A) \[\frac{1}{{{e}^{2}}}\]
B) \[\frac{1}{e}\]
C) e
D) \[{{e}^{2}}\]
Correct Answer: C
Solution :
Let the initial number of atoms at time t = 0 be \[{{N}_{0}}.\] Let N be the number of atoms at any instant t. Mean life \[\tau =\frac{1}{\lambda },\]where \[\lambda \] is disintegration constant. Given, \[t=\tau \] According to radioactive disintegration law, \[N={{N}_{0}}{{e}^{-\lambda t}}\] or \[N={{N}_{0}}{{e}^{-\lambda }}\times \frac{1}{\lambda }=\frac{{{N}_{0}}}{e}\] or \[\frac{{{N}_{0}}}{N}=e\]
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