Question

Two radioactive sources $A$ and $B$ initially contain an equal number of radioactive atoms. Source $A$ has the lift of $1hour$ and source $B$ has a half life of $2hours$, the end of $2hours$, the ratio of the rate of disintegration of $A$ to that of $B$ is:

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $1:4$

Answer 1

The correct option is C $1:1$

$\begin{array}{c}\text{Rate of disintegration}\left(\frac{dN}{dt}\right)=\lambda N\\ \text{Let, initially no. of atoms be N0.}\\ \text{After two hrs,}\\ N_A=\frac{N_0}{4}{N}_B=\frac{N_0}{2}\end{array}$

$\begin{array}{c}\text{Ratio of rate of disintegration}\\ {\lambda }_A{N}_A:{\lambda }_B{N}_B\\ \frac{\ln 2}{{\left(t_1/2\right)}_A}\frac{N_0}{4}:\frac{\ln 2}{{\left(t_{1/2}\right)}_B}\frac{N_0}{2}\\ \frac{1}{1}\frac{1}{4}:\frac{1}{2}\frac{1}{2}\text{=1:1}\end{array}$