In the previous lesson we looked at the subatomic particles that act as building blocks to create atoms. But not every single element has a fixed recipe. There are actually different formulations that you can use to form a given element, and we call those isotopes.

Now, elements are defined by the number of protons they possess. That is to say, if an element has 16 protons, that is defined as sulfur. And if you have a silver atom, it must have 47 protons. That is the defining characteristic of an element. So isotopes are atoms of the same element, but with different mass numbers. If they’re of the same element, they must have the same number of protons, but if they have different mass numbers, that means they vary based on the number of neutrons they possess in their nucleus. Isotopes of the same element have similar chemical properties, but they vary on their mass. In order to understand this, let’s look at a concrete example.

Let’s look at the example of carbon-12. Carbon-12 has an atomic number of 6, that’s its defining characteristic, and a mass number of 12. This means that it has 6 protons and 6 neutrons. But there’s another formulation of carbon that exists called carbon-13. Like carbon-12 it has 6 protons, but it has an additional neutron. So, while it’s still carbon – as defined by its number of protons – it’s slightly heavier than carbon-12. There are many formulations of carbon, including carbon-14, which has 6 protons and 8 neutrons. You may have encountered carbon-14 in a biology class, as it’s often used to date old living matter, like dinosaur bones. So while all these formulations of carbon – and there are many others – have similar chemical properties, they vary based on one important attribute, and that’s their atomic mass.

Atomic mass is measured in units called unified atomic mass units, that we just abbreviate “u.” Protons and neutrons weigh approximately 1 u. It’s not exactly 1, but it’s very, very close. As a result, the mass number of a given atom or isotope will be very, very close to its atomic mass. With the example of carbon-14, it has a mass number of 14, and it has a mass of 14.0032 unified atomic mass units. So the numbers are very close. The terms isotope comes from the Greek word meaning same location, meaning that all isotopes of a given element occupy the same location on the periodic table. So that one cell of information needs to convey atomic mass information for all the different isotopes, and we do that through something called the average atomic mass.

Average atomic mass is the mass value shown in the periodic table, and it’s just a weighted average of all the different isotopes of a given element. Each isotope occurs at a predictable percentage frequency, and has a very specific mass. So we can take the frequency with which an isotope occurs in nature, and the mass of that isotope, and plug it into an equation that will give us a weighted average for the atomic mass. So the equation for average atomic mass here, shown as m-sub-a with a bar over it, is the percentage frequency with which isotope 1 occurs, divided by 100, times the mass of isotope 1, plus the percentage frequency of isotope 2 divided by 100 times the mass of isotope 2, on and on, through every single naturally occurring isotope of that element.