The decay constant of radio isotope is `lambda`. If `A_(1) and A_(2)` are its activities at times `t_(1) and t_(2)` respectively, the number of nuclei which have decayed during the time `(t_(1)-t_(2))`

Options

A. `A_(1)t_(1)-A_(2)t_(2)`
B. `A_(1)-A_(2)`
C. `(A_(1)-A_(2))//lambda`
D. `lambda(A_(1)-A_(2))`

Answer

C

Explanation

Activity at time `t_(1), A_(1)=lambdaN_(1) or N_(1)A_(1)//lambda`
Activity at time `t_(2), A_(2)=lambdaN_(2) or N_(2)A_(2)//lambda`
Therefore, the number of nuclei decayed during time interval `(t_(1)-t_(2))` is
`N_(1)-N_(2)=(A_(1))/lambda-(A_(2))/lambda=((A_(1)-A_(2))/lambda)`