1) A radioactive nucleus A with a half-life T, decays into a nucleus B. At t=0, there is no nucleus B. After sometimes t. the ratio of the number of B to that of A is 0.3. Then, t is given by A) t=Tlog1.3loge2 B) t=Tlog1.3 C) t=Tlog1.3 D) t=Tloge22log1.3 Answer: Option AExplanation:Decay scheme is, Given NBNA=0.3=310 ⇒NBNA=30100 So, N0 =100+30=130 atoms By using N=N0e−λt We have , 100=130e−λt ⇒113=e−λt⇒log1.3=λt If T is half-life, then t=loge2T ⇒log1.3=loge2T.t ∴t=T.log(1.3)loge2