Question

A sample of radioactive material $A$, that has an activity of $10mCi(1Ci=3.7\times {10}^{10}decays/s)$, has twice the number of nuclei as another sample of a different radioactive maternal B which has an activity of $20mCi$. The correct choices for half-life of $A$ and $B$ would then be respectively :

• A. 20 days and 5 days
• B. 10 days and 20 days
• C. 5 days and 10 days
• D. 10 days and 40 days

Answer 1

The correct option is A 20 days and 5 days

Activity $A=\lambda N$
For $A$ $10=\left(2N_0\right){\lambda }_A$
For $B$ $20=N_0{\lambda }_B$
$\therefore {\lambda }_B=4{\lambda }_A\Rightarrow (T_{1/2}{)}_A=4(T_{1/2}{)}_B$