Question

Radioactive material '$A$' has decay constant '$8\lambda$' and material '$B$' has decay constant '$\lambda$'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be $e$?

• A. $\frac{1}{9\lambda }$
• B. $\frac{1}{\lambda }$
• C. $\frac{1}{7\lambda }$
• D. $\frac{1}{8\lambda }$

Answer 1

The correct option is C $\frac{1}{7\lambda }$

$N_A=N_{A_o}{e}^{(-8\lambda )t}$

$N_B=N_{B_o}{e}^{-\lambda t}$

$N_{A_o}=N_{B_0}$

$\Rightarrow \frac{N_B}{N_A}=e$

$\Rightarrow \frac{e^{-\lambda t}}{e^{-8\lambda t}}=e^1$

$\Rightarrow e^{7\lambda t}=e^1$

$7\lambda t=1$

$t=\frac{1}{7\lambda }$