Question

Four different radioactive elements are kept in separate containers. In the beginning the container $A$ has $200$ g-atom with half-life of 2 days, $B$ has $20$ g-atom with half-life of $20$ days, $C$ has $2$g-atom with half-life $200$ days and $D$ has $100$ g-atoms with half-life of $10$ days. In the beginning the maximum activity exhibited by the container is:

• A. $a$
• B. $b$
• C. $c$
• D. $d$

Answer 1

The correct option is A $a$

Initial maximum activity $R=\lambda N=\frac{\ln 2}{T_{1/2}}N$

where $T_{1/2}$ is the half-life of the substance and $N$ is the number of atoms present initially.

(A) : $R_A=\frac{\ln 2}{2}\times 200=100\ln 2$

(B) : $R_B=\frac{\ln 2}{20}\times 20=\ln 2$

(C) : $R_C=\frac{\ln 2}{200}\times 2=0.01\ln 2$

(D) : $R_D=\frac{\ln 2}{10}\times 100=10\ln 2$

Hence maximum activity is exhibited by container A.