Question

What is the half - life of a radioactive substance if $75\%$ of any given amount of the substance disintegrates in $60$ minutes?

• A. $2$ Hours
• B. $30$ Minutes
• C. $45$ Minutes
• D. $20$ Minutes

Answer 1

Answer: (B)

$30$ Minutes

$k=\frac{2.303}{t}log\frac{100}{100-x}$

Substituting the values,

$k=\frac{2.303}{60}log\frac{100}{25}$

$k=0.023{min}^{-1}$

$t_{1/2}=\frac{0.693}{k}$

$t_{1/2}=30min$

Hence, the correct option is $B$