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# There are two radioactive substances X & Y . If Decay constant of Y is 2 times of X . Initially both have equal number of nuclei . Then after n half lives of X rate of disintegration of both are equal . The value of n is

$(a)\;1\qquad(b)\;4\qquad(c)\;3\qquad(d)\;5$

Explanation :
Let
$\lambda x=\lambda \qquad$ & $\qquad\; \lambda y=2 \lambda$
Initially rate of disintegration of X is $\;\lambda N_{0}\;$ and that of Y is $\;2 \lambda N_{0}\;.$
After one half life of X , rate of disintegration of X will becomes $\;\large\frac{\lambda N_{0}}{2}\;$ and that of Y would also be $\;\large\frac{\lambda N_{0}}{2}\;$ ( half - life of B=$\large\frac{1}{2}\;$ half life of A )
So after one half of A or two half lives of B
$(-\large\frac{dN}{dt})_{A}=(-\large\frac{dN}{dt})_{B}$
$n=1$