The activity of a sample of radioactive material is A at time T and A/3 at time 2T. Then mean life of the sample is
A=A0e−λT and A3=A0e−λ.2T
∴AA/3=A0e−λTA0e−2λT ⇒ 3=eλT⇒λT=ln3⇒tm=1λ=Tln3