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Questions  

A radioactive nucleus A with a half life  T decays into a nucleus  B. At t=0 , there is no nucleus  of  B. At some time t , the ratio of the number of nuclei of  B to that of A is 0.3 then,  t is given by

a
Tloge1.3
b
T2loge2loge1.3
c
Tloge1.3loge2
d
Tloge1.3

detailed solution

Correct option is C

Number of Nuclei of  B = Number of decayed nuclei of ANB=No−Noe−λt Number of nuclei of A is NA=Noe−λt⇒NBNA=N0−N0e−λtN0⋅e−λt⇒0.3=eλt−1⇒eλt=1.3⇒λt=ln⁡1.3⇒t=1λln⁡1.3⇒t=Tln⁡2ln⁡1.3

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