Answer
$N=8.5\times10^{19}\;nuclei$.
Work Step by Step
Calculate the activity using equation 30–3b.
$$|\frac{\Delta N}{\Delta t}|=\lambda N$$
Combine this with equation 30–6, which relates the decay constant to the half-life.
$$|\frac{\Delta N}{\Delta t}|=\frac{ln 2}{T_{1/2}}N$$
Solve for the number of nuclei.
$$N=|\frac{\Delta N}{\Delta t}|\frac{T_{1/2}}{ln 2}$$
The half-life for U-238 is found in Appendix B.
$$N=(420\;decays/s)\frac{(4.468\times10^9y)(3.156\times10^7s/y)}{ln 2}$$
$$N=8.5\times10^{19}\;nuclei$$