Question

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))`

Answer 1

Correct Answer - 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`