Explanation:
From the question,
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,N = \frac{{{N_0}}}{{100}}\)
and \({\mkern 1mu} \,\,\,\,\,\,{T_{1/2}} = T\,yr\)
So, \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\lambda = \frac{{0.693}}{T}\)
\(\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,t = \frac{{2.303}}{\lambda }\log \left[ {\frac{{{N_0}}}{N}} \right]\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2.303\;T}}{{0.693}}\log 100\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6.65\;T{\text{ }}\)