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The radioactivity of a sample is R(1) at...

The radioactivity of a sample is `R_(1)` at a time `T_(1)` and `R_(2)` at time `T_(2)`. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time `(T_(2) -T_(1))` is proporational to

A

`(R_(1)T_(1) - R_(2)T_(2))`

B

`(R_(1)-R_(2))T`

C

`(R_(1) - R_(2))//T`

D

`(R_(1) - R_(2))(T_(1) - T_(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
`N_(1)=N_(0)e^(-lambdaT_(1)), N_(2)=N_(0)e^(-lambdaT_(2))`
`R_(1)=lambdaN_(1), R_(2)= lambdaN_(2)`
`(N_(1)-N_(2))=lambda/lambda (N_(1)-N_(2))=((R_(1)-R_(2)))/(lambda)`
`T=(log_(e)2)/(lambda), lambda=(log_(e)2)/(T)`
`(N_(1)-N_(2))=((R_(1)-R_(2))T)/((log_(e)2))`
`(N_(1)-N_(2)) prop (R_(1)-R_(2)) T`
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