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 N 0 and that of Q are N 0 . Half-life of P (for conversion to R ) is 1

Question

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 N 0 ​ and that of Q are N 0 ​ . 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 beNEET 2011 (Mains)

TestHub · Accepted Answer

Initially P → 4 N 0 ​ Q → N 0 ​ Half life T p ​ → 1 min T Q ​ → 2 min Let after time t number of nuclei of P and Q are equalie, 2 t /1 4 N 0 ​ ​ = 2 t /2 N 0 ​ ​ 4 2 2 2 t ​ t ​ = 2 t /2 = 2 t /2 = 2 = 4 min ​ Disactive nucleus or Nuclei of R ​ = ( 4 N 0 ​ − 2 4 4 N 0 ​ ​ ) + ( N 0 ​ − 2 2 N 0 ​ ​ ) = 4 N 0 ​ − 4 N 0 ​ ​ + N 0 ​ − 4 N 0 ​ ​ = 5 N 0 ​ − 2 N 0 ​ ​ = 2 9 ​ N 0 ​ ​

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