# A sample of radioactive material a that has an activity of NMC has twice the number of nuclear as other sample of a different radioactive material be which has an activity of 20 MCI the correct choices for half life of a and b would be then respectively

Arun
25758 Points
2 years ago

-\frac{dN}{dt}= \lambda N

- wherein

Ratio of disintegration is propotional to number of nuclei

\lambda= disintegration constant

Activity A = \lambda N

For A , A = 2 No \lambda_{A} = 10

For B , A = No \lambda_{B} = 20

\frac{10}{20} = \frac{2 \lambda_{A}}{\lambda_{B}}

\lambda_{B} = 4 \lambda_{A}

t_{\frac{1}{2} }= \frac{ln 2 }{\lambda}

\frac{t_{\frac{1}{2}A }}{t_{\frac{1}{2}B }}= \frac{\lambda_{B}}{\lambda_{A}} = \frac{\lambda_{B}}{\frac{\lambda_{B}}{4}} = 4

t_{\frac{1}{2}A } = 4 t_{\frac{1}{2}B }

So option 20 days and 5 days satisfies this condition .