A) 32 days
B) 8 days
C) 64 days
D) 28 days
Correct Answer: B
Solution :
From Rutherford-Soddy law \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] where \[n\] is number of half-lives. Given, \[\frac{N}{{{N}_{0}}}=\frac{25}{100}=\frac{1}{4}\] \[\therefore \] \[\frac{1}{4}={{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[\frac{1}{{{2}^{2}}}=\frac{1}{{{2}^{n}}}\] \[\Rightarrow \] \[n=2\] Also, \[\text{n =}\frac{\text{elapsed}\,\text{time}}{\text{half}-\text{life}}\] \[\Rightarrow \] \[2=\frac{16}{{{T}_{1/2}}}\] \[\Rightarrow \] \[{{T}_{1/2}}=8\,days\]
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