ln 2}{T_{1 / 2}}            (42-20)

N_{40}=\left(1.17 \times 10^{-4}\right) \frac{M_{ sam } N_{ A }}{M}       (42-21)

M_{\mathrm{sam}}=N \frac{M_{\mathrm{K}}}{M_{\mathrm{A}}}=\left(\frac{R T_{1 / 2}}{\ln 2}\right)\left(\frac{40 \mathrm{~g} / \mathrm{mol}}{6.02 \times 10^{23} / \mathrm{mol}}\right)

which gives 0.66 g for the mass of the sample once we plug in 1.7 \times 10^5 / s for the decay rate and 1.28 \times 10^9 y=4.04 \times 10^{16} s for the half-life.