16.1 Nuclear Notation

Ok, today we're gonna start our next chapter, Chapter 16, and what we're gonna look at is what nuclear reactions are all about and how to calculate them and so on. So, our first lesson, first of all, is just getting used to the new notation and things of how we're going to use the periodic table a little bit differently than you might have in chemistry. First of all, we call it nuclear physics and nuclear reactions because we're dealing with what's happening to the nucleus of the atom. In chemistry, quite often we mostly pay attention to the electrons because it's the electrons that determine the bonds and how the chemicals react to each other and so on. In nuclear physics, we're worried about just the nucleus because it's the nucleus that's determining what the element is and how it's gonna disintegrate or give off energy or absorb energy and so on. So, first thing we'll do is let's make sure we know what the nucleus is made of. We call them nucleons, so it's basically anything inside the nucleus which is basically protons and neutrons. So, remember, a proton is positive, so we write it as P+. And, we know it's the same charge as an electron, so it's a positive elementary charge, the positive 1.6 to the negative 19. And, we know the mass of a proton is 1.67 to the negative 27. And, so it's the atomic number on your periodic table that's telling you how many protons. So, if you look on your periodic table and we look at something like sodium, we see that sodium is 11, so we say that's the atomic number. 11 is based on how many protons are there. And then, neutrons are the other particles, they're neutral, they have no charge. The mass is almost the same as a proton, just slightly bigger. And, the total number of neutrons added to the total number of protons gives us the atomic mass number. So, if you look at sodium, we have 11 protons, so sodium is number 11. And, if we normally would have 11 neutrons, that would give us a total mass of 22. With 11 protons, 11 neutrons would give us 22. But, when you look on your periodic table, you can see the atomic mass is about 22.99. So, it's almost 23. So, what that means is typically sodium then has actually one extra neutron. It has one extra neutron and still just our 11 protons. So, when we write these things, that's how we're going to do it. So, the top number is the number of protons, the bottom number is the total number of nucleons. And, I think I just said that backwards, I guess. So, let's go back to the previous page. I wrote that backwards. This actually should be 23 on top and 11 on bottom. So, 11 is the protons, 23 would be the total. Alright, let's look at this one. So, if we have 15 on top and 7 on bottom, that's 15/7. So, that's nitrogen. So, nitrogen is 7 on our periodic table, so we have 7 protons. And, 8 neutrons would give us 15. So, we write it as 15N, and we mean that as nitrogen-15 or N-15 for that chemical. So, if we look at 23/11 Na, that's what we just talked about. So, 23Na, 11. So, it's 11, which means it's sodium. And, 23 would mean we have 11 protons and then we'd have 12 neutrons. And that's it. So, in chemistry, when we say with if a chemical has more electrons or less electrons, we call it a positive or negative ion because it's affecting the charge. But, in this case, if we're only gaining or losing neutrons, the charge doesn't get affected. But, we still get a different mass and things like that. So, we call these isotopes. An isotope is when you have different numbers of neutrons. Isotopes will be similar in terms of chemistry, but we do need to worry about it in terms of the nucleus being a different size and a different mass. So, for example, if we look at carbon in nature, carbon is 6. So we should have 6 protons, and it actually comes in abundance most often as 6C 12, which is normal. If we have six protons and six neutrons, we'd have a total of 12. In reality, that happens almost 99% of the time. But there are some cases where it's either missing a neutron, so we get 11C 6, or it has an extra neutron, which is 13C 6. Rarely, it might even have an extra 4, so sometimes it has an extra 2 neutrons. So you can see, 98% of the time it's carbon-12, 1% of the time it's carbon-13, and then rarely does it happen as the other two. But if you think of these as being sort of a weighted average, if 1% of the time carbon is actually one extra neutron, that's why when we look at the molar mass of carbon on your periodic table, it's 12.01. So it's mostly off than 12, but 1% of the time it happens to be one extra, so that's why we're getting that little bit extra weight to it. So the masses on your periodic table are based on averages. It's not what's actually always gonna happen. So you can see here, carbon is close to 12, but we get a little bit extra, so that's why we call it 12.1. So that's an average mass. The number of neutrons will affect the stability of the nucleus. So if we have it as 12C 6, we'd say that's a stable nucleus. That means not much is going to change. If all of a sudden we have way more neutrons or way less, we'd say they're unstable, and that nucleus is likely going to decay and release radiation. So that's why a chemical like radium, uranium, or plutonium, things like that, they are radioactive because the number of neutrons is typically too many, so they always want to try to get rid of them to balance things out. One more thing, there's one more calculation in terms of mass. Masses of atoms are usually given as atomic mass units. It's not part of the metric system, but it makes more sense because we're not dealing with kilograms. The mass of a proton is really tiny, it's 10^-27 kilograms. So just like we do with electron volts, it's just a simpler way of doing it. So if we have a neutral carbon atom of 12, we would say it has 12 atomic mass units. So that means one unit would then be 1/12. So one atomic mass unit works out to be 1.33 x 10^-27. Actually, I think that number's wrong. If you look on your periodic table, it is 1.66 x 10^-27. So there is a table here. So