Answer
86 nuclei/second are decaying in the sample.
Work Step by Step
The fraction of atoms that are C-14 is very small. Use the atomic weight of C-12 to find the total number of carbon atoms in the sample.
$$N_{C}=\frac{345g}{12g/mol}(6.02\times10^{23}nuclei/mol)=1.731\times10^{25}$$
Now find the number of C-14 nuclei.
$$N_{C-14}=\frac{1.3}{10^{12}}(1.731\times10^{25})=2.250\times10^{13}\;nuclei$$
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 carbon-14, 5730 years, is found in Appendix B.
$$|\frac{dN}{dt}|=\frac{ln 2}{(5730y)(3.156\times10^7s/y)}(2.250\times10^{13}\;nuclei)=86\;nuclei/s$$
