Question

Element $X$ is radioactive and decays via $\alpha$ decay with a half-life of $4$ days. Determine $N$ if $12.5$% of an original sample of element $X$ remains after $N$ days.

• A. $N=22$ days
• B. $N=12$ days
• C. $N=24$ days
• D. $N=16$ days

Answer 1

The correct option is B $N=12$ days

Half life $=4$ days.

The decay constant, $\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{4}$

$t=\frac{2.303}{\lambda }log\frac{a}{a-x}$

$N=\frac{2.303\times 4}{0.693}log\frac{100}{12.5}$

$N=12$ days

Hence, option B is correct.