Worked example: Atomic weight calculation

we have listed here we know that carbon 12 is the most common isotope of carbon on earth ninety eight point eight nine percent of the carbon on earth is carbon-12 and we know that by definition its mass is exactly 12 atomic mass units now that's not the only isotope of carbon on earth there are other isotopes the next most frequent one is frequent one is carbon 13 one point one one percent of the carbon on earth is carbon 13 and we can experimentally find that its mass is 13 point zero zero three for atomic mass units so these numbers that we have here just as a review these are atomic mass these are atomic mass and so we're going to think about in this video as well how do they come up with the atomic weight number that they'll give you on a periodic table like that so atomic atomic weight where it is where does that come from well in the video on atomic weight and on atomic mass we see that the atomic weight is the weighted average of the atomic masses of the various isotopes of that element so to find this roughly 12.01 we take the weighted average of these two things and what are we weighted by will we wait about we weighted by how common that that isotope actually is so what we want to do is we could take ninety eight point eight nine percent and multiply it by twelve and I'll rewrite this percentage as a decimal so it'll be zero point nine eight eight nine times twelve and to that we are going to add we are going to add one point one one percent times thirteen point zero zero three four so as a decimal that's going to be zero point zero one one per or that's one point one one percent is zero point zero one one oh one one one and I'm going to multiply that times thirteen point zero zero three four atomic mass units so what does that give us let's get our calculator out here so we are going to have zero point nine eight eight nine times 12 is equal to eleven point eight six six eight and to that we are going to add we are going to add zero point zero one one one times thirteen point zero zero three four and I know it's going to do this multiplication first because the calculator knows about order of operations and so that's all going to be as you can see twelve point zero one one one three seven seven four which if you were to round to the hundreds place is how this this atomic weight was gotten so that's hat there you go that's how we calculate atomic weight so I could write this as approximately twelve point zero one it's the weighted average of the atomic masses now another thing that you might want to note is what's the difference between carbon-12 and carbon-13 carbon-12 this right over here is six protons the six protons are what make it carbon so both of these will have six protons and the difference is in the neutrons this right over here has six neutrons six neutrons and this right over here is going to have one more Neutron seven neutrons so when you look at the difference in atomic mass notice the change is looks like it's plus one point zero zero three for atomic mass units so from this you can see hey look if I add a neutron plus one Neutron plus one Neutron it's roughly equal to an atomic mass unit it's not exactly an atomic mass unit but roughly speaking a lot of kind of very broad high-level terms you can kind of view it as being very close to one atomic mass unit and the same thing is true of protons but anyway hopefully you now have appreciation for the difference between atomic mass which is the mass and atomic weight which is the weighted average of the various isotopes of that element on earth how to calculate it and roughly what the mass of a neutron News