Question

What is the half life period of a radioactive substance if 87.5$\%$ of any given amount of the substance disintegrates in 40 minutes?

• A. 160 min
• B. 10 min
• C. 20 min
• D. 13.58 min

Answer 1

The correct option is D 13.58 min

t = 40 min
$k=\frac{2.303}{t}log\frac{a}{a-x}k=\frac{2.303}{40}log\frac{a}{a-0.875a}=\frac{2.303}{40}log\frac{a}{0.125a}=\frac{2.303}{40}log8=0.051min{t}_{\frac{1}{2}}=\frac{0.693}{K}=\frac{0.693}{0.051}=13.58min$