How is the average atomic mass of an element determined using isotopes?

The average atomic mass of an element is determined by the relative abundance and mass of its isotopes.

To understand this in more detail, let's first define what isotopes are. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This means they have the same atomic number but different mass numbers. For example, carbon-12 and carbon-14 are isotopes of carbon. They both have 6 protons, but carbon-12 has 6 neutrons while carbon-14 has 8 neutrons.

The average atomic mass of an element is not simply the arithmetic mean of the masses of its isotopes. Instead, it is a weighted average, which takes into account both the mass of each isotope and its relative abundance in nature. The relative abundance of an isotope is the percentage of atoms of that isotope in a sample of the element.

To calculate the average atomic mass, you multiply the mass of each isotope by its relative abundance (expressed as a decimal), then add up these products. For example, if an element has two isotopes, one with a mass of 20 atomic mass units (amu) and a relative abundance of 90%, and the other with a mass of 22 amu and a relative abundance of 10%, the average atomic mass would be (20 x 0.9) + (22 x 0.1) = 18 + 2.2 = 20.2 amu.

This method of calculating the average atomic mass reflects the fact that the mass of an element's atoms in a sample is not evenly distributed, but is skewed towards the mass of the most abundant isotope. It provides a more accurate representation of the mass of a typical atom of the element.