A) \[\text{3}{{\text{N}}_{\text{0}}}\]
B) \[\frac{\text{9}{{\text{N}}_{\text{0}}}}{\text{2}}\]
C) \[\frac{\text{5}{{\text{N}}_{\text{0}}}}{\text{2}}\]
D) \[\text{2}{{\text{N}}_{\text{0}}}\]
Correct Answer: B
Solution :
Initially \[P\to 4{{N}_{0}}\] \[Q\to {{N}_{0}}\] Half life\[{{T}_{p}}\to 1\,\min \] \[{{T}_{Q}}\to 2\,\min \] Let after time t number of nuclei of P and Q are equal ie, \[\frac{4{{N}_{0}}}{{{2}^{t/1}}}=\frac{{{N}_{0}}}{{{2}^{t/2}}}\] \[4={{2}^{t/2}}\] \[{{2}^{2}}={{2}^{t/2}}\] \[\frac{t}{2}=2\] \[t=4\,\min \] Disactive nucleus or Nuclei of R \[=\left( 4{{N}_{0}}-\frac{4{{N}_{0}}}{{{2}^{4}}} \right)+\left( {{N}_{0}}-\frac{{{N}_{0}}}{{{2}^{2}}} \right)\] \[=4{{N}_{0}}-\frac{{{N}_{0}}}{4}+{{N}_{0}}-\frac{{{N}_{0}}}{4}\] \[=5{{N}_{0}}-\frac{{{N}_{0}}}{2}\] \[=\frac{9}{2}{{N}_{0}}\]
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