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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 $X_1$ and $X_2$ have decay constant $5\lambda$ and $\lambda$ respectively intially they have the saame number of nuclei, then the ratio of the number of nuclei of $X_1$ to that $X_2$ will be $\frac{1}{e}$ after a time
  • A
    $4λ$
  • B
    $2λ$
  • C
    $\frac{1}{{2\lambda }}$
  • ✓
    $\;\frac{1}{{4\lambda }}$
✓

Answer

Correct option: D.
$\;\frac{1}{{4\lambda }}$
d
$X_{1}=N_{0} e^{-\lambda_{1} t}$ ;  $X_{2}=N_{0} e^{-\lambda_{2} t}$

$\frac{X_{1}}{X_{2}}=e^{-1}$ $=e^{\left(-\lambda_{1}+\lambda_{2}\right) t}$ ; ${e^{ - 1}} = {e^{ - (\lambda 1 - \lambda 2)t}}$

$\therefore t=\left|\frac{1}{\lambda_{1}-\lambda_{2}}\right|=\frac{1}{(5 \lambda-\lambda)}=\frac{1}{4 \lambda}$

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