If the half-life of a radioactive nuclide is 16 hours, what fraction of original sample will remain undecayed after 48 hours?
Answer & explanation
Correct answer: option 3
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
$\frac{1}{8}$