Question

The half-life of a radioactive substance is $100$ years. The number of years after which the activity will decay to $\frac{1}{10}th$ of its initial value is:

• A. 250 years
• B. 300 years
• C. 332.3 years
• D. 350.3 years

Answer 1

The correct option is C 332.3 years

Given : $R=R_o/10$ $T_{1/2}=100$ years where $R_o$ is the initial activity

Using $\frac{0.693}{T_{1/2}}t=\ln \frac{R_o}{R}$

$\therefore$ $\frac{0.693}{100}\times t=\ln \left(10\right)$

$⟹$ $t=\frac{100}{0.693}\times 2.303=333.3$ years