A) \[3{{N}_{0}}\]
B) \[\frac{9{{N}_{0}}}{2}\]
C) \[\frac{5{{N}_{0}}}{2}\]
D) \[2{{N}_{0}}\]
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 i.e., \[\frac{4{{N}_{0}}}{{{2}^{t/1}}}=\frac{{{N}_{0}}}{{{2}^{t/2}}}\] |
| \[4={{2}^{t/2}}\] |
| \[{{2}^{2}}={{2}^{t/2}}\] |
| \[\frac{t}{2}=2\] |
| \[t=4\,\min \] |
| 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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