Okay. So, next we're going to look at the neutrons. We haven't really discussed them other than to say that they're neutral and also to say that they are in the nucleus. Okay. So that's what we know so far that it's neutral in the nucleus approximately the same mass as a proton. So how do they come into play for the elements? So when we answer this question what we're going to look at is we're going to look at atomic mass. Okay. Now if we look at um the periodic table remember there are three things that you are going to see. You're going to see the symbol. You're also going to see the atomic number. And then you're going to see the atomic mass and it's going to be in units of amu. So the question is actually what is the atomic mass? Well, the atomic mass that is listed on the periodic table. So, this part's actually important. What is listed on the periodic table is a weighted average of all of the isotopes of that given element. So, two things. One, what is a weighted average? And two, what is an isotope? Okay, so we're going to address both of those. So first of all um we will need to know what the isotopes are and we need to know something about their what's called percent abundance but then we also need to know what a weighted average is. Okay. So what I'm going to do is on the next slide and I'm going to actually just add one in really quickly. What I'm going to do is I'm going to talk about a normal average versus a weighted average. Okay, so a normal average places equal weight on all numbers or measurements. Okay. So, for example, let's say we are going to measure um something and we measure it as 15.5 g. We're going to not use units here. So, let's say we have a 15.5 and we have a 16.5. Okay? So, those are our two values. So, if I want to take my normal average, I would say 15.5 + 16.5 and I would just divide it by two and I should come up with 16 for that. Okay, what a weighted average does is it places a weight by a percent on each value. Okay. So, it's like as though we were looking at different numbers and we would say that 15.5 happens 40% of the time, but 16.5 happens 60% of the time. Okay? So, from a decimal standpoint, remember that 40% is equal to 04. And the reason for that is because it's 40 over 100. 60% is equal to 6 because it is the same thing as 60 over 100. So when we take the weighted average, we take into account that 15.5 is only present 40% of the time. So 15.5 * 0.4 4 and then 16.5 is present 60% of the time and then we would add um appropriately. So 15.5 *4 is 6.2 16.5 * 6 is 9.9 9.9 + 6.2 2 is 16.1. So notice that the weighted average is actually greater than the regular average or the normal average because the 16.5 carries more weight. Okay, a normal average when there's only two numbers is the equivalent of saying 15.5 *.5 which remember that's going to be 50%. Plus 16.5 *.5 also for 50%. And so we should get exactly 16.0. Okay, so that's important to know the difference between the normal and the weighted average and how you would actually get those two numbers. We're going to actually apply that. In order to apply it though, we do need to know what an isotope is. Okay, so an isotope of elements. So almost all elements um have multiple isotopes. Okay. But for an isotope, they have the same number of protons. So they all have the same oops, sorry atomic number. Remember that's the identity of the element. However, they have differing number of neutrons. Okay? Now, if you remember that a proton and a neutron have the have the approximate mass of 1 amu. Every time you add a neutron to the nucleus, you are adding one amu to the atomic mass. So it is getting heavier and heavier. Okay? The number of protons plus the number of neutrons is equal to what we are now going to refer to as the mass number. So now we're going to represent elements and isotopes of elements in two different ways. Okay? So if we want to represent what we're going to call carbon 14. So that's the isotope of carbon that we're going to call carbon 14. What we're going to do is we're going to represent it by putting the element symbol. So the C on the lower side. So I'm going to put a box here for you to see. That is my Z. Remember my Z is my atomic number. That atomic number I can get from the periodic table. So when I look it up, it's six. And then my a, which is my new number that I just introduced, this mass number, this value up here is this 14. And that 14 is my total of my protons plus my neutrons. Okay. So before doing the next representation, so I'm going to like actually just write this out. So we would write it as 146 carbon. That's how we would write that isotope. Okay. So very quickly if we want to figure out number of protons, number of neutrons and then number of electrons in carbon 14. The number of protons is equal to six because of that lower number. That's the atomic number. Same number for my electrons. But to get my number of neutrons, this is going to be 14 - 6. 14 - 6 is 8. So carbon 14 has eight neutrons. The other way to represent this is the element with a dash and then our mass number. So C-14. And the reason why we don't have to represent the atomic number is because we can find that on the periodic table. Okay. Now every isotope has its own natural abundance. So if I look at my natural abundance, natural abundance is reported as a percentage. And what it actually means is if we have a sample that contains the element each isotope is present. in its natural abundance. So if we were to look at carbon for example, carbon has three isotopes. Carbon 12, carbon 13. Oh, it didn't include carbon 14. Okay, carbon 14 has a very very small percent um abundance. I'm going to put it on here so that you know that it's there. But what you can see is the percent abundance that is listed. You never have to memorize those numbers. Okay, but carbon 12, remember carbon 12 is our standard. That's our standard for all masses. That's why it's set to be exactly 12 amu. But carbon 12 is 98.89% abundance percent abundant. So that means that if I have a sample of carbon, 98% or almost 99% of all carbon atoms are going to be carbon 12. A little over one, so about 1.1% of them would be carbon 13. And there would be a very very small number of the carbon 14s. Okay. So, the way that this is actually going to work into our atomic masses is that each of these is going to actually contribute to the overall atomic mass. of the element because it is a weighted average.