A radioactive nucleus A with a half-life T , decays into a nucleus B . At t = 0 , there is no nucleus B . At some time t , the ratio of the number of B to that of A is 0 . 3 . Then, t is given by: Consider log e x = log x

Step-by-step solution

Let N A and N B be the number of molecules of A and B after time t . Also, after time t , N B N A = 0.3 (given). Also, let N 0 be the total number of nucleus initial After time t , N A + N B = N 0 N A + 0.3 N A = N 0 ∴     N A = N 0 1.3 Also, the rate of disintegration of A N A = N 0 e − λ t ⇒ N 0 1.3 = N 0 e − λ t ;   1 1.3 = e − λ t       o r     log ( 1.3 ) = λ t t = l o g ( 1 .3 ) λ ∴ t = T l o g ( 1 .3