Two radioactive substances A and B have decay constants 5 and res… - Vidyadip

MCQ

Two radioactive substances $A$ and $B$ have decay constants $5\lambda $ and $\lambda $ respectively. At $t = 0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(\frac {1}{e})^2$ will be

A
$1/\lambda $
B
$1/4\lambda $
C
$2/\lambda $
✓
$1/2\lambda $

✓

Answer

Correct option: D.

$1/2\lambda $

d
$\frac{1}{{{e^2}}} = {e^{\lambda t - 5\lambda t}}$

$t\, = \,\frac{1}{{2\lambda }}$

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