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  • A sample of radioactive material has mass , decay constant , molecular weight <i

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

Option: 1

\lambda \mathrm{m}


Option: 2

\frac{\lambda m}{M}


Option: 3

\frac{\lambda \mathrm{mN}_{\mathrm{A}}}{\mathrm{M}}


Option: 4

\mathrm{mN}_{\mathrm{A}} \mathrm{e}^\lambda


Answers (1)

best_answer

Activity = number of disintegration per unit time

            =\left|\frac{\mathrm{dN}}{\mathrm{dt}}\right|=\lambda \mathrm{N} \text {, where } \mathrm{N}=\text { the total number of nuclei. }

      \text { Also, } \mathrm{N}=\text { number of moles } \times \mathrm{N}_{\mathrm{A}}=\left(\frac{\mathrm{m}}{\mathrm{M}}\right) \mathrm{N}_{\mathrm{A}}

        \therefore \text { Activity }=\left(\frac{\lambda \mathrm{mN}_{\mathrm{A}}}{\mathrm{M}}\right)

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