# Binding Energy

by Jared Rovny

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00:01 When we have these nucleons on the nucleus there's something holding them together.

00:05 Since they are bound together we can try to insert some energy or hit them or try to mess with them and break them apart.

00:12 The amount of energy it takes to break them apart is called the "Nuclear Binding Energy." So this is the amount of energy we would have to introduce to a particular to nucleus take these forces away from each other and split the protons and neutrons entirely into their separate species.

00:30 If we flipped this process around and thought about how an atom was formed by putting the protons and the neutrons together.

00:36 We know that some amount of energy goes into holding them together.

00:41 And it turns out by Einstein's law that energy and mass are equivalent.

00:45 The fact that there is this extra energy in the nucleus it's going into holding these things together.

00:50 Will mean that the total mass of the combined protons and neutrons will in fact be less than the total mass of the individual things added together.

00:59 So for example, in this case we've joined a particle which has two protons bound to two neutrons.

01:05 The total mass we might think is the sum of the two masses of the protons plus the two masses of the neutrons.

01:12 But in fact the total mass of this particular particle will even be less than that.

01:17 Because some of the mass actually goes into the energy of holding these objects together.

01:24 Again I remember if not to flip this around so this is something that is often done.

01:28 Sometimes people will think it is heavier because they are together.

01:31 But in fact the total object where everything is put together, is going to be lighter rather than heavier than some of the constituent parts.

01:39 And this is why we call the mass defect.

01:42 So that might be a better way to remember.

01:44 As the mass defects it again and the total mass is less than the individual masses all added together.

01:51 This missing mass by the way you can always find.

01:53 So for example, if I gave you a particle and told you what it's "m" total was, the total mass of this object.

01:59 But you also knew what the masses of the individual protons and neutrons were in that object.

02:04 You could find the difference in the mass, the amount of mass that seemed to be missing.

02:08 This amount of mass that would seemed to be missing is given exactly by Einstein's relation that E = mc2.

02:14 So "E" the amount of energy that went into binding these together and that seems to be missing will be equal to "M" where M would be that mass defect.

02:22 However, much was missing or different between the total mass and some of the individual parts of the mass times the speed of light square.

02:29 So again this is an energy you can find by doing exactly this.

02:33 Taking the difference between the total energy and the some of the individual parts of that nucleus and then multiplying by the speed of light square.

02:43 Nuclei are held together by a particular force.

02:45 And we're going to have to go into this but not in too much detail.

02:48 But we'll talk about it briefly.

02:50 The force holding protons together is called the Strong Nuclear Force.

02:55 And we call it strong for number of reasons but one of which is that we also have this repulsive electromagnetic force trying to fight the strong nuclear force.

03:04 So we've already talked about how two similar charges, two light charges will always repel each other.

03:11 So we need to get two protons close enough that the strong force takes over.

03:15 And that's the key issue with the strong force.

03:18 While it is a very strong force, it is a very short range force as well.

03:23 So the only way we get two protons to stick together is to somehow get them very, very,very close to each other even while they are fighting.

03:30 So that if at any point I let go they would zip away in different directions until I got them close enough that the strong nuclear force took over and they actually bound to be part of the new nucleus.

03:41 In a big nucleus, we actually have this issue that these large nuclei have a very strong repulsive force.

03:49 And the reason for this is as follows.

03:51 We take a look at these two nuclei, a small one and a big one.

03:54 Notice the key difference here.

03:56 For the small nucleus, the two protons are very close to each other.

04:00 And so they experience the strong nuclear force keeping them together.

04:03 Because they are so close and that strong nuclear force is so short ranged.

04:06 And the electromagnetic force trying to push them outwards, can't compete at all with a strong nuclear force.

04:14 However, what happens if I start putting in more and more and more and more protons, once we have this large nucleus something strange happens.

04:22 If we look at this large nucleus we can see that we have many protons.

04:26 But look at one proton on one side of the nucleus and compare it to proton on the far other side of the nucleus.

04:32 They are not close to each anymore.

04:34 And therefore, the strong force is not quite as strong.

04:36 It doesn't have quite the strength it should.

04:39 Whereas the electromagnetic force which is large range, still get's to act and still get's to push these guys away from each other.

04:46 So if you look at all the different objects in this nucleus here, you can see that the strong force is losing power as the object get's bigger and bigger and bigger.

04:54 Because that strong force is only acting of those very close ranges.

04:59 And for this reason these large nuclei become more and more unstable.

05:03 Protons are only going to feel the strong force from their neighbors.

05:07 Whereas the electromagnetic force is going to push all of the protons no matter which ones are in the nucleus away from each other, creating instability for atoms that are higher up in the periodic table.

05:18 We can ask our selves exactly what is this energy, we can measure it.

05:22 This is called the "Total Binding Energy Per Nucleon Curve." The way you would bind the energy per nucleon in a particular atom is first to add up the total amount of energy keeping that object together.

05:34 And then divide by the total number of nucleons in that nucleus.

