c
(c) 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 \( = 1 - \frac{N}{{{N_0}}} = 1 - \frac{1}{e} = \frac{{e - 1}}{e}\)