A sample of radioactive element has rate `R_(1)` at time `t_(1) and R_(2)` at time `t_(2)` `(t_(2) gt t_(1))`. Which one is correct if `lambda` is rate constant and `tau` is average life ?

Options

A. `R_(1) gt R_(2)`
B. No. of atoms decayed in time `(t_(2)-t_(1)) = ((R_(2) - R_(1) ))/(lambda)`
C. No. of atoms decayed in time `(t_(2)-t_(1)) = (R_(1) - R_(2)) xx tau`
D. No. of atoms decayed in time `(t_(2)-t_(1)) = (R_(2) - R_(1))(lambda)`

Answer

D

Explanation

Rate decreases with time : `R_(1) = lambdaN_(1), " "R_(2) = lambdaN_(2) " "therefore R_(1) - R_(2) = lambda (N_(1) - N_(2))`
`therefore` No. of atoms decayed in time ` t_(2) - t_(1) = N_(1) - N_(2) = (R_(1) - R_(2))/(lambda) = (R_(1) - R_(2)). tau`