A half-life of a radioactive nuclide is $100$ hours. The fraction of original activity that will remain after $150$ hours would be:

1. A
   $\frac{2}{3}$
2. B
   $\frac{2}{3\sqrt{2}}$
3. C
   $\frac{1}{2}$
4. D
   $\frac{1}{2\sqrt{2}}$