There are two radioactive substances and . Decay constant of is two times that of . Initially, both have an equal number of nuclei. After n half-lives of , the rate of disintegration of both is equal. The value of is
Step 1: Given data:
Let decay constant of A and B are respectively.
If No is the number of atoms in A and B at t=0, then
Initial rate of disintegration of
Initial rate of disintegration of
Step 2: Calculation
Since
So
After one-half life of A
Similarly after two-half lives of B
From equations (1) and (2)
Hence the value of n=1
This implies that after one-half life of A, the rate of disintegration of both will be equal
So the correct option is (C).