Question:

The decay constant of a radio isotope is λ. If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1 - t2)

A1 - A2

(A1 - A2)/λ

A1t1 - A2t2

λ(A1 - A2)

A1 = λN1 at time t1
A2 = λN2 at time t2
Therefore, number of nuclei decayed during time interval (t1 - t2) is N1 - N2 = (A1 - A2)/λ