In this video, we will learn how to define and identify isotopes of an element. We’ll look at the properties of isotopes, their uses, and see how the abundance of different isotopes affects the average atomic mass of their element.
Let’s start with a quick recap of what atoms, ions, and elements are. Chemists concern themselves most with three different particles, protons, neutrons, and electrons because it is these that make up atoms and ions. Protons and neutrons are to be found in the nucleus of atoms or ions. And protons and neutrons have about the same mass of one unified atomic mass unit. The unified atomic mass unit is like the atomic mass unit, and we’ll come to the full definition later in the video.
Since protons are positively charged and neutrons are neutral, nuclei are positive overall. And since the positive nucleus will attract negatively charged electrons, we often find electrons around nuclei. If the number of electrons equals the number of protons, then the combination is neutral overall, and we call that an atom. If there are fewer electrons than protons, then the combination is overall positively charged, and we call that a cation. And if, on the other hand, there are more electrons than protons, then the combination overall is negatively charged, and we call that an anion.
Collectively, we call cations and anions ions. Ions can be made from more than one atom. But in this video, we’re only going to show examples with a single nucleus, what we call simple ions. The chemical behavior of atoms or simple ions is strongly determined by the number of protons in their nuclei. This is why scientists group together atoms and simple ions into elements like carbon. All atoms or simple ions of carbon contain exactly six protons. If you took all the atoms or simple ions in the universe, currently, you’d divide them into 118 groups or elements. You can find information about the elements on the periodic table. But we already know that nuclei can also contain neutrons, which affect the mass and stability of the nucleus.
If we take all the carbon atoms on Earth, we’ll find the vast majority have six neutrons in their nuclei, some have seven, and the very occasional one has eight. This is why chemists talk about isotopes, which is the second level where we group atoms or ions of an element by the number of neutrons they contain. The number of neutrons in an atom generally doesn’t affect the chemical behavior, but it does change the mass. And chemists need to know the mass to work out how much of a substance to weigh out in the lab.
Let’s imagine three different atoms of carbon, all with six protons in their nuclei. Since atoms are neutral and protons and electrons have equal and opposite charge, each atom must have six electrons as well. But in the first atom, we have six neutrons. In the second atom, we have seven. And in the third atom, there are eight. The mass of a proton and the mass of a neutron are about the same, but the mass of an electron is negligible compared to a proton or neutron. So comparing to a proton or neutron, the mass of our atoms is about 12, 13, or 14.
Scientists, for reasons that are beyond the scope of this video, chose a reference point that wasn’t one proton or one neutron, but was instead the carbon atom with six protons, six electrons, and six neutrons. And they gave this a relative atomic mass of 12. So the mass in unified atomic mass units of these atoms is exactly 12, about 13, and about 14. One unified atomic mass unit is the equivalent of a twelfth of the mass of an atom made of six protons, six neutrons, and six electrons, an atom of carbon with six neutrons. It’s much easier to work in unified atomic mass units or with relative atomic masses than it is to do with kilograms because one unified atomic mass unit is about 1.6 times 10 to the negative 27 kilograms.
Now, we’re left with just one problem. What do we call these variations of carbon? One option would be to call it carbon-6, the version of carbon with six neutrons. Another option is we could call it carbon-12, where 12 indicates the mass in unified atomic mass units. But we run into trouble when we try to name the version of carbon with seven neutrons because their isotopic mass isn’t exactly 13 unified atomic mass units. Instead, scientists came up with a workaround called mass number. The mass number is how we identify each unique variation of an element. The mass number is simply equal to the number of protons plus the number of neutrons for atoms or simple ions of an isotope.
And for convenience, the mass number is very close to the numerical value of the isotopic mass in unified atomic mass units or the relative atomic mass. We end up with carbon-12 which is six plus six or carbon-13 which is six plus seven or carbon-14 which is six plus eight. We call each variation an isotope. So isotopes are atoms or simple ions of the same element. So they have the same atomic number with different numbers of neutrons. So they have different mass numbers.
Now, let’s have a look at the ways you might see isotopes written down. Let’s say we have an atom or ion, and we take a peek inside the nucleus. And then we count the number of protons and the number of neutrons. The number of protons tells us the atomic number of the atom or ion. The next thing we do is go to the periodic table and find the element with the same atomic number. And then you can find out the symbol and the name for that element. You now have the start of the name of the isotope. We then return to the nucleus and add the number of protons and the number of neutrons together to get the mass number of the atom or ion. And we add that to the end.
So let’s imagine we’ve got an example like hydrogen-2. We go to the periodic table and we look for hydrogen and then we find the atomic number. For the element hydrogen, the atomic number is one. So atoms or ions of hydrogen-2 contain one proton. We then return to the name and see that the number two is at the end. So we know our mass number. To work out the number of neutrons, we simply take the atomic number away from the mass number, which gives us one, telling us we have one neutron and one proton in an atom or ion of hydrogen-2.
The other way you might see isotopes written is in nuclide notation. Nuclide notation takes the information about the isotope and condense it in a way that can be used in chemical equations. The element symbol for the isotope is used. And in the top left, we have the mass number telling us the isotope. And the bottom left, we have the atomic number. If we wanted to write hydrogen-2 in nuclide notation, we’d start by looking up hydrogen on the periodic table and seeing that its element symbol is H. The mass number, as given in the name, is two. And the atomic number for hydrogen is one. Atomic number can always be found from the element’s symbol by looking at the periodic table. So sometimes, the atomic number is left out. And you can indicate charge in the same way you would with a normal chemical formula.
