Question
Chemistry Question on Decay Rate
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, rate of disintegration of both are equal. The value of n is
A
4
B
2
C
1
D
5
Answer
1
Explanation
Solution
Let λA=λ∴λB=2λ If N0 is total number of atoms in A and B at t=0, then initial rate of disintegration of A=λN0, and initial rate of disintegration of B=2λN0 As λB=2λA(∵λ=T1/2ln2) ∴(T1/2)B=21(T1/2)A i.e., half-life of B is half the half-life of A. After one half-life of A (−dtdN)A=2λN0…(i) Equivalently, after two half lives of B (−dtdN)B=42λN0=2λN0…(ii) From (i) and (ii), we get (−dtdN)A=(−dtdN)B, After n=1, i.e., one half-life of A, the rate of disintegration of both will be equal.