d
\({{\text{X}}_{{\text{1 }}}}\)  માટે  \({{\text{N}}_{\text{1}}} = {{\text{N}}_{\text{0}}}{{\text{e}}^{{\text{ - 10}}{\lambda _{\text{0}}}t}}\),

\({{\text{X}}_{\text{2}}}\)  માટે \({{\text{N}}_{\text{2}}} = {N_0}{e^{ - {\lambda _0}t}}\) 

આપેલ \(\frac{{N_1}}{{N_2}} = \frac{{1}}{{e}}\)

\(\Rightarrow\) \(\frac{{{{\text{N}}_{\text{0}}}{{\text{e}}^{{\text{ - 10}}{\lambda _{\text{0}}}t}}}}{{{N_0}{e^{ - {\lambda _0}t}}}}\) \(= \frac{{1}}{{e}}\)

\(\frac{1}{{{e^{a{\lambda _0}t}}}} = \frac{1}{e}\,\,\,\,\, \Rightarrow \,\,\,\,9{\lambda _0}t = 1\,\)

\(\therefore\) \(t = \frac{1}{{9{\lambda _0}}}\)