Answer
$N = 5.3 \times 10^{22} $ nuclei
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,
$N = \frac{R}{\lambda} = \frac{R}{ln2/T_{1/2}} = \frac{R (T_{1/2} )}{ln 2}$
Where
$R = 6000 Ci \times (3.7 \times 10^{10} s^{-1} Ci^{-1})$
$R = 2.22 \times 10^{14} s^{-1}$
and $ T_{1/2} = 5.27 y \times (3.16 \times 10^{7} s/y)$
$ T_{1/2} = 1.67 \times 10^8 s$
Substitute all values that solves for N
$N = \frac{(2.22 \times 10^{14} s^{-1})(1.67 \times 10^8 )}{0.693}$
$N = 5.3 \times 10^{22} $ nuclei
