c
\(N = {N_0}{\left( {\frac{1}{2}} \right)^{t/{T_{1/2}}}}\)

\(\Rightarrow\) \(t = \frac{{{T_{1/2}}{{\log }_e}\left( {\frac{{{N_0}}}{N}} \right)}}{{{{\log }_e}(2)}}\)

\(\Rightarrow\) \(t \propto {\log _e}\frac{{{N_0}}}{N}\)

\(\Rightarrow\) \(\frac{{{t_1}}}{{{t_2}}} = \frac{{{{\left( {{{\log }_e}\frac{{{N_0}}}{N}} \right)}_1}}}{{{{\left( {{{\log }_e}\frac{{{N_0}}}{N}} \right)}_2}}}\) \(\frac{6}{{10}} = \frac{{{{\log }_e}(8/1)}}{{{{\log }_e}({N_0}/N)}}\)

\(\Rightarrow\) \({\log _e}\frac{{{N_0}}}{N} = \frac{{10}}{6}{\log _e}(8) = {\log _e}32\)

\(\Rightarrow\) \(\frac{{{N_0}}}{N} = 32\)

અવિભંજીત ભાગ \( = 1 - \frac{1}{{32}} = \frac{{31}}{{32}}\).