A) \[e\]
B) \[\frac{1}{e}\]
C) \[\frac{e-1}{e}\]
D) \[\frac{e}{e-1}\]
Correct Answer: C
Solution :
The relation for the ratio of disintegration and initial values of a radioactive element is \[\frac{N}{{{N}_{0}}}={{e}^{-\lambda T}}\] and average life \[(t)=\frac{1}{\lambda }.\] Hence, \[\frac{N}{{{N}_{0}}}={{e}^{-\lambda \cdot \frac{1}{\lambda }}}={{e}^{-1}}\] Thus disintegrated amount \[=1-\frac{N}{{{N}_{0}}}=1-{{e}^{-1}}=1-\frac{1}{e}=\frac{e-1}{e}\]
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