Question

A sample of radioactive material has mass m, decay constant $\lambda$ molecular weight M and Avogadro s constant $N_A$. The activity of the sample after time will be :

• A. $\frac{m{N}_A}{M}{e}^{-\lambda t}$
• B. $\frac{m{N}_A\lambda }{M}{e}^{-\lambda t}$
• C. $\frac{m{N}_A}{M\lambda }{e}^{-\lambda t}$
• D. None of these.

Answer 1

The correct option is B $\frac{m{N}_A\lambda }{M}{e}^{-\lambda t}$

$\begin{array}{c}\text{Given-}\text{mass of radioactive material}=m\\ \ast \text{Molecular weight}=M\\ \text{* Avogadro's constant = NA}\\ \text{Number of moles of radioactive can be given by}n=\frac{m}{M}\end{array}$

$\begin{array}{c}\text{So the the numbers of nuclei}\left(N_0\right)\\ N_0=N_A\cdot n=\frac{m}{M}\cdot N_A\\ \text{By Radioactive law of disintegration we have}\\ \text{activity}=N_0\lambda \cdot e^{-\lambda t}\text{at any time}=t\end{array}$

$\begin{array}{cc}\Rightarrow & \text{activity}=\frac{m}{M}\cdot N_A\cdot \lambda e^{-\lambda t}\\ & \text{Hece, option (b) is correct.}\end{array}$