Fraction remains after n half lives N0N=(21)n=(21)t/T Given N=eN0⇒eN0N0=(21)5/T or e1=(21)5/T Taking log on both sides, we get log1−loge−1⇒T= T5log21= T5(−log2)=5loge2 Now, let t′ be the time after which activity reduces to half ⇒(21)⇒t′=(21)t′/5loge2=5loge2