Let N0 be initial number of nuclei at time t = 0 . The number of undecayed nuclei in time t is N = N0e−λt The number of nuclei decayed in time t is n = N0 - N = N0 - N0e−λt (i) The number of undecayed nuclei in next time t, N' = Ne−λt = (N0e−λt)e−λt = N0e−2λt (ii) Number of decayed nuclei in next time t, 0.75 n = N - N' = N0e−λt - N0e−2λt (iii) = N0e−λt(1−e−λt) Dividing Eq. (ii) by Eq. (i), we get 0.75 = e−λt ⇒