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

Options

A. `(R_(1) T_(1) - R_(2) T_(2))`
B. `(R_(1) - R_(2))`
C. `(R_(1) - R_(2)) T`
D. `(R_(1) - R_(2)) T`

Answer

D

Explanation

Radioactivity at `T_(1) , R_(1) = lambda N_(1)`
Radioactivity at `T_(2) , R_(2) = lambda N_(2)`
`therefore` Number of atoms decayed in time `(T_(1) - T_(2)) = (N_(1) - N_(2)) = ((R_(1) - R_(2)))/(lambda) = ((R_(1) + R_(2)))/(0.693) T prop (R_(1) - R_(2)) T`