Law of Radioactive Decay question from NEET 2000 (AIPMT)

Answer: (a)

1. $N = N_0 e^{-\lambda t}$; at $t = T_{1/2}$, $N = \frac{N_0}{2}$.
2. $e^{-\lambda T_{1/2}} = \frac{1}{2} \Rightarrow \lambda T_{1/2} = \ln 2$.
3. So the answer is (a) $T_{1/2} = \frac{\ln 2}{\lambda}$.