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Current time:0:00Total duration:8:33

if we wanted to find the mass of one atom of carbon-12 right one chemistry class we 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 it's going to give us the mass of our carbon-12 atom and normally in chemistry we measure things in grams right 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 em U and chemists took the mass of one atom of carbon-12 as the definition that one atom of carbon 12 is equal to 12 am use and everything else is relative to that value just to give you an idea of the mass of an amu so one amu is equal to one point six six zero five three nine times ten 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 am use 1 amu is equal to this many grams and so if you multiply 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 amu s-- and if you look over here at what you would see on a periodic table all right so this number right here is the atomic mass of carbon but notice it's not exactly 12 am use this number is exactly 12 twelve point zero zero zero zero zero and so on so this is a exactly twelve 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 and so let's look at this this grade distribution here so let's say your teacher weights tests more than homework so 70% of your overall grade in the class right is is it earned 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 a hundred percent 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 a hundred in the homework category so what is your grade in the class alright 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 right so 70 percent all right so this is a simple calculation but we have 0.7 right here so let's go ahead and write 0.7 so all we have to do is move the decimal place right if we're dividing by 100 just move the decimal place one two to give you a point seven all right so point seven times 90 gives you 63 right here and then let's do the same thing for homework right so convert the percentage into a fraction so we can just move our decimal place 2 over here so we have point three and then we're gonna multiply this by 100 so 0.3 times 100 and so is a simple calculation you can probably do this one in your head so 0.3 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 a hundred and so this is the idea of a weighted average all right let's do the exact same thing except this time we're going to talk about carbon so 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 most pretty much every carbon atom in the world is one of these two isotopes I'm not worried about things like carbon-14 because they're extremely extremely small so if you just take these approximate numbers that I have here so ninety-eight point eight nine percent of the atoms of carbon in the world are carbon-12 right and one point one one zero percentage of atoms are carbon 13 I add all this up right I should get a hundred percent so this represents a hundred percent of all the carbon atoms all right by definition carbon-12 has an atomic mass of 12 am use and experimentally you can figure out that carbon 13 has a mass of 13 amu so remember the difference between carbon-12 and carbon-13 carbon 13 has one more Neutron so one more Neutron than carbon-12 does it's what the 13 is referring to and notice what happened to the mass right the mass went from 12 to approximately 13 so you can see right away that a neutron has approximately a mass of one am use now these numbers are not exact was just to give you an idea of adding a neutron right make sure isotope have more mass right there's more stuff all right so we're gonna do the exact same thing that we did for the grave 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 to so so right here's our decimal so 1 2 so we have 0.98 8 9 and then we're going to multiply that by 12 which is the mass of the carbon 12 isotope so 0.9 8 8 9 times 12 that is equal to 11 point H 6 7 do the same thing for carbon 13 so we need to move the decimal place 2 so we move it 1 and 2 so we'd have point 0 1 there so point 0 1 1 1 0 times this number 13 point zero zero three fours point 1 4 4 3 so we add those two numbers together all right 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 and so twelve point zero one is what we saw on our periodic table earlier so remember this number twelve point zero one so let's go back up to our are what we would see on the periodic table for carbon so at the very beginning of the video and there's our number twelve point zero one so it's a weighted average right 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