In the previous post, we have seen that the **average atomic mass** is calculated by the **weighted average of the atomic masses of all the isotopes**. The formula we can use for this calculation can be written as:

Average mass = (% isotope 1) x (% isotope 2) + … (% isotope n)

**For example**, naturally occurring chlorine consists of 75.77% chlorine-35 atoms with an atomic mass of 34.97 amu, and 24.23% chlorine-37 atoms that are 36.97 amu. To find the average atomic mass, we can write that:

Average mass = (Fraction ^{35}Cl x Mass of ^{35}Cl) + (Fraction ^{37}Cl x Mass of ^{37}Cl)

Average mass = 0.7577 x 34.97 + 0.2423 x 36.97 = 35.45

** **

Notice that the average atomic mass is closer to 35 because the isotope with an atomic mass of 35 is more abundant in nature.

**Percent Abundance of Isotopes **

Let’s now suppose we **need to determine the percent abundance** of the two main isotopes of copper: ^{65}Cu and ^{63}Cu. These isotopes have an atomic mass of 64.9278 amu and 62.9296 amu respectively, and the average atomic mass of Cu is 63.5456 amu.

To do this, we set up the same equation we use for calculating the average atomic mass. The only difference is that we do not know their **percent abundance**, so we can **set them as x** and **1-x**. Let’s set x for the ^{65}Cu, and 1-x for the ^{63}Cu isotope.

We can, therefore, write that:

Average mass = 63.5456 = 64.9278 (x) + 62.9296 (1 – x)

Simplifying the equation, we get:

63.5456 = 64.9278x + 62.9296 – 62.9296x

63.5456 – 62.9296 = 64.9278x – 62.9296x

0.616 = 1.9982x

**X = 0.3083**

Now, for the percentage, we multiply the answers by 100%. So, for the ** ^{65}Cu**, we have:

3083 x 100% = **30.83%**

And for the ** ^{63}Cu** isotope, we have:

(1 – 0.3083) x 100% = **69.17%**