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A radioactive material of half-life T wa...

A radioactive material of half-life T was kept in a nuclear reactor at two different instants. The quantity kept second time was twice of the kept first time. If now their present activities are `A_1` and `A_2` respectively, then their age difference equals

A

`(T)/(1n2)1n(2A_1)/(A_2)`

B

`T1n(A_1)/(A_2)`

C

`(T)/(1n2)1n(A_2)/(2A_1)`

D

`T1n(A_2)/(2A_1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Activity `Aprop` Number of atoms`
`A_1=A_0e^(-lambdat_1)`
`:.` `t_1=1/lambda1n((A_0)/(A_1))=(T)/(1n2)1n(A_0)/(A_1)`
`A_2=2A_0e^(-lambda_(t_2))`
`t_2=(T)/(1n2)1n((2A_0)/(A_2))`
`t_1-t_2=(T)/(1n2)(A_0/A_1xx(A_2)/(2A_0))`
`=(T)/(1n2)1n((A_2)/(2A_1))`
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