If the half-life of a radioactive nuclide is 16 hours, what fraction of original sample will remain undecayed after 48 hours?

$\frac{1}{8}$

The correct answer is Option (3) → $\frac{1}{8}$

Given:

Half-life, $t_{1/2} = 16\ \text{hours}$

Total time, $t = 48\ \text{hours}$

Number of half-lives elapsed:

$ n = \frac{t}{t_{1/2}} = \frac{48}{16} = 3 $

Fraction of undecayed sample:

$ \left(\frac{1}{2}\right)^n = \left(\frac{1}{2}\right)^3 = \frac{1}{8} $

Hence, the fraction of original sample remaining undecayed after 48 hours is

$\frac{1}{8}$