Question

There are two radioactive substances A and B. Decay constant of B is two times that of A. Initially, both have equal number of nuclei. After 'n' half-lives of A, rates of disintegration of both are equal. The value of ${}^{\prime }n{}^{\prime }$ is

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

Answer 1

The correct option is A $1$

Let

${\eta }_x=\eta$ and ${\eta }_y=2\eta$

λy=2λ

Initially rate of disintegration of X s $\eta N_0$ and that of Y is $2\eta N_0$2λN0.

After one half life of X , rate of disintegration of X will becomes $\eta N_0/2$and that of Y would also be $\eta N_0/2$λN02 ( half - life of B=$\frac{1}{2}$12half life of A )

So after one half of A or two half lives of B

$(-\frac{dN}{dt}{)}_A=(-\frac{dN}{dt}{)}_B$

So,
(−dNdt)A=(−dNdt)B

$n=1$