# How would you calculate the average atomic mass of copper if 69.2% of copper has a mass of 62.93 amu and 30.8% has a mass of 64.93 amu?

Dec 5, 2015

$\text{63.546 u}$

#### Explanation:

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

Simply put, each isotope will contribute to the average atomic mass of the element proportionally to its percent abundance.

$\textcolor{b l u e}{{\text{avg. atomic mass" = sum_i ("isotope"_i xx "abundance}}_{i}}$

As far as the actual calculations go, you will use decimal abundances, which are simply percent abundances divided by $100$.

So, you know that the atomic masses of these two copper isotopes are $\text{62.93 u}$ and $\text{64.93 u}$, respectively. Their decimal abundances will be $0.692$ and $0.308$, respectively.

The average atomic mass of copper will thus be

"avg. atomic mass" = overbrace("62.93 u" xx 0.692)^(color(red)(1^"st" "isotope")) + overbrace("64.93 u" xx 0.308)^(color(red)(2^"nd" "isotope"))

"avg. atomic mass " = color(green)(" 63.546 u")

I'll leave the answer is rounded to four sig figs, despite the fact that the values you have for the percent abundances justify only three sig figs.