Half-Life and Mean Life

Problems from IIT JEE

Problem (IIT JEE 1989): The decay constant of a radioactive sample is $\lambda$. The half-life and mean-life of the sample are respectively given by

1. $1/\lambda$ and $(\ln 2)/\lambda$
2. $(\ln 2)/\lambda$ and $1/\lambda$
3. $\lambda(\ln 2)$ and $1/\lambda$
4. $\lambda/(\ln 2)$ and $1/\lambda$

Solution: The half life and average life of a radioactive sample with decay constant $\lambda$ are given by, $T_{1/2}=\ln(2)/\lambda=0.693/\lambda$ and $\tau=1/\lambda$.