Atomic Mass: Introduction

In this video, we're going to talk about

atomic

mass

. Now sometimes people call

atomic

mass

by other names; your teacher might call it one of these things instead.

Atomic

mass

is a really important characteristic for elements. Each element like Copper, Oxygen, Sulfur, and so forth has its own

atomic

mass

and

atomic

mass

is this number that's written underneath the element's sign on the periodic table. Now

atomic

mass

is an average, it's an average of the

mass

es of a number of

different atoms but it's a special kind of average called a weighted average and this is different than the kind of average that you probably already learned in math. So in order to talk about and really understand

atomic

mass

, we first have to understand weighted averages, what they are, and how to calculate them. So we're going to start out by talking about weighted average using an analogy to cars. So let's imagine that there's a type of car called the Lemona and the Lemona is

called a Lemona because it looks like a lemon, it has this very distinct shape. For the purposes in this video, we'll imagine that the Lemona comes in two models, the Lemona GX and the Lemona GXL and these two models have different features that are unique to each one of them. The GX is blue, the GXL is red and this one's kind of a luxury model. Its got

mass

aging seats and platinum spinner wheels whereas this one only has cloth seats and cheap aluminum wheels. Either way, even though

these are different models that have different features they are both Lemonas because they have this distinct lemon like shape. In this way, the models of the Lemonas are very much like isotopes of an element. Copper for example comes in two models, Copper 63 and Copper 65. Both of these isotopes of Copper have the same number of protons, twenty-nine, because the

atomic

number of Copper is 29. But they have different numbers of neutrons. So just as long as we have 29 number of protons, it makes

you copper. It doesn't matter how many neutrons you have, just the way that if you have the shape of a lemon, the car is a Lemona and it doesn't matter what other features come in that car. This is all we're going to talk about with isotopes right now but just keep this in the back of your mind that the models of a car are very similar to the isotopes of an element. Anyway, we said that

atomic

mass

is going to have a lot to do with the idea of averages. So let's think about

averages for these two cars. The Lemona GX weighs 4,000 pounds whereas the Lemona GXL weighs 5,000 pounds. It's probably the platinum spinner wheels that really add to that heft. So let's say you have this question. What is the average weight of the two cars? Knowing what you probably already know about averages, you could do this math. You could take 4000 pounds for the GX, add it to the 5,000 pounds for the GXL and then divide by two because we have two things here. That would give you

an average of 4,500 pounds which gives us a number that is right between the weights of the two models. So I'm going to refer to this as a regular average, it's a kind of average you probably already learned how to do. Now what if I made this problem a little bit more complicated by giving you some extra information? Let's say that there aren't the same number of GX's and GXL's out there. Maybe because the GXL is a little bit more expensive there are a lot fewer of them.

If we look at all the Lemonas that have been sold everywhere, only five percent of them are GXL's whereas the vast majority, ninety-five percent them, are GX's. We could show these graphically. If we were to pull 100 random Lemonas off the street, all the Blues would be the GX's whereas the ones in red show the GXL's. Obviously there are many more but this is a hundred taken at random and we can see the same thing on a pie chart with just five percent GXL's and the vast

majority ninety five percent are GX's. So there's that. Now let's take this information into account when we're asked this question. What is the average weight of Lemonas taking into account the amount of each model? Now we have to calculate an average that is different than the regular average that we did up here because in this case we just found a number that was right between 4,000 and 5,000 but if we're taking into account the amount of each of these, is it really fair

to say the average weight is 4,500, right in the middle of these two weights? Because there are so much more of the Lemona GX's and they weigh less, we need to come up with an average that takes this into account and gives us a number that's not just right in the middle but would be closer to this because they're so many more of them. Here's how we do it. This is where we get to the idea of weighted average. So to calculate the weighted average, I'm going to take the amount

that the Lemona G weighs which is 4,000 pounds and then I'm going to multiply it by the percent abundance. Abundance is just a really fancy word that means how much of something you have. So here, we have ninety-five percent of the total Lemonas are GX's so I'm going to multiply it by the abundance of the GX. I have to turn this percentage into a decimal. So the decimal point would be here, I move it two spaces to the left so I'm going to get 0.95. Now what this expression is

