Question

Ther average atomic mass of a sample of an element X is 16.2 units. ____ and ____ are the percentages of isotopes ${}_8^{16}X$ and ${}_8^{18}X$ in the sample.

• A. 85% and 15%
• B. 90% and 10%
• C. 10% and 90%
• D. 15% and 85%

Answer 1

The correct option is B 90% and 10%

Let the percentage of isotope ${}_8^{16}X=\text{x}$
and percentage of isotope ${}_8^{18}X=100-\text{x}$

Average atomic mass of an element (X) = 16.2

$Averageatomicmass=\frac{\text{Mass of}{}_8^{16}X\times \text{Percentage of}{}_8^{16}X+\text{Mass of}{}_8^{18}X\times \text{Percentage of}{}_8^{18}X}{100}$
$16.2=\frac{\text{16}\times \text{x}+\text{18}\times \text{(100 - x)}}{100}$

$1620=16\text{x}+1800-18\text{x}$
$2\text{x}=1800-1620$
$\text{x}=\frac{180}{2}$
$\text{x}=90$

The percentage of isotope ${}_8^{16}X$ or $\text{x}=\text{90\%}$
The percentage of isotope ${}_8^{18}X=(100-x)=(100-90)=\text{10\%}$