The half-life of a radioactive nuclide is 100 hours. The fraction...

Given,

$T\dfrac{1}{2} = 100hours$

$t = 150hours$

As we know that the number of nuclide remain after $n$ half life is given by,

$N = \dfrac{{N}_{0}}{{2}^{n}}$

$∵ 100$ hours $= 1$ half life

$150$ hours$= \dfrac{1}{100} \times 150$

$= \dfrac{3}{2}$ half life

So, Fraction remain after $\dfrac{3}{2}$ half life

$\dfrac{N}{{N}_{0}} = {\left(\dfrac{1}{2}\right)}^{3 / 2} = \dfrac{1}{2\sqrt{2}}$