Answer
2.5 billion decays/second.
Work Step by Step
Calculate the activity using equation 30–3b.
$$\frac{\Delta N}{\Delta t}=-\lambda N$$
We are interested in the number of counts per second, which is a positive number. Combine this with equation 30–6, which relates the decay constant to the half-life.
$$\frac{\Delta N}{\Delta t}=\lambda N=\frac{ln 2}{T_{1/2}}N$$
The half-life for carbon-14, 5730 years, is found in Appendix B.
$$|\frac{dN}{dt}|=\frac{ln 2}{(5730y)(3.16\times10^7s/y)}(6.5\times10^{20}\;nuclei)=2.5\times10^9$$