Two radioactive nuclei P and Q , in a given sample decay into a stable nucleous R . At time t=0 , number of P species are 4 N₀ and that of Q are N₀ . Half-life of P (for conversion to R ) is 1 min where as that of Q is 2 ~min . Initially th

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Two radioactive nuclei P and Q , in a given sample decay into a stable nucleous R . At time t=0 , number of P species are 4 N₀ and that of Q are N₀ . Half-life of P (for conversion to R ) is 1 min where as that of Q is 2 ~min . Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be

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Correct answer: B. 9 N₀ 2

Initially P 4 N₀ Q N₀ Half life T_p 1 ~min T_Q 2 Let after time t number of nuclei of P and Q are equalie, 4 N₀ 2^ t / 1 = N₀ 2^ t / 2 aligned 4 & =2^ t / 2 2^2 & =2^ t / 2 t 2 & =2 t & =4 ~min aligned Disactive nucleus or Nuclei of R aligned & = (4 N₀- 4 N₀ 2^4 )+ (N₀- N₀ 2^2 ) & =4 N₀- N₀ 4 +N₀- N₀ 4 & =5 N₀- N₀ 2 & = 9 2 N₀ aligned

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