Answer
$N = 4.96 \times 10^9$
Work Step by Step
The equation of rate of decay, $R = \lambda N$ and $\lambda = \frac{ln2}{T_{1/2}}$
Rearrange the equation to solve for number of nuclei, N,
$N = \frac{R}{\lambda} = \frac{R}{ln2/T_{1/2}} = \frac{R (T_{1/2} )}{ln 2}$
From the question,
$R = 8.60 \times 10^{-6} Ci \times (3.7 \times 10^{10} s^{-1} Ci^{-1})$
$R =3.18 \times 10^{5} s^{-1}$
and $ T_{1/2} = 3.0 h \times (3.6 \times 10^{3} s/h)$
$ T_{1/2} = 1.08 \times 10^{4} s$
Now solve for N
$N =\frac{(3.18 \times 10^{5} s^{-1}){(1.08 \times 10^{4} s} )}{0.693}$
$N = 4.96 \times 10^9$
