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13.Nuclei
medium
Two radioactive materials $X_1$ and $X_2$ contain same number of nuclei. If $6\,\lambda {s^{ - 1}}$ and $4\,\lambda {s^{ - 1}}$ are the decay constants of $X_1$ and $X_2$ respectively the ratio of number of nuclei, undecayed of $X_1$ to that of $X_2$ will be $\left( {\frac{1}{e}} \right)$ after a time
A
$\frac{1}{{2\lambda }}\,\sec$
B
$\frac{1}{{10\lambda }}\,\sec$
C
$\frac{1}{{5\lambda }}\,\sec$
D
$\frac{1}{{\lambda }}\,\sec$
Solution
$\frac{\mathrm{N}_{\mathrm{x}_{1}}}{\mathrm{N}_{\mathrm{x}_{2}}}=\frac{\mathrm{N}_{0} \mathrm{e}^{-6 \lambda \mathrm{t}}}{\mathrm{N}_{\mathrm{e}} \mathrm{e}^{-4 \lambda \mathrm{t}}}=\frac{1}{\mathrm{e}}$
Standard 12
Physics
