[MUSIC] So what about nuclear bonds? After all, I said energy is the rearrangement of chemical, which we just discussed or nuclear bonds into a more stable state. The really neat things about nuclear bonds is, you can learn so many things from this next simple term. This is a chart of the stability of the different nuclei. And to put it in those terms, you have to actually do this as the average binding energy per nucleon. A nucleon is a neutron or a proton. The simplest fusion reaction is to take hydrogen, which is down here, and turn it into helium which is up here. You go to something more tightly bound. A bigger number here. Fission is taking things like uranium and breaking them up into lighter elements. The most stable elements of all are iron and nickel, which are at the top. Now, illustrating nuclear reactions is something that's a little bit trickier to do. Of course, sometimes you do try it in class. It's down to eight, nine. Give me a countdown. What wire do I cut? >> Red one. >> Red one. [SOUND] What's the count? >> [LAUGH] >> Well, of course, we didn't really make a nuclear explosion in class, but the one I'm going to give you the math for is this reaction. This is the simplest to do of all the fusion reactions. It takes deuterium, that's H2, because its atomic weight is two, one proton, one neutron. And tritium, H3, because its atomic weight is three, it has three nucleons. Two neutrons and one proton and neutrons and protons don't disappear. You simply rearrange them in the nucleus into more stable states, into a free neutron and into helium. This reaction ,If you did it in large scale looks more like this. We're not going to do that one in class. What we are going to do is, use the same well technique. I'm going to start with Deuterium and tritium, all right. Now to do that, this is a proton and a neutron, all right. So, this is deuterium. This is tritium. This has one proton being hydrogen and two neutrons. Now to figure out what numbers, how tightly bound to make this, we need to look at our chart. The binding energy per nucleon. So, we look at 1H2, it says -4.25, but remember, that's per nucleon, right? And there are 2 nucleons, so we multiply that by 2, and this becomes -8.5. That's the depth of this well, -8.5. Tritium 1H3 -0.73. I multiply that by 3 since there are 3 nucleons and I'm going tot get -2.2, that's the depth of this well, -2.2. What does this turn into? Turns into a free neutron and it turns into helium. Standard, fill up my balloon with helium 4. It's binding energy per nucleon minus 7.08, but there are four nucleons. So this is -28.3, very deep well, very tightly bound nucleus, -28.3. Take these numbers. We've got minus 8.5 plus minus 2 is, equal to minus 28.3 plus energy released, plus the Q, right. The energy that comes out. Do this and we're going to get that Q is equal to -117.6 mega electron volts. These aren't, kilocalories anymore. It's a different unit, a unit of energy. Quite a different unit. Minus 7.6 MeV. What happened to the neutron? After all I've got two protons three neutrons. Here this helium is two protons and two neutrons and we have an extra free neutron. Just like for chemical bonds the oxygen was at zero, a free neutron is at zero as well. Two protons, three neutrons, two protons, three neutrons. They don't disappear, they are just recombined into a much more stable state Into helium itself. This energy released isn't some magic fluid. This energy released is simply the speed of the products. This neutron carries away 14.1 of the MeV and the helium nucleus takes away the rest, at 3.5 mega-eV. These were barely moving by comparison and these are moving really fast and that's where the energy goes. So how does that amount of energy in a nuclear reaction compare to amount of energy in a chemical reaction we saw? We have different units and here, where there's a wonderful thing to always convert from one unit to another. A technique, a mathematical technique called factor label. Let's do it. So, if we start out with 17 point 6 Mega electron Volts. Well, Mega is a million, so my first thing I'm going to do is, say it takes one Mega e V And that's a million, 10 to the sixth eV. Now, eV is an energy unit. It's an electron volt and we can compare that to joules. The conversion factor is that 1 eV Is equal to 1.6 times 10 to the -19 joules. So in other words, an eV is not very much energy. Of course, we wanted to compare this to the kilocalorie. Remember the shot of alcohol, 161 kilocalories? We're going to actually need to get this into calories. If we take the other definition I gave you, where it was one calorie with a small c with four point one eight six eight jewels. Pretty close, except we're going to need that one kilocalorie is equal to 1000 calories. And then if I did this right, MeV cancels EV cancels joules cancel, calorie is cancel and my number will be in kilo calories. The amount of energy that we're going to get in the same units now, from doing that one nuclear reaction. So, we can multiply these numbers and we're going to get 6.7 x 10 to the -16 kilocalories. All right, now you're thinking, wait a minute, Professor, I thought nuclear reactions gave you so much more energy. You showed me the hydrogen bomb going off. And I saw that burning in that shot glass of that methanol sitting there in your classroom for minutes at a time. Clearly, these aren't sixteen maritors of magnitude off and you're right. This reaction was for one molecule. The 161 kilocalories right that we got from that burning of the shot glass this was for an entire mole. A mole is Avogadro's number of atoms 6.02 x 10 to the 23rd. I have to multiply this number by this number and when I do that, I get 404,000,000 kcal. If I had a whole mole, in Avogadro's number of atoms of deuterium and tritium turning into fusion. This is the comparison that you want to make. Chemical reactions. Nuclear reactions. Millions, about 2 million times more powerful and that's what you need to know about calculating energy from nuclear bombs. [MUSIC]