05:39 In this case, what you would get is the binding energy per nucleon after you've divided by the total number of nucleons in that nucleus.

05:47 And for the reasons we just described as the nucleus gets bigger and bigger and bigger, we start losing out on our binding energy.

05:54 So first, we start on the far left of the graph with the smallest atoms which start with hydrogen and then move to helium and then slightly bigger and bigger and bigger.

06:03 And then we get to very, very, very big atoms.

06:06 And once we do that again, we start losing our binding energy because that strong force begins to lose to that repulsive electromagnetic force.

06:14 The place where this change takes place, the place where this occurs, is in fact at iron.

06:19 At iron this change occurs from one kind of behavior to another.

06:25 From becoming more and more strongly bound because you get more and more of the strong nuclear force to weaker and weaker and weaker in your bindings because the electromagnetic force takes over and starts trying to push your particular nucleus apart.

06:38 For this reason if we wanted to create a more stable nucleus, we could start at the far left.

06:44 And try to push atoms together.

06:46 Taking two protons for example.

06:48 May be two hydrogens and putting them together to create a helium.

06:52 In which case, they would be more tightly bound because of the strong nuclear force.

06:56 And that would move us up this energy per nucleon curve.

07:00 And this process is called " Nuclear Fusion." When you take two positive charges like two protons and you put them together.

07:06 And again that's a very difficulty process.

07:08 Because they don't want at all to be together until they are very, very close to each other.

07:12 And so there is a slippery problem of trying to push them together and then sliding off each other.

07:17 Because they don't want to be close to each other.

07:19 On the other hand, we could do the exact opposite.

07:21 And start with a very, very heavy atom something closer to Uranium or higher.

07:25 And then we can break it down and it would split into two different atoms.

07:30 And that is called "Fission." When you have a big particle that splits.

07:34 And so long as we are moving higher up in the curve as it's drawn here, we are always going to places of more energy.

07:43 So when we fuse two particles together, fusing two protons.

07:47 Starting with hydrogen for example and going to helium, we gain energy in that reaction.

07:52 Because again a strong nuclear force is going to act and give us more energy.

07:56 On the other hand, with a very big particles when they break apart, it's the electromagnetic force that's the dominating force.

08:04 And we gain energy because that force has already taken over.

08:07 And so for this reason we can get energy from these reactions, from these processes.

08:12 We can get energy from fission energy which is what's conventionally used in nuclear energy plants now.

08:18 We could also get energy from fusion which turns out as you can see from this graph, would be a much more efficient and much more energy saving technique of getting that fusion energy.

08:29 This is still a very difficult task and not something we've been able to do yet.

08:32 But if we did, we would get a huge amount of energy from it.

08:36 Again the energy can be released in either of these paths.

08:39 But it would be the opposite going the other way.

08:41 So starting with iron, which is the most stable nucleus as we discussed.

08:45 If we moved in the other directions we would be becoming slightly more unstable with slightly different amounts of energy.

08:51 Since iron is the most stable and something like star as everything is compressed with more and more gravity, you end up stabilizing with huge iron cores in you objects in the galaxy.

09:02 And this is where in fact the iron comes from.

09:06 So this summarizes our basic introduction to the Atomic Nucleus.

09:09 We've gone over the proton, the neutron and how to discuss the proton and neutron in relative numbers in different isotopes of the same or particular nucleus.

09:17 Now that we've laid out the ground work, we're going to go into one more discussion and then get into the thermodynamics of how these atoms and molecules and specially the chemicals work together.

09:28 But that's next time.

09:29 Thanks for listening.

The lecture Binding Energy by Jared Rovny is from the course Atomic Nucleus.

### Included Quiz Questions

1. The degree to which the mass of nuclei is smaller because of binding energy.
2. The loss of mass from collisions of different nuclei.
3. The missing mass from nuclei when they are on their own.
4. The amount of force required to break a nucleus apart.
5. The missing mass from molecules because of the binding of electrons.
1. The strong nuclear force
2. The weak nuclear force
3. The electromagnetic force
4. The gravitational force
5. None of these forces
1. The strong nuclear forces and repulsive electromagnetic forces.
2. The weak nuclear forces and attractive electromagnetic forces.
3. The strong electromagnetic forces and weak gravitational forces.
4. The strong spring forces and strong gravitational forces.
5. The strong electromagnetic and strong frictional forces.
1. Fission is the breaking apart of nucleons; fusion is the binding of nucleons.
2. Fission is the breaking apart of molecules; fusion is the binding of nucleons.
3. Fission is the breaking apart of molecules; fusion is the binding of molecules.
4. Fission is the binding of electrons; fusion is the breaking apart of electrons.
5. Fission is the binding of molecules; fusion is the breaking apart of molecules.
1. The strong force is short range, and the electromagnetic force is long range.
2. The strong force is long range, and the electromagnetic force is short range.
3. The weak nuclear force is weaker than the electromagnetic force.
4. The weak nuclear force is long range, and the electromagnetic force is short range.
5. The binding energy depends inversely on the number of nucleons.

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