Question

A sample of radioactive material has mass '$m$', decay constant $\lambda$ and molecular mass '$M$'. If $N_A$ is Avogadro's number, the initial activity of the sample is:

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

Answer 1

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

We know that activity of any radioactive material is $\lambda N,$

where $N$ is number of undecayed nuclei at time $t$

and $\lambda$ is decay constant

we also know that $N=N_o{e}^{-\lambda t}$

where $N_o=$ number of undecayed nuclei at $t=0s$

$⟹$ initial activity $=\lambda N_o$

we know that

$N_o=\frac{m}{M}\times N_A$

where $m=$initial mass of radioactive sample,

$M=$molecular mass of sample,

and $N_A=$avogadro number

$⟹initial$ activity =$\lambda \frac{m{N}_A}{M}$