Question

The half-life of a radioactive nuclide is $100$ hours. The fraction of original activity that will remain after $150$ hours would be

• A. $\frac{2}{3\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{1}{2\sqrt{2}}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{1}{2\sqrt{2}}$

The activity of a radioactive substance is given as,

$A=A_0{\left(\frac{1}{2}\right)}^{\frac{T_H}{t/2}}$

Substituting the values,

$\Rightarrow \frac{A}{A_0}={\left(\frac{1}{2}\right)}^{\frac{150}{100}}$

$\Rightarrow \frac{A}{A_0}={\left(\frac{1}{2}\right)}^{\frac{3}{2}}$

$\Rightarrow \frac{A}{A_0}=\frac{1}{2\sqrt{2}}$

Hence, $\left(c\right)$ is the correct answer.