A) 5
B) 20
C) 15
D) 30
E) 25
Correct Answer: A
Solution :
From Rutherford-Soddy law \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[n=\frac{t}{T}\] \[\therefore \] \[{{10}^{6}}=1.414\times {{10}^{6}}{{\left( \frac{1}{2} \right)}^{t/T}}\] \[\Rightarrow \] \[\frac{1000}{1414}={{\left( \frac{1}{2} \right)}^{t/T}}\] \[\Rightarrow \] \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{10}{12} \right)}^{2}}\] (Approximately) \[\Rightarrow \] \[n=2\] \[\Rightarrow \] \[n=\frac{t}{T}=2\] \[\Rightarrow \] \[T=\frac{10}{2}=5\,\min \]
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