Question

The decay constant of a radioactive sample is $\gamma$. Its half-life is $T_{1/2}$ and mean life is $T$.

• A. $T_{1/2}$ = $\frac{1}{\lambda }$, $T$ = $\frac{In2}{\lambda }$
• B. $T_{1/2}$ = $\frac{In2}{\lambda }$, $T$ = $\frac{1}{\lambda }$
• C. $T_{1/2}$ = $\lambda In2$, $T$ = $\frac{1}{\lambda }$
• D. $T_{1/2}$ = $\frac{\lambda }{In2}$, $T$ = $\frac{In2}{\lambda }$

Answer 1

The correct option is B $T_{1/2}$ = $\frac{In2}{\lambda }$, $T$ = $\frac{1}{\lambda }$

$\frac{-dN}{dt}=\lambda N$

$N=N_o{e}^{-\lambda t}$

for $t=T_{1/2}$ $\Rightarrow N=\frac{N_o}{2}$

$\frac{N_o}{2}=N_o{e}^{-\lambda T_{1/2}}$

$T_{1/2}=\frac{ln2}{\lambda }$