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The rate at which a particular decay pro...

The rate at which a particular decay process occurs in a radio active sample, is proportional to the number of radio active nuclei present. If N is the number of radio active nuclei present at some instant, the rate of change of N is `(dN)/(dt) = - lambdaN`.

Consider radioavtive decay of A to B which may further decay, either to X or to Y, `lambda_(1),lambda_(2)` and `lambda_(3)` are decay constants for A to B decay, B to X decay and B of Y decay respectively. If at `t = 0` number of nuclei of A, B, `X` and Y are `N_(0), N_(0)`, zero and zero respectively and `N_(1),N_(2),N_(3),N_(4)` are number of nuclei `A,B,X` and `Y` at any intant.
At `t = oo`, which of the following is incorrect ?

A

`N_(2) = 0`

B

`N_(3) = (N_(0)lambda_(2))/(lambda_(2) + lambda_(3))`

C

`N_(4) = (2N_(0)lambda_(3))/(lambda_(2) + lambda_(3))`

D

`N_(3) + N_(4) + N_(1) + N_(2) = 2N_(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
`N_(2)=0, N_(1)=0` as both will decay completely :
`N_(3)=(2N_(0) lambda_(2))/(lambda_(2)+N_(3))` therefore B is incorrect
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Radio Activity

Radio Activity

Show that the decay rate R of a sample of radionuclide is related to the number of radioactive nuclei N at the same instant by the expression R=lambdaN .