Question

The half-life period of a radio active element is $140$ days. After $560$ days, one gram of the element will reduce to:

• A. $\frac{1}{2}\text{g}$
• B. $\frac{1}{4}\text{g}$
• C. $\frac{1}{8}\text{g}$
• D. $\frac{1}{16}\text{g}$

Answer 1

The correct option is D $\frac{1}{16}\text{g}$

$560\text{days}=\frac{560}{140}=4\text{Half-lives}$
Amount of reactant remaining after n-initial half lives
$={\left(\frac{1}{2}\right)}^n\times \text{initial amount}={\left(\frac{1}{2}\right)}^4\times \text{1.0 g}$
$=\frac{1}{16}\text{g}$