Question

The average atomic mass of a sample of an element $X$ is $16.2u$. What are the percentages of isotopes ${}_8^{16}X$ and ${}_8^{18}X$ in the sample?

Answer 1

Let the percentage of ${}_8^{16}X$ be $A$ %. Then the percentage of ${}_8^{18}X$ be $(100-A)$ %.

Calculating Average Atomic Mass

The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance (the decimal associated with the percent of atoms of that element that are of a given isotope).

Average atomic mass = $f_1{M}_1+f_2{M}_2+----f_n{M}_n$

where f is the fraction representing the natural abundance of the isotope and M is the mass number (weight) of the isotope.

$\therefore$ $16\times \frac{A}{100}+18\times \frac{100-A}{100}=16.2$

$⟹1800-2A=1620$

$⟹A=90$

So the answer is 90% ${}_8^{16}X$ and 10% ${}_8^{18}X$