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Atomic Mass Units
Scientists measure atomic mass in atomic mass units. A single atomic mass unit is 1/12 the mass of a carbon-12 atom, so it's a tiny number. Scientists use this definition rather than just defining it as the mass of a proton or neutron because although the two masses are close, they are not identical. Despite its status as the yardstick by which other atomic masses are measured, carbon itself has an average atomic mass of 12.0107. This discrepancy arises because other isotopes of carbon weigh more than carbon-12, and although they occur less frequently, they drive up the overall atomic mass of a carbon sample.
Data Points
To determine the average atomic mass of an element, you must have data on the relative abundances of its isotopes. A listing of known stable isotopes will include a percentage and a mass number. This mass number describes the quantity of protons and neutrons in the isotope's nucleus, so it is always a positive whole number. Scientists can derive average atomic mass from these two data points. The periodic table of the elements lists average atomic masses based on natural abundance of isotopes, but specific samples may vary slightly from the listed figure.
Equations
Multiplying each isotope's mass number by its abundance, then adding these figures together will give you the element's average atomic mass. For example, copper has two known stable isotopes: copper-63 and copper-65. Of all the copper in the world, 69.17 percent of it is copper-63, while the remaining 30.83 percent is copper-65. Express the percentages as a ratio, then multiply it by the mass number to find that 63 x 0.6917 = 43.5771 and that 65 x 0.3083 = 20.0395. Add these two results together to arrive at the average atomic mass of copper: 43.5771 + 20.0395 = 63.6166. If a copper sample contains only these stable isotopes, this figure is that sample's average atomic mass.
Checking Your Work
The figures for average atomic mass that you calculate may differ slightly from the listed figures on the periodic table of the elements. This difference arises because the listed average atomic masses include traces of unstable isotopes. However, the two numbers should be close enough that you can easily tell if you've made a mistake. The derived value of 63.6166 is close enough to copper's listed average atomic mass of 63.546 that you can accept the figure. Had you arrived at a three-digit number or a negative number, you would know that you'd committed an error in your work.