A radioactive sample contains two different types of radioactive nuclei A-with half-life 5 . 0 days and B-with half-life 30 . 0 days initially the decay rate of the A-type nuclei is 64 time that of B type of nuclei. Their decay rates will be equal when time is 9 n days Find the value of n

Question

A radioactive sample contains two different types of radioactive nuclei A-with half-life 5 . 0 days and B-with half-life 30 . 0 days initially the decay rate of the A-type nuclei is 64 time that of B type of nuclei. Their decay rates will be equal when time is 9 n days Find the value of n,

MARKS App · Accepted Answer

λ A = ln 2 5 d a y - 1 a n d λ B = ln 2 30 d a y - 1 G i v e n d B O A d t = 64 d N O S d t ∴ λ A N O A = 64 λ B N O B A t t i m e t , d N A d t = d N B d t ∴ λ A N A = λ B N B D i v i d i n g e q u a t i o n 1 a n d 2 N O A N A = 64 N O B N B B u t N A = N O A e - λ A t a n d N B = N O B e - λ B t ∴ e q u a t i o n 3 b e c o m e s e λ A t = 64 e λ B t ∴ e λ A - λ B t = 64 ∴ λ A - λ B t = l n 64 ∴ t = ln 64 ln 2 5 - ln 2 30 = 36 d a y s

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