Question

A sample of radioactive material has mass m , decay constant $\lambda$ molecular weight M and Avogadro constant $N_{A}$ The initial activity of the sample is

• A. $\lambda m$
• B. $\frac{\lambda m}{M}$
• C. $\frac{\lambda mN_{A}}{M}$
• D. $mN_{A}\lambda$

Answer 1

Answer: (C)

$\frac{\lambda mN_{A}}{M}$

Answer 2

: Activity = number of disintegrations per unit time

Activity $= \left| \frac{dN}{dt} \right| = \lambda N.$

Where N = the total number of nuclei

Also N= number of moles $\times N_{A} = \left( \frac{m}{M} \right)N_{A}$

$\therefore$Initial activity $= \frac{\lambda mN_{A}}{M}$