d
The number of radioactive nuclei \('N'\)  at any time \(t\) is given as

\(N(t)=N_{0} e^{-\lambda t}\)

where \(N_{0}\) is number of radioactive nuclei in the sample at some aribitrary time \(t=0\) and \(\lambda\) is the radioactive decay constant.

Given: \(\lambda_{A}=8 \lambda, \lambda_{B}=\lambda, N_{0 A}=N_{0 B}=N_{0}\)

\( \therefore \quad \frac{N_{B}}{N_{A}} =\frac{e^{-\lambda t}}{e^{-8 \lambda t}} \)

\(\frac{1}{e}=e^{-\lambda t} e^{8 \lambda t}=e^{7 \lambda t}\)

\(\Rightarrow-1=7 \lambda t\) or \(t=\frac{-1}{7 \lambda}\)