First slide

Radio activity

Question

There are two radioactive substance A & 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 ‘h’ is

Moderate

A

4
B

2
C

1
D

5

Solution

Let $λ_{A} = λ ∴ λ_{B} = 2 λ .$
If is total number of nuclei in A & B at t = 0, times initial rate of distntegration of $A = λ N_{o},$
and initial rate of disintegration of $B = 2 λ N_{o}$
$A s λ_{B} = 2 λ_{A} \Rightarrow T_{B} = \frac{T_{A}}{2}$
After one half life of A ${(- \frac{d N}{d t})}_{A} = \frac{λ N_{o}}{2}$
Equivalently, after two half lives of B ${(- \frac{d N}{d t})}_{B} = \frac{2 λ N_{o}}{4} = \frac{λ N_{o}}{2}$
$∴ {(- \frac{d N}{d t})}_{A} = {(- \frac{d N}{d t})}_{B}$
$n = 1, i . e$ After one half life of A

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