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13.Nuclei
medium
At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be
A
$\frac{1}{5 \lambda}$
B
$\frac{1}{11 \lambda}$
C
$\frac{1}{6 \lambda}$
D
$\frac{1}{9 \lambda}$
(IIT-2000) (NEET-2022)
Solution
(d) ${N_1} = {N_0}{e^{ – 10\lambda t}}$ and ${N_2} = {N_0}{e^{ – \lambda t}}$$ $
$\Rightarrow \frac{{{N_1}}}{{{N_2}}} = \frac{1}{e} = {e^{ – 1}} = {e^{( – 10\lambda + \lambda )t}} = {e^{ – 9\lambda t}} $
$\Rightarrow t = \frac{1}{{9\lambda }}$.
Standard 12
Physics
