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Two radioactive substance A and B have d...

Two radioactive substance `A` and `B` have decay constants `5 lambda` and `lambda` respectively. At `t=0` they have the same number of nuclei. The ratio of number of nuclei of nuclei of `A` to those of `B` will be `(1/e)^(2)` after a time interval

A

`1/lambda`

B

`1/(2lambda)`

C

`1/(4lambda)`

D

`2/lambda`

Text Solution

Verified by Experts

The correct Answer is:
B
`(N_(1))/(N_(2)) = (N_(0)e^(-5lambdaxxt))/(N_(0)e^(-lambdat)) = 1/(e^(2))`
`e^(-4lambdat) = 1/(e^(2))`
`- 4 lambdat = - 2 rArr t = 1/(2lambda)`
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