Question

The radioactivity of a sample is $ {{A}_{1}} $ at time $ {{t}_{1}} $ and $ {{A}_{2}} $ at time $ {{t}_{2}} $ . If the mean life of the specimen is $T$, the number of atoms that have disintegrated in the time interval of $ ({{t}_{2}}-{{t}_{1}}) $ is

• A. $ ({{A}_{1}}-{{A}_{2}}) $
• B. $ \frac{({{A}_{1}}-{{A}_{2}})}{T} $
• C. $ ({{A}_{1}}-{{A}_{2}})T $
• D. $ ({{A}_{1}}{{t}_{1}}-{{A}_{2}}{{t}_{2}}) $

Answer 1

Answer: (C)

$A_{1}=N_{1} \lambda, \quad A_{2}=N_{2} \lambda$
Mean life, $T=\frac{1}{\lambda}$
$A_{1}-A_{2} =\left(N_{1}-N_{2}\right) \lambda $
$=\left(N_{1}-N_{2}\right) \frac{1}{T}$
So, number of atoms disintegrated in $\left(t_{2}-t_{1}\right) s$
$=\left(N_{1}-N_{2}\right)=\left(A_{1}-A_{2}\right) T$