Question

A sample of radioactive material has mass $m$, decay constant $\lambda$ and molecular weight $M$. The initial activity of the sample is ___
[Take : Avogadro constant =$N_A$ ]

• A. $\lambda m$
• B. $\frac{\lambda m}{M}$
• C. $\frac{\lambda m{N}_A}{M}$
• D. $m{N}_A{e}^{\lambda }$

Answer 1

The correct option is C $\frac{\lambda m{N}_A}{M}$

Activity of a material is, $A=\lambda N$

Where,
$\lambda =\text{Disintegration constant}N=\text{Total number of atoms}$

Here, $N=\left(\frac{m}{M}\right)N_A$

$\therefore A=\frac{\lambda m{N}_A}{M}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.