Answer
13 decays/s.
Work Step by Step
The fraction of atoms that are K-40 is very small. Use the atomic weight of K-39 to find the total number of K atoms in the sample.
$$N_{K}=\frac{0.420g}{38.9637g/mol}(6.02\times10^{23}nuclei/mol)=6.49\times10^{21}$$
Now find the number of K-40 nuclei.
$$N_{K-40}=0.000117(6.49\times10^{21})=7.59\times10^{17}$$
Calculate the activity using equation 30–3b.
$$\frac{\Delta N}{\Delta t}=\lambda N=\frac{ln 2}{T_{1/2}}N$$
The half-life for K-40 is found in Appendix B.
$$|\frac{dN}{dt}|=\frac{ln 2}{(1.248\times 10^9y)(3.156\times10^7s/y)}( 7.59\times10^{17}\;nuclei)$$
$$=13\;decays/s$$