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The rate at which a particular decay pro...

The rate at which a particular decay process occurs in a radio 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 radioactive 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 instant.
At `t=oo`, which of the following is incorrect ?

A

`N_1lambda_1+N_2lambda_2+N_3lambda_3`

B

`N_1lambda_1 - N_3lambda_2-N_4lambda_3`

C

`N_1lambda_1- N_2lambda_2-N_2lambda_3`

D

`N_1lambda_1 + N_2lambda_2 -N_2lambda_3`

Text Solution

Verified by Experts

The correct Answer is:
C
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The rate at which a particular decay process occurs in a radio 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 radioactive 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 instant. The number of nuclei of B will first increase then after a maximum value, it will decreases, if

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Knowledge Check

  • In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life ?

    A
    `63%`
    B
    `69.3%`
    C
    `37%`
    D
    `50%`

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