Question

There are two radio active substance A and B . Decay constant of B is two times that of A . Initially bot have equal number of nuclei. After n half lives of A , rate of disintegration of both are equal . The value of n is

• A. 1
• B. 2
• C. 4
• D. all of these

Answer 1

The correct option is A 1

Let ${\lambda }_A=\lambda$

Let ${\lambda }_B=2\lambda$

If $N_o$ is the total number of atoms in A and B at $t=0$, then

$A=\lambda N_o$

$B=2\lambda N_o$

As ${\lambda }_B=2{\lambda }_{\alpha }$, $T_B=\frac{1}{2}{T}_{\alpha }$

$(-\frac{dN}{dt})A=\frac{\lambda N_o}{2}(-\frac{dN}{dt})B=2\frac{2\lambda N_o}{8}=\frac{\lambda N_o}{2}$

Clearly, $(-\frac{dN}{dt})A=(-\frac{dN}{dt})B$

After $n=1$, i.e., first life of A.