Video: The Definition of Atomic Mass

Protons and neutrons have masses of approximately 1 unified atomic mass unit (u) and cannot easily be split into smaller particles. Magnesium consists of protons, neutrons, and electrons and has an atomic mass of 24.3 u. Why is the atomic mass of magnesium significantly greater than 24 u?

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Video Transcript

Protons and neutrons have masses of approximately one unified atomic mass unit, u, and cannot be easily split into smaller particles. Magnesium consists of protons, neutrons, and electrons and has an atomic mass of 24.3 u. Why is the atomic mass of magnesium significantly greater than 24 u?

You might see instead of unified atomic mass units, simply, atomic mass units or amu. While definitionally slightly different, they can be treated interchangeably. One unified atomic mass unit is one twelfth of the mass of a carbon-12 atom. The question tells us that, individually, protons and neutrons have a mass of about one unified atomic mass unit. So, 12 protons have about the same mass as a carbon-12 atom. The question tells us that magnesium has an atomic mass of 24.3 unified atomic mass units. But atoms are made of whole particles. We can’t add 0.3 of a proton or 0.3 of a neutron. So, what does this atomic mass mean?

Well, the question also tells us that magnesium contains electrons. But the mass of an electron is about 2000 times smaller than a proton or a neutron. If we had 24 protons and neutrons in total, we’d have a mass of about 24 unified atomic mass units. But if the rest of the atomic mass was made up by the mass of electrons, it would take about 5500 electrons to do the job. Magnesium atoms have as many protons as they have electrons. This is way too many electrons for this to be the reason why the atomic mass is much greater than 24. So, let’s take a step back and review what we know about magnesium and its atoms.

A magnesium atom consists of a densely packed, positively charged nucleus surrounded by an electron cloud. The nucleus is made of protons and neutrons. And it’s the nucleus that contains most of the mass of the atom. If you look up magnesium on your periodic table, you can see that above its symbol is the number 12. That’s the atomic number. The atomic number tells you how many protons there are in each nucleus of magnesium. But there are actually three main types of magnesium atom called isotopes. These are magnesium-24, magnesium-25, and magnesium-26. This number here is called the mass number, and it tells us the number of protons and the number of neutrons in that particular isotope.

Each isotope has the same number of protons. They’re all magnesium. Therefore, they have atomic numbers of 12, and therefore there are 12 protons in each atom. But magnesium-24 has 12 neutrons, magnesium-25 has 13, and magnesium-26 has 14. The next thing to do is to figure out what the mass of an individual atom of each of those isotopes is. For this question, we can ignore the mass of the electrons because it really doesn’t make that much difference. To work out the approximate mass of an atom of each isotope, we just take the mass of the protons and the mass of the neutrons and add them together. So, the mass of an atom of magnesium-24 is about 24 unified atomic mass units. The mass of an atom of magnesium-25 is about 25 u. And the mass of an atom of magnesium-26 is about 26 u.

You can see that the mass of an atom in unified atomic mass units is numerically very close to the mass number of the isotope. Well, where does that leave us? We know that magnesium the element is generally composed of three different isotopes: magnesium-24, magnesium-25, and magnesium-26. And the atoms of these isotopes have slightly different masses. Well, we can think about a sample of magnesium being made up of a mixture of magnesium-24, 25, and 26. For samples of magnesium found on Earth, on average, 79 percent of the atoms are magnesium-24. 10 percent of the atoms are magnesium-25. And 11 percent of the atoms are magnesium-26. So, the average mass of a magnesium atom is 79 percent of the mass of a magnesium-24 atom plus 10 percent of the mass of a magnesium-25 atom plus 11 percent of the mass of a magnesium-26 atom, which is about 24.3 unified atomic mass units.

So, the atomic mass is actually the weighted average of the mass of the atoms of all the isotopes of an element. Magnesium has three stable isotopes found on Earth in decent proportions. There are other isotopes, but these are the ones that matter to work out the average mass of a magnesium atom. So, the answer to our question, why is the atomic mass of magnesium significantly greater than 24 u, is that the atomic mass is calculated based on the relative abundances of natural isotopes.

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