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Two radioactive materials X(1) and X(2) ...

Two radioactive materials `X_(1)` and `X_(2)` have decay constants `5 lambda` and `lambda` respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of `X_(1)` to that of `X_(2)` will be `1/e` after a time
(1.) λ
(2.) 1/ 2 λ
(3.) 1/ 4 λ
(4.) e/ λ

A

`(1)/(4lambda)`

B

`(e)/(lambda)`

C

`lambda`

D

`(1)/(2)lambda`

Text Solution

Verified by Experts

The correct Answer is:
A
`x_(1)=N_(0)e^(-5lambdat)`
`x_(2)=N_(0)e^(-lambdar)`
`(x_(1))/(x_(2))=e^(-5lambdat+lambdat)`
`(1)/(e)=e^(-4lambdat)`
`e^(-1)=e^(-4lambdat) rArr t=(1)/(4lambda)`
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