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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

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a

Tloge1.3

b

T2loge2loge1.3

c

Tloge1.3loge2

d

Tloge1.3

answer is C.

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Detailed Solution

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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