Question

Decay constants of two radio-active samples $A$ and $B$ are $15x$ and $3x$ respectively. They have equal number of initial nuclei. The ratio of the number of nuclei left in $A$ and $B$ after a time $\frac {1}{6x}$ is .

• A. $e$
• B. $e^{2}$
• C. $e^{-1}$
• D. $e^{-2}$

Answer 1

Answer: (D)

$N_{1}=N_{01} e^{-\lambda_{1} t}=N_{0} e^{-15 x \times \frac{1}{6 x}}=N_{0} e^{-5 / 2}$
and $ N_{2}=N_{02} e^{-\lambda_{2} t}=N_{0} e^{-3 x \times \frac{1}{6 x}}=N_{0} e^{-1 / 2} $
$\therefore \frac{N_{1}}{N_{2}}=e^{-2}$