Question

The radioactivity of a sample is x at time $t_1$ and is y at time $t_2$. If the mean life of the specimen is $\tau$, the number of atoms that have disintegrated in the time interval $(t_2 - t_1)$ is

• A. x - y
• B. $(x - y) / \tau$
• C. $(x - y) \tau$
• D. $x t_1 - y t_2$

Answer 1

The Correct Option is C

Activity $ \frac{dN}{dt} = - \lambda N$
$\therefore x = - \lambda N_{t_1}, y = - \lambda N_{t_2}$
$\Rightarrow N_{t_1} = - \frac{x}{\lambda} , N_{t_2} = - \frac{y}{\lambda}$
The number of atoms disintegrated in time interval
$\Rightarrow N_{t_2} - N_{t_1} = - \frac{y}{\lambda} - \big(-\frac{x}{\lambda}\big)$
$ = \frac{x - y}{\lambda} = (x - y) \tau$