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Consider radioactive decay of A to B wit...

Consider radioactive decay of `A` to `B` with which further decays either to `X` or `Y`, `lambda_(1), lambda_(2)` and `lambda_(3)` are decay constant for `A` to `B` decay, `B` to `X` decay and Bto `Y` decay respectively. At `t=0`, the number of nuclei of `A,B,X` and `Y` are `N_(0), N_(0)` zero and zero respectively.
`N_(1),N_(2),N_(3)` and `N_(4)` are the number of nuclei of `A,B,X` and `Y` at any instant `t`.

The number of nuclei of `B` will first increase and then after a maximum value, it decreases for

A

`lambda_(1) gt lambda_(2) + lambda_(3)`

B

`lambda_(1) = lambda_(2) = lambda_(3)`

C

`lambda_(1) = lambda_(2) + lambda_(3)`

D

For any values of `lambda_(1),lambda_(2)` and `lambda_(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
B will increase when `lambdaN_(1) gt (lambda_(2)+lambda_(3))N_(2)`
as initially `N_(1)=N_(2)=N_(0)implies lambda_(1) gt lambda_(2)+lambda_(3)`
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