Question

At a certain time, a radioactive sample contains $2\times {10}^{20}\text{atoms}$ and its disintegration rate is $3\times {10}^{10}\text{atoms/sec}$. When $2\times {10}^{15}$ atoms are left to decay, its disintegration rate will be ($\text{atoms/sec})$

• A. $1\times {10}^5$
• B. $2\times {10}^5$
• C. $3\times {10}^5$
• D. $4\times {10}^5$

Answer 1

The correct option is C $3\times {10}^5$

We know that,

Disintegration rate$=R=\frac{dN}{dt}=-\lambda N$

$\Rightarrow R\propto N$

$\Rightarrow \frac{R_1}{R_2}=\frac{N_1}{N_2}$

$\Rightarrow \frac{3\times {10}^{10}}{R_2}=\frac{2\times {10}^{20}}{2\times {10}^{15}}$

$\therefore R_2=3\times {10}^5\text{atoms/sec}$

Hence, $\left(C\right)$ is the correct answer.