# An imaginary element Y occurs 30% of the time with a mass of 57.9 a.m.u. The remaining sample of Y has a mass of 60.9 a.m.u. What is the average atomic mass of Y?

May 11, 2016

$\text{60.0 u}$

#### Explanation:

The average atomic mass of an element is calculated by taking the weighted average of the atomic masses of its naturally occurring isotopes.

In essence, this means that each stable isotope will contribute to the average atomic mass of the element In proportion to its abundance.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {\text{avg. atomic mass" = sum_i "isotope"_i xx "abundance}}_{i} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

This equation uses decimal abundance, which is simply percent abundance divided by $100$.

So, you know that your imaginary element $\text{Y}$ has two stable isotopes, one with an atomic mass of $\text{57.9 u}$ and 30% abundance, and the other one with an atomic mass of $\text{60.9 u}$ and 70% abundance.

How do you know that this second isotope has a 70% abundance?

That is the case because the percent abundances of the stable isotopes must add up to give 100%.

The average atomic mass of $\text{Y}$ will thus be

$\text{avg. atomic mass" = "57.9 u" xx 30/100 + "60.9 u} \times \frac{70}{100}$

"avg. atomic mass " = color(green)(|bar(ul(color(white)(a/a)" 60.0 u"color(white)(a/a)|)))