Answer
(a) $0.115\ h^{-1}$
(b) $1.7\times 10^9$ nuclei
Work Step by Step
(a) We can find the decay constant as
$\lambda=\frac{\ln 2}{T_{\frac{1}{2}}}$
$\lambda=\frac{\ln 2}{6.05h}$
$\lambda=0.115\ h^{-1}$
(b) We can find the required number of nuclei as follows:
$N=\frac{R}{\lambda}$
We plug in the known values to obtain:
$N=\frac{1.50\times 10^{-6}}{0.1146h^{-1}}(\frac{3600}{h})(\frac{3.7\times 10^{-10}s^{-1}}{1})=1.7\times 10^9$ nuclei.
