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

Answer

d

Explanation

Rate = `lambda xx` Number of atoms of element yet not decayed
`R_(1) = lambda xx N_(1)`
`R_(2) = lambda xx N_(2)`
Number of atoms decayed in time `(T_(2) - T_(1))`
`= (R_(2))/(lambda) - (R_(1))/(lambda) = ((R_(2) - R_(1)))/(lambda) = (T (R_(2) - R_(1)))/(0.693)`
`:.` Number of atoms decayed in time `(T_(2) - T_(1)) prop T (R_(2) - R_(1))`