Given, activity pf radioactive element at time t1, A1=A and at time t2,A2=A∕5 As we know that, activity at any time(A)=A0e−λt where A0 is activity at time t=0. ∴A=A0e−λt1 . . . (i) and A∕5=A0e−λt2 . . . (ii) ⇒5=e−λt1+λt2 Taking log on both sides, we get ln5=λ(t2−t1)lne ⇒ln5=λ(t2−t1)[∵lne=1] ⇒λ=ln5∕(t2−t1) ⇒ Also, average life, τ=