Answer
$1.29\times10^{5}\,years$
Work Step by Step
Rate= $\frac{382\,atoms}{60\,s}=6.37\,\frac{atoms}{s}$
$N=3.75\times10^{13}\,atoms$
$Rate=kN \implies k=\frac{Rate}{N}=\frac{6.37\,\frac{atoms}{s}}{3.75\times10^{13}\,atoms}=1.70\times10^{-13}\,s^{-1}$
$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{1.70\times10^{-13}\,s^{-1}}=4.08\times10^{12}\,s$
$=4.08\times10^{12}\,s\times\frac{1\,hr}{3600\,s}\times\frac{1\,day}{24\,hr}\times\frac{1\,year}{365.25\,day}=1.29\times10^{5}\,years$
