Question

Half life of radioactive decay of $C^{14}$ is $5730$ years. How much time it will take so that $25\%$ of $C^{14}$ was found in sample ?

• A. $5730years$
• B. $11460years$
• C. $22920years$
• D. $930years$

Answer 1

The correct option is B $11460years$

Since radioactive decay is first order reaction. So Half life is given by -:
$⟹t=\frac{0.693}{k}$
$⟹k=\frac{0.693}{5730}$

$k=\frac{2.303}{t}\log \frac{[A{]}_0}{\left[A\right]}$
$t=\frac{2.303\times 5730}{0.693}\log \frac{\left[100\right]}{\left[25\right]}$
$t=19042\times 0.6020$
$t\approx 11460years$