 How do we find the mass of an atom? Well, the mass of an atom is approximately equal to the mass of protons in the atom plus the mass of the neutrons in the atom. This is the mass of a proton and this is the mass of a neutron. These numbers are very awkward to use because of the exponents. Fortunately, chemists use a different unit of measurement called the atomic mass unit. One atomic mass unit, or 1AMU, is approximately the mass of a proton or a neutron. The mass of electrons is so small that we can ignore it when we talk about the mass of an atom. If we want to know the atomic mass of a single atom, we add up the masses of the protons and the neutrons. For example, to calculate the approximate mass of a carbon atom, we add up six protons and six neutrons and get an atomic mass of 12 atomic mass units. You have probably noticed that the boxes in a periodic table have numbers on the bottom that have decimals rather than nice even numbers and that's because these numbers represent average atomic masses. In nature, you don't usually just have one type of atom. You have several isotopes. Remember isotopes are atoms of the same element with different numbers of neutrons. Some isotopes are more common in nature than others. For example, a single chunk of carbon could have some carbon 12 in it with six protons and six neutrons. It might also have a little bit of carbon 13 with six protons and seven neutrons and maybe a tiny, tiny amount of carbon 14 which has six protons and eight neutrons. Carbon 12 is the most abundant isotope. The atomic mass reported in the periodic table is what we call a weighted average and this means it accounts for the mass of each isotope as well as how much of each isotope there is. So because carbon 12 is most common in nature and because the other isotopes of carbon are present in very, very small amounts, the average atomic mass is 12.01 AMU, mostly carbon 12 with a little bit of the other isotopes. So let's give some examples of how we calculate a weighted average. We're gonna do this example using cats. We have three kittens on the left. They weigh five pounds each and then we have this big old 20 pound cat on the right. So to calculate our average, we could average it like this where we take three five pound cats. So we have five pounds plus five pounds plus five pounds plus 20 pounds for this big old 20 pound cat. We add all of these up, we divide by the number of cats and we get 8.75 pounds. Now this is easy when you have four cats but when you have really, really big numbers like we work with when we're dealing with isotopes, it's really not practical to do it this way. Rather than counting all the atoms of each isotope up, we're going to use something called percent abundance. Percent abundance is a measurement of the percentage of a specific isotope on earth. For example, we might ask what percentage of the carbon in this carbon sample is carbon 14. If we were in a lab, we could figure this out using a technique called mass spectrometry but in high school chemistry, you will usually be given these numbers and you'll use them to calculate weighted averages just like we'll be doing with our cats in a second. For our cats, we see that three out of four or 75% of them are small cats. One out of four or 25% of them are large cats. When we calculate a weighted average, we typically want to use our percent abundance in its decimal form but this is pretty easy to get. Because percent means how many over 100, 75% basically means 75 over 100. If we simplify this fraction and turn it into a decimal, it becomes 0.75. 25% would be 25 over 100 and we can simplify this to be 0.25. Okay, now what do we do with these? First, let's change those percentages to their decimal forms. We just calculated them and we will put them in here now. Now, we're going to take the percent abundance of each type of cat and we're going to multiply it by the weight of each cat. And then we're gonna add all these numbers up. Our equation will look like this. 0.75 times five pounds plus 0.25 times 20 pounds equals 8.75 pounds. We can do something similar with isotopes. So let's say we have a random sample of an element in nature such as a chunk of carbon. This chunk is usually gonna have more than one isotope in it. And each isotope is going to have a different mass like we see here in our carbon example. Each of these isotopes is gonna make up a different percentage or a different proportion of our total chunk. So in this case, we see that 98.89% of our chunk of carbon is carbon 12, 1.11% is carbon 13 and we have trace carbon 14. That means a very, very tiny small amount. Now let's do an example and calculate the average atomic mass for a sample of carbon. We know that 98.89% of our atoms are carbon 12 and that's gonna give us a mass of approximately 12.00 atomic mass units. 1.11% of atoms are carbon 13, which gives us an atomic mass of about 13.00 atomic mass. And there is also a trace amount of carbon 14. First we're gonna translate our relative abundances from percentages into decimal form. We know that 98.89% of our sample is carbon 12. We're gonna just translate this into 0.9889. We're gonna do the same thing with our carbon 13. 1.11% becomes 0.0111. And we can ignore the trace amount of carbon 14 because this percentage is gonna be very, very tiny and it's not gonna make a big difference in our overall calculation. So our average atomic mass is going to be the relative abundance of our carbon 12 isotope times a mass of 12 atomic mass units. And we're gonna add that to the relative abundance of our carbon 13 isotope, which will be 0.0111. We'll multiply that by 13 atomic mass units. And we're gonna add those all up. That's gonna give us 12.01 atomic mass units. And that happens to be the value that we see in the periodic table. So here's another example. We're going to try to find the average atomic mass of chlorine. We'll notice from our table that we have two different isotopes of chlorine. They both have the same atomic number. They're atomic number 17, but they have different numbers of neutrons. The first thing we're gonna do is translate our percentages to decimals. We're gonna put it into our equation for average atomic mass. And this is what we get. We're going to take our relative abundance of the chlorine 35. And we're gonna multiply that by the atomic mass of chlorine 35 in atomic mass units. Then we're gonna add that to the relative abundance of chlorine 37, multiplied by the atomic mass of that particular isotope. That gives us 35.45 atomic mass units, which just happens to be the number that's given to us for the average atomic mass on our periodic table. In summary, the numbers you see at the bottom of the squares in the periodic table refer to the average atomic mass, which is a weighted average of the masses of the various isotopes in a sample found in nature. You can calculate the average atomic mass if you know the mass of each isotope in a sample, as well as the percent abundance of each isotope.