Question

The decay constant of a radioactive sample is ${}^{\prime }\lambda {}^{\prime }$. The values of its half life and mean life will be respectively be

• A. $\frac{1}{\lambda }$, ${\log }_{e}2$
• B. $\frac{{\log }_{e}2}{\lambda },\frac{1}{\lambda }$
• C. $\frac{1}{\lambda },\frac{1}{{\lambda }^2}$
• D. $\lambda lo{g}_{e}2$, $\frac{1}{\lambda }$

Answer 1

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

Radioactive decay is a first-order reaction for which: $C_t=C_0{e}^{-\lambda t}$

For half life,

$C_t=\frac{C_0}{2}$

$⟹\frac{1}{2}=e^{-\lambda t}$

$⟹t=\frac{ln2}{\lambda }$

Average life $=\frac{{}_0^{\infty }\int C_{t}dt}{C_0}=\frac{1}{\lambda }$