Answer
$5.05\times10^{12}\,s$
Work Step by Step
If Original activity $N_{0}=100$,
Present activity $N=1$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{2.4\times10^{4}\,y}=2.8875\times10^{-5}\,y^{-1}$
$\ln(\frac{N_{0}}{N})=kt$ where $t$ is the time required.
$\implies \ln(\frac{100}{1})=4.605=(2.8875\times10^{-5}\,y^{-1})\times t$
Or $t= \frac{4.605}{2.8875\times10^{-5}\,y^{-1}}= 1.6\times10^{5}\,y$
$=1.6\times10^{5}\times3600\times24\times365\,s$
$=5.05\times10^{12}\,s$