The next special thing about different isotopes we’re going to look at is radioactivity. Without going into too much detail, neutrons play a major part in how nuclei hold together. If there are too many neutrons or too few neutrons, nuclei can become unstable. An unstable nucleus has a chance of undergoing nuclear decay and becoming a different type of nucleus. For example, carbon-11, carbon-14, and carbon-15 are unstable. If you have a sample of carbon-11, it will take about 20 minutes for half of those nuclei to decay. For carbon-14, it’s 5700 years, a good deal longer. And for carbon-15, it’s only 2.4 seconds. While radioactive isotopes are hazardous, they can be used usefully for medical imaging, or to treat cancer. The radiation they emit can be tracked or can be used to damage cancer cells.
Now, we’ve had a good look at what isotopes are. Let’s have a look at their consequences in the real world. Generally speaking, chemists don’t get to choose which isotopes they work with. We’re stuck with what we get from the air, the water, and the ground. Some places on Earth have slightly different levels of different isotopes. But if you were to take 100 atoms of carbon from anywhere on Earth, on average, one of them would be carbon-13 and 99 of them would be carbon-12. When these abundances are expressed as percentages, we call them percentage isotopic abundances.
Now, why is this important? If we had a sample that was 100 percent carbon-12, then the mass per atom would be 12 unified atomic mass units. However, if we had a sample that was 100 percent carbon-13, it will be 13 unified atomic mass units per atom. But because samples of carbon found on Earth are actually a mixture of the two isotopes, the average mass is about 12.1 u. This may not seem like a big difference, and in many cases, it’s not. But for some elements, the difference is quite substantial. When we’ve done enough analysis to say we have a representative sample of the whole planet, we’ll have worked out the average atomic mass for the element. For any element, we can work out the average atomic mass by taking the percentage isotopic abundances of each isotope and multiplying them by the isotopic mass and summing them all together.
For carbon, we only really need to take into account carbon-12 and carbon-13. But for some elements, there might be three abundant isotopes or more. Let’s have a crack at calculating the average atomic mass of an element from the abundance of its isotopes. Let’s have a look at lithium. On Earth, lithium has two common abundant isotopes, lithium-6 and lithium-7. They’re both lithium, and so they both have an atomic number of three. But the mass number of lithium-6 is six, and the mass number of lithium-7 is seven. A lithium-6 atom, therefore, has three protons and three neutrons. And a lithium-7 atom has three protons and four neutrons. We can estimate the isotopic mass of lithium-6 to be about six unified atomic mass units.
Isotopic masses may be given to much higher degrees of accuracy. Here, we’re just going to use the estimate. And our estimate for the mass of a lithium-7 atom is about seven unified atomic mass units. To the nearest percentage point, the percentage isotopic abundance of lithium-6 is eight percent. And for lithium-7, it’s 92 percent on Earth. For a simple case like this where we just have two abundant isotopes, this is the formula for the average atomic mass. For more complicated cases, we just had to add more terms. This is what we get when we substitute in our terms. Effectively, our average atom is eight percent lithium-6 and 92 percent lithium-7. So we get 0.48 u plus 6.44 u, which is 6.92 unified atomic mass units.
The value of the average atomic mass we got doesn’t quite match up with what we find for lithium on the periodic table. This is because we used rounded numbers for the isotopic percentage abundances and the isotopic masses. If we used more accurate numbers, we’d get a better estimate. Let’s try something different. Let’s flip things on their heads and figure out the abundance of the isotopes from the average atomic mass. We know from the periodic table that the average atomic mass of a lithium atom is 6.94 unified atomic mass units. You could also use the relative atomic mass where we simply don’t include u.
The next thing we need to know is what isotopes of lithium are abundant. In this case, it’s just lithium-6 and lithium-7. And the last thing we need are the isotopic masses, which we’re going to estimate from the mass numbers of the isotopes to be about six u and about seven u. We know that the average atomic mass of lithium must be equal to the percentage isotopic abundance of lithium-6 multiplied by six u plus the percentage isotopic abundance of lithium-7 multiplied by seven u. All the percentage isotopic abundances must add up to 100 percent. So we can substitute in that the percentage of lithium-7 is equal to 100 percent minus the percentage of lithium-6. This expands to the percentage of lithium-6 multiplied by six u plus seven u minus the percentage of lithium-6 multiplied by seven u. This simplifies to negative the percentage of lithium-6 multiplied by one u plus seven u.
Then, we can substitute in the value of the average atomic mass of lithium, 6.94 u, cancel the mass units, subtract seven from both sides, rearrange, and express our final answer 0.06 as a percentage by multiplying by 100 percent. Then, we can calculate the percentage isotopic abundance of lithium-7 by taking away six percent from 100 percent, giving us 94 percent. The abundances we’ve calculated here don’t quite match what we had in the previous exercise. This is because we started with the average atomic mass on the periodic table. If we’d been working with a different element, perhaps one with three or more abundant isotopes, we would’ve had to have more information, like the abundances of some of those other isotopes.
Now, let’s have a look at the key points. Simply put, an isotope is simply a type of atom or simple ion with a specific number of protons and a specific number of neutrons in their nuclei. So isotopes are atoms or simple ions with the same number of protons in their nuclei, but different numbers of neutrons. For example, the isotopes of carbon all have the same number of protons, six, in their nuclei, but different numbers of neutrons.
Isotopes can be represented using nuclide notation, where the mass number and atomic number are attached to the element’s symbol for the isotope. Or you may see the full name of the isotope, which is the name of the element the isotope is of, followed by the mass number. Isotopes of elements on Earth have natural percentage abundances, which are used to calculate the average atomic masses of the elements. You may see average atomic mass referred to as atomic weight. And finally, you can calculate the average atomic mass of any element or sample by taking the percentage isotopic abundances, multiplying them by the isotopic masses, and summing them together.