Question

Two radioactive elements A and B (decay constant = $10\lambda$ and $\lambda$ respectively), initially have the same number of nuclie. The ratio of nuclei of A and B left will be 1/e after time :

• A. $(10\lambda {)}^{-1}$
• B. $(11\lambda {)}^{-1}$
• C. $11\times (10\lambda {)}^{-1}$
• D. $(9\lambda {)}^{-1}$

Answer 1

The correct option is D $(9\lambda {)}^{-1}$

$(N_o{)}_B$
$N=N_o{e}^{-\lambda t}$
$\frac{N_A}{N_B}=\frac{N_o{e}^{-{\lambda }_{A}t}}{N_o{e}^{-{\lambda }_{B}t}}=e^{(\lambda -10\lambda t)}$
= $e^{-9\lambda t}$
$\therefore e^{-9\lambda t}=1/e$
$9\lambda t=1$
$\therefore t=1/9\lambda$