Atomic mass

- [Voiceover] If we wanted to find the mass of one atom of carbon 12, right, one chemistry class, we'd put things on a balance. So just use your imagination here and pretend like you could take one atom of carbon and put it on this tiny little balance here. So we have this tiny balance that's going to give us the mass of our carbon 12 atom. And normally in chemistry we measure things in grams, so you could just imagine getting a number in grams. And since atoms are extremely small, this number would be extremely small and it's annoying to work with small numbers and so instead of working with these extremely small numbers chemists came up with a new term called atomic mass units. So let me go ahead and write this here. So atomic mass units. So we could abbreviate that A-M-U. And chemists took the mass of one atom of carbon 12 as the definition. The one atom of carbon 12 is equal to 12 A-M-Us and everything else is relative to that value. Just to give you an idea of the mass of an A-M-U, so one A-M-U is equal to 1.660, 539 times 10 to the negative 24 grams. So if you wanted to know the mass of a carbon 12 atom in grams, one atom of carbon 12 is equal to 12 A-M-Us. One A-M-U is equal to this many grams and so if you multiplied this number on the right by 12, you'll get the mass of one atom of carbon 12 in grams. But once again, that number is kind of annoying, it's kind of small, and so it's easier to use this definition of one atom of carbon 12 has a mass of 12 A-M-Us and if you look over here at what you would see on a periodic table, alright, so this number right here is the atomic mass of carbon, but notice it's not exactly 12 A-M-Us. This number is exactly 12, 12.00000 and so on. So this is exactly 12 and this is not, it's 12.01 and so where does the point zero one come from? Well that's because the definition of atomic mass includes the average masses of all the isotopes, alright. So this is just talking about carbon 12, but there are other isotopes of carbon and so the definition for atomic mass is the average mass of all of the isotopes of an element and that's what this number refers to. And so let's see how we can calculate this number that you'll see on the periodic table for the different elements. So before we do it for carbon, let's do it for a grade calculation first because this number is actually a weighted average and calculating your grade can sometimes be a weighted average too. So let's look at this grade distribution here. So let's say your teacher weights tests more than homework, so 70% of your overall grade in the class is determined by your test grades. And 30% of your overall grade in the class is determined by your homework and so obviously 70 plus 30 gives you 100%. So that's 100% of your grade. Let's say that you're a good student and so you average a 90 on all of your tests and you always do all of your homework and so you have 100 in the homework category. So what is your grade in the class? So I'm sure some of you guys know how to do this. What you need to do first is convert your percentage into a decimal, alright. So 70%, so this is a simple calculation, but we have point seven right here so let's go ahead and write point seven. So all we have to do is move the decimal place. If you're dividing by 100 just move the decimal place one, two, to give you point seven. So point seven times 90 gives you 63 right here. And then let's do the same thing for homework. So convert the percentage into a fraction so we just move our decimal place two over here so we have point three and then we're going to multiply this by 100. So point three times 100 and so this is a simple calculation, you can probably do this one in your head. So point three times 100 is 30. And to find your grade in the class just add those two numbers together. So 63 plus 30 gives you a grade of 93. So 93 is your grade in the class. And again, this makes sense because your tests are weighted more than your homework so your final grade is closer to your grade for the test. It's closer to a 90 than it is to 100. And so this is the idea of a weighted average. Alright, let's do the exact same thing except this time we're going to talk about carbon. Now let's look at these numbers here for carbon. And so we have two different isotopes for carbon here, so this is carbon 12 and this is carbon 13 and pretty much every carbon atom in the world is one of these two isotopes so I'm not worried about things like carbon 14 because they're extremely small. So if you just take these approximate numbers that I have here, so 98.89% of the atoms of carbon in the world are carbon 12, right, and 1.110% of atoms are carbon 13. I add all this up and I should get 100%. So this represents 100% of all the carbon atoms. Alright by definition, carbon 12 has an atomic mass of 12 A-M-Us and experimentally you can figure out that carbon 13 has a mass of 13 A-M-Us. So remember the difference between carbon 12 and carbon 13. Carbon 13 has one more neutron. So one more neutron than carbon 12 does. That's what the 13 is referring to. And notice what happened to the mass. The mass went from 12 to approximately 13. So you can see right away that a neutron has approximately a mass of one A-M-Us. Now these numbers are not exact, but it's just to give you an idea of adding a neutron, make sure isotope have more mass, there's more stuff. Alright, so we're going to do the exact same thing that we did for the grade calculation. We're going to do a weighted average here. And so the first thing we need to do is to convert our percentage into a fraction and so we just move our decimal place two. So right here's our decimal, so one, two. So we have .9889 and then we're going to multiply that by 12, which is the mass of the carbon 12 isotope. So .9889 times 12, that is equal to 11.867. We'll do the same thing for carbon 13. So we need to move the decimal place two. So we move it one and two, so we have .01 there. So .01110 times this number 13.0034 is .1443. So we add those two numbers together, alright. So we take this number and we take this number and we add them together, so 12.011. And notice this number that we got is much closer to 12 than it is to 13 because again most of the atoms are carbon 12 and so this is a weighted average. So 12.01 is what we saw on our periodic table earlier. So remember this number, 12.01. So let's go back up to what we would see on the periodic table for carbons so at the very beginning of the video and there's our number, 12.01. So it's a weighted average. It's the average mass of all of the isotopes of an element and so you'll be using this number a lot on the periodic table.