a
\({{\text{(}}{{\text{T}}_{{\text{1/2}}}})_1} = 1620 = \frac{{0.693}}{{{\lambda _1}}},\,\,\,{({T_{1/2}})_2} = 810 = \frac{{0.693}}{{{\lambda _2}}}\,\,\,\)

\(\,{\lambda _1} = \frac{{0.693}}{{1620}}yr{s^{ - 1}},\,\,\,{\lambda _2} = \frac{{0.693}}{{1620}}y{s^{ - 1}}\frac{{0.693}}{{810}}y{s^{ - 1}}\,\,\,\)

તો \({\lambda _{{\text{Net}}}}{\text{ }} = {\lambda _{\text{1}}} + {\lambda _2}\,\,\, \)

\(\Rightarrow \,\,\,{\lambda _{{\text{Net}}}} = \frac{{{\text{0}}{\text{.693}}}}{{1620}} + \frac{{0.693}}{{810}}\)

\( \Rightarrow \,{T_{1/2}} = \frac{{0.693}}{{{\lambda _{net}}}}\,\, = \frac{{0.693}}{{0.693\left( {\frac{1}{{1620}} + \frac{1}{{810}}} \right)}}\)

\( = \frac{{1620 \times 810}}{{2430}} = \frac{{1620}}{3}year\)

આથી જયારે \(1/4\)  ભાગ બાકી રહ્યો તે દરમિયાન લાગતો  સમય વર્ષ

\(= 2 × t_{1/2} = 2 ×540 = 1080\) વર્ષ