First slide

Radio activity

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 n is

Moderate

A

1
B

2
C

4
D

all of these

Solution

let $λ_{A} = λ, λ_{B} = 2 λ$ . Initially the rate of disintergration of A is $λ N_{0}$ and that of B is $2 λ N_{0}$ . After one half life of A, rate of disintegration will become $λ N_{0} / 2$ ( half life of B = one half the half life of A). n=1

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