A) e
B) \[\frac{1}{e}\]
C) \[\frac{e-1}{e}\]
D) \[\frac{e}{e-1}\]
Correct Answer: C
Solution :
By using \[N={{N}_{0}}{{e}^{-\lambda t}}\]and average life time \[t=\frac{1}{\lambda }\] So \[N={{N}_{0}}{{e}^{-\lambda \times 1/\lambda }}={{N}_{0}}{{e}^{-1}}\Rightarrow \frac{N}{{{N}_{0}}}={{e}^{-1}}=\frac{1}{e}\] Now disintegrated fraction \[=1-\frac{N}{{{N}_{0}}}=1-\frac{1}{e}=\frac{e-1}{e}\]
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