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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