Answer
33.8 mg.
Work Step by Step
Calculate the number of nuclei from the activity.
$$Activity=\lambda N=\frac{ln 2}{T_{1/2}}N=4.20\times10^2 nuclei/s$$
The half-life for U-238 is found in Appendix B.
$$N=\frac{(4.468\times 10^9 y)(3.156\times10^7s/y)( 4.20\times10^2 nuclei/s)} {ln 2} $$
$$=8.544\times10^{19}\;nuclei$$
Calculate the mass from the number of nuclei, and the atomic weight.
$$m=\frac{8.544\times10^{19}\;nuclei }{6.02\times10^{23}nuclei/mol}(238.05g/mol)=3.38\times10^{-2}g$$
