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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 A

Explanation:

Decay scheme is,

                 18102019770_tools.PNG

Given        NBNA=0.3=310

                 NBNA=30100

  So,    N0  =100+30=130 atoms

     By using  N=N0eλt

   We have , 100=130eλt

           113=eλtlog1.3=λt

    If T is half-life, then t=loge2T

                 log1.3=loge2T.t

                               t=T.log(1.3)loge2