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

Average atomic mass of an element (X) = 16.2

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

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

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