Nucleus A decays into B with a decay constant λ 1 and B further decays into C with a decay constant λ 2 . Initially, at t = 0 , the number of nuclei of A and B were 3 N 0 and N 0 respectively. If at t = t 0 number of nuclei of B becomes con

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Nucleus A decays into B with a decay constant λ 1 and B further decays into C with a decay constant λ 2 . Initially, at t = 0 , the number of nuclei of A and B were 3 N 0 and N 0 respectively. If at t = t 0 number of nuclei of B becomes constant and equal to 2 N 0 , then

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Correct answer: A. t 0 = 1 &#x3BB; 1 ln 3 &#x3BB; 1 2 &#x3BB; 2

N A = 3 N 0 e &#8211; &#955; 1 t d N A d t = - 3 &#955; 1 N 0 e - &#955; 1 t d N B d t = 3 &#955; 1 N 0 e - &#955; 1 t - &#955; 2 N B At t = t 0 , d N B d t = 0 &#8658; 3 &#955; 1 N 0 e - &#955; 1 t - &#955; 2 N B = 0 &#8658; 3 &#955; 1 N 0 e - &#955; 1 t = &#955; 2 2 N 0 e &#955; 1 t 0 = 3 &#955; 1 2 &#955; 2 &#8658; t 0 = 1 &#955; 1 ln 3 &#955; 1 2 &#955; 2

Nucleus A decays into B with a decay constant λ 1 and B further decays into C with a decay constant λ 2 . Initially, at t = 0 , the number of nuclei of A and B were 3 N 0 and N 0 respectively. If at t = t 0 number of nuclei of B becomes constant and equal to 2 N 0 , then

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