it's 1.66 x 10^-27, is our atomic mass unit. So then, if we divide the mass of a proton by an atomic mass unit, you can see we actually get a little bit more. And if we divide the mass of a neutron by an atomic mass unit, we get a different number. And if we divide the mass of an electron, we also get a different number. So these are the actual atomic units of a proton, neutron, and electron. So if you actually did those calculations for something like lithium, we'd have three protons. So three times 1.007, and typically lithium quite often has an extra neutron. So we'd have four times that, averaged it out when it has one has three, and so on. And that's the number that's on your periodic table. So that mass number may or may not be exact depending on whatever state the situation it is. We know that a nucleus, like we think of a nucleus as being positive charges for the proton. So that's supposed to be if we have something like helium, we have two positive charges, and we'd have to Neutral charges, two neutrons, so we know that those two positives are gonna want to repel, right? If we have two electric charges that are the same, they're gonna want to push apart. So, a question is, why do they stick together then? What's keeping these things together? So, if the electric force, which is quite strong, is trying to push them apart, then we have to have something holding them together. We call that a strong nuclear force. The strong nuclear force is pulling them together, while the electrostatic force is pushing them apart. And if it's stable, then that means the nuclear force is kind of holding its own and winning the battle. If it's not, if the electric force is bigger, then we're gonna start losing neutrons or whatever, and it's gonna start to decay. So, as long as the nucleus is stable, we need energy to get those things apart. If we're gonna have these things together, there's always going to be this energy. So, Einstein basically did some work on this area and he found out that the masses of the neutrons and protons, when they're separate, was actually bigger than when you put them all together in an element. So, if you think about that for a minute, it's kind of like having LEGO pieces. So, you have ten different LEGO pieces separate, they have a certain mass. You stick all ten of them together and if you weigh it on the scale, it'd be the exact same mass. Or what Einstein found out is that it was different. The ten LEGO pieces separate to start with have more mass than when you put them together. So, we're losing some energy. So, what he thought then is that there's some energy that's being wasted to stick these things together. Which kind of makes sense. If you took two pieces of metal and tried to stick them together, you're gonna need to use some of that energy, welding or whatever, to make it work. So, what Einstein then figured out is some of those mass parts of the masses get lost as that mass gets converted to energy. So, the most famous formula in physics, E = mc², is that formula to calculate how much energy is produced based on how much mass is being lost. So, you're going to get some calculations on mass defect. And basically, what we want to do is just figure out how much mass is lost when we put these things together, and then convert that to energy, how much energy was used in the system. So, it was due to this that nuclear bombs and things started to get developed afterwards. So, Einstein didn't develop the bomb, but it was his idea that mass can be converted to energy. So, what they found out is if they take plutonium that's quite unstable, break it apart, there's energy that gets released. And that energy is then the effect of the bomb. Okay, so let's do this last example. So, we've got Zirconium-93, and it tells us the mass is 92.9 atomic units. The question is, what is the mass of just the nucleus? So, what we have to do to get the nucleus is, we know that zirconium is 40 on our table, so we have 93 protons that are 40. So that means we've got our mass at 92.9, and I'll just leave it at that. We have to actually subtract for the electrons, and the atomic mass of electrons on the previous page was 0.005486. So, we just have to subtract that to figure out what the mass is with just the nucleus, which turns out to be 92.88 rounded off. So now, what we want to do is, we know that's the total mass energy. Now we want to figure out what the energy is before. So, we have 40 protons plus 53 neutrons to give us a total of 93. And that mass plus some sort of energy is going to equal 92.88. So, we just have to calculate that. 40 protons, the proton is 1.00727, and on the previous page 53 neutrons was 1.0086866... plus. Some sort of energy equals 92.88, so we do this math to calculate it and solve for energy, or solve it from a story. That means the mass that didn't end up being left over ends up being. So, if we go to the forty times 1.007 plus 53 times 1.38, we subtract it from 92.88, we get an answer of 0.86577 atomic mass units. Let's time that by the mass of one atomic mass unit, which is 1.662 * 10^-27, and that gives us 1.437 * 10^-27 kilograms. So, it doesn't seem like much, but it's close to like half a proton or something like that. That's the amount of mass that was lost in the transfer. Then, Einstein... we can use this formula to figure out how much energy that is. Take that number and multiply it by the speed of light squared, and we get a total mass of our sort of total energy of 1.29 * 10^-10 joules. Which still doesn't sound like a lot, but if we change that to electron volts with time or divide that by 1.6 * 10^-19, we actually get 809 million electron volts, or a mega electron volt. So, one atom of zirconium, you can see, it's 800 million electron volts. So, that is a somewhat significant amount of energy. So, you can see why one atom of plutonium is gonna release a significant amount. So, if we had a big block of it, like they put in a bomb, then we got billions and trillions of joules of energy that gets released. And that's it for this topic.