Question

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

• A. $\frac{m}{\lambda }(1-e^{-\lambda t})$
  
• B. $\left(\frac{m{N}_A}{M\lambda }\right)e^{-\lambda t}$
  
• C. $\left(\frac{m{N}_A\lambda }{M}\right)e^{-\lambda t}$
  
• D. $\left(\frac{m{N}_A}{M}\right)e^{-\lambda t}$
  

Answer 1

The correct option is C $\left(\frac{m{N}_A\lambda }{M}\right)e^{-\lambda t}$


The activity of the substance is,
$\text{Activity}=\lambda N=\lambda N_0{e}^{-\lambda t}$

$=\lambda \left(\frac{m}{M}{N}_A\right)e^{-\lambda t}$

Where, $N_0=\frac{m}{M}{N}_A$, the total number of atoms in the sample present initially.

$\therefore \text{Activity}=\left(\frac{m{N}_A\lambda }{M}\right)e^{-\lambda t}$

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