here is this is the contribution from the GX that I have 95 percent of. Now I'm going to take that and I'm going to add it to the amount that I have of the GXL. So I'm going to take its weight which is 5,000 pounds and multiply by its abundance also expressed as a decimal. So again the decimal places is here, I'm going to move it two spaces to the left so I'll have 0.05 and this right here is the GXL which accounts for 5 percent of my total. I multiply these two things

together and then I do the addition and I'm going to end up with a weighted average of 4,050 pounds. Now as you can see, here's an average that takes into account the weights of both of these models but it also takes into account the amount the amount we have of each and so because there are so many more of the GX's, the average isn't right in the middle, that average is much closer to the weight of the GX's. And because there is few of the GXL's, their weight doesn't

have a whole lot of impact on this final average. I mean it's higher than 4,000 but it's not right in between and so this calculation is what we refer to as a weighted average where we take into account the amount or the abundance of how much we have of each thing. So now that we learned how to do weighted averages with different types of cars, let's talk about how to do weighted averages with different isotopes of an element. So the

atomic

mass

is a weighted average of the

mass

for all the isotopes of a certain element. Copper as we said earlier has two versions or models, Copper 63 and Copper 65. Just like the Lemona, these two versions of Copper or these two isotopes of Copper have different

mass

es. So, the

mass

of Copper 63 is about 63 amu and the

mass

of Copper 65 is about 65 amu but also just like the Lemona we don't have the same number of Copper 63 and Copper 65 atoms. If we randomly pulled a 100 Copper atoms out of the world, we find that 69 percent of them

are Copper 63. Here my 100 copper atoms and the 63 ones are represented by blue dots. And we'd find that 31 percent of those are Copper 65 atoms. So the point is you pull a Copper atom at random from somewhere in the world and it can be either 63 or it can be 65. You have a 69 percent chance of getting Copper 63 and 31 percent chance of getting Copper 65. So to find the

atomic

mass

, we need to do a weighted average calculation that takes into account the

mass

of each of these isotopes but

also their percent abundance and here's how we're going to do it. Remember how we did it with the Lemona? What we do is we start with the

mass

. So Copper 63, I'll do 63 amu. Now I multiply that by its abundance expressed as a decimal. Sixty-nine percent move the decimal place two spots to the left and I have 0.69 and this expression right here is for Copper 63. Now I'm going to add that to Copper 65. I'm going to do 65 amu times its abundance 0.31 expressed as a decimal and

just to keep track of this I'll put Copper 65 (Cu-65) here. Now the math really isn't that hard, it's just setting it up that's tricky. Multiply this, multiply this, and add them together, I'm going to get 63.62 amu. Now look at this, 63 and 65, if we did a regular average we would come up with a number that was right in the middle, 64 ,okay? But there are a lot more of the 63's so that's going to mean that the weighted average isn't going to be right in the

middle, it's going to be closer to 63 and that's exactly what we see. We see a weighted average that is not 64 but is down closer to 63 because we have more of these and the heavier Copper 65's are not contributing as much to this weighted average. Now I told you that this number here on the periodic table represents the

atomic

mass

. You might be wondering why the

atomic

mass

I calculated here came out to 63.62 and not to the .55 that I see here. Well the reason is because I took

some shortcuts here. I used cleaner numbers so that it didn't confuse you as much when we were doing the calculations for the first time. It turns out that Copper 63 doesn't really weigh exactly 63 amu but it's actually 62.93. It's also not 69 percent abundant but it's 69.17 abundant. So they're just some extra decimals on the end that I chose to leave off for these calculations because they're kind of a pain. The same is true of 65 where the numbers aren't the

perfectly nice even ones that I used for this problem but the point is when you do take these numbers into account and you do the weighted average calculation, you end up with an

atomic

mass

in amu that is exactly the same as what you find on the periodic table. So now that you understand what a weighted average is, how to calculate it, and how to work through