A) \[\sqrt{2}\]
B) \[\frac{1}{\sqrt{2}}\]
C) \[\frac{\sqrt{2}-1}{\sqrt{2}}\]
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
According to Rutherford-Soddy law the fraction left after n half-lives is given by \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Where n is the number of half-lives. \[n=\frac{time(t)}{half-life}=\frac{2}{4}=\frac{1}{2}\] So, \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{1/2}},\] \[\frac{N}{{{N}_{0}}}=\frac{1}{\sqrt{2}}\]
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