Question

The decay constant of a radioactive sample is $\lambda$. The half-life and mean life of the sample are respectively given by:

• A. $\frac{1}{\lambda }$ and $\frac{{\log }_{e}2}{\lambda }$
• B. $\frac{{\log }_{e}2}{\lambda }$ and $\frac{1}{\lambda }$
• C. $\lambda {\log }_{e}2$ and $\frac{1}{\lambda }$
• D. $\frac{\lambda }{{\log }_{e}2}$ and $\frac{1}{\lambda }$

Answer 1

The correct option is B $\frac{{\log }_{e}2}{\lambda }$ and $\frac{1}{\lambda }$

The half life is given as

$t_{1/2}=\frac{{\log }_{e}2}{\lambda }=0.693/\lambda$

The mean life or average life can be given as follow:

Average life$=\frac{1}{\lambda }=1.44t_{1/2}$