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