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STD 12 - 13. Nuclei — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. Nuclei4 Marks
MCQ
Two radioactive materials $A$ and $B$ have decay constants $10\,\lambda $ and $\lambda $, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of $B$ will be $1/e$ after a time
  • A
    $\frac{1}{{11\lambda }}$
  • B
    $\frac{1}{{10\lambda }}$
  • ✓
    $\frac{1}{{9\lambda }}$
  • D
    $\frac{11}{{10\lambda }}$
✓

Answer

Correct option: C.
$\frac{1}{{9\lambda }}$
c
${{\text{N}}_1} = {{\text{N}}_0}{{\text{e}}^{ - 10\lambda t}}$ ;  $\mathrm{N}_{2}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}}$

$\frac{1}{e}=\frac{N_{1}}{N_{2}}=e^{-9 \lambda t}$

$\Rightarrow 9 \lambda t=1$

$\Rightarrow t=\frac{1}{9 \lambda}$

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