When the nucleuses of atoms undergo fission or fusion, whether in stars, bombs, or power plants, does the energy released come from a conversion of mass to energy (through E=mc^2), or from the breakdown (release?) of the strong nuclear force?
Also, in Quantum Physics, what is momentum as it relates to waves? And what does electromagnetic mean? Are the charges of subatomic particles (i.e. electrons) like the charges of a magnet? What is an electric charge? Thank you.
Okay, this’ll take a little explaining, but we’ll get there… hopefully even correctly!
To begin with, the answer to your first question is, basically, both. The mass of a nucleus can be written as the sum of the masses of the pieces, plus a binding energy term. It’s differences in binding energy that account for the energy from fission or fusion. This is, of course, differences in the effects of the strong force. On the other hand, you start out with one nucleus with a given mass, you end up with two or more, plus some energy. The overall energy is conserved, and this implies a conversion of mass to energy (some physicists get really picky about this phrase, by the way, but I won’t worry about it). So you ARE looking at E=mc[sup]2[/sup] here, but it’s manifesting itself as an effect of the strong force.
The term electromagnetic comes about basically because electric fields create magnetic fields and magnetic fields create electric fields; the two are really aspects of the same force. The charges of subatomic particles are the same types of things as the charges of bigger particles, and just tell you how strongly the object is coupled to the electromagnetic field. I’m not entirely sure what you mean by the “charge” of a magnet.
Finally, momentum as it relates to waves is the same as momentum anywhere else, it’s just a little harder to visualize. It turns out, for instance, that there’s momentum stored in light waves, so that if someone were to shine a laser at you, in addition to the transfer of energy (which would manifest in you heating up and eventuallyy dying a painful death), there’s a transfer of momentum (think about this loosely, if you want, as the sum of the momenta of the photons in the laser beam), which you probably won’t notice before you die but which ultimately could cause your body to move appreciably because the momentum that was in the laser beam is transferred to your body.
I think by “charge of a magnet” he means the poles, north and south.
And it can even be demonstrated with a simple,macroscopic (i.e. non quantum) device. A wheel with paddles on the ends of thin spokes is mounted on jewel bearings. One side of the paddles is shiny and reflects virtually all of the incident light. The other side of the paddles is black so as to absorb the incident light.
On the absorptive side the light is brought to a stop relative to the paddle this losing its momentum. On the reflective side the light is reversed thus reversing its momentum. So the change in momentum on the reflective side is twice that on the absorpting side and the wheel spins on its bearing.
Light pressure isn’t what makes your run-of-the-mill (forgive the pun) light mill work: http://math.ucr.edu/home/baez/physics/General/LightMill/light-mill.html
But it’s possible:
Interesting. Live and learn, I guess. At least we can hope we learn.
Are you saying that the mass of a nucleus is greater than the mass of the protons and neutrons that compose it? The binding energy term adds mass? Or are you saying that the mass of a nucleus that is created from fusion is less (or greater?) than the sum of the masses of the nucleuses that were fused, and the binding energy term shows this difference? When mass is converted to energy, is an entire particle converted? For example, if two hydrogen nucleuses are fused to form a helium nucleus, does this always result in the conversion of an entire neutron (or other entire subatomic particle, if this particular example does not actually occur), rather than a fractional piece, to energy? I would assume so, but what about the conversion of energy to mass? Can particles be created that have different mass/energy from electrons, protons, and neutrons?
The thing that bugs me is that if fission involves a conversion of mass to energy, then shouldn’t fusion be the reverse? Why don’t we have to add tremendous energy to make fusion work? How do we gain energy from fusion?
I think I see why electric and magnetic fields are tied. If I create a magnetic field, then the electrons inside it are attracted to the positive side, which creates a flow of electrons and thus electricity? But how is a magnetic field created from an electric field? I really don’t understand what an electric field is. Please enlighten me. By “charge” of a magnet, I just mean the way like charges repel and oppositive charges attract. A magnet has a positive side and a negative side, right? Well, is the negative charge on an electron the same type of charge on the negative side of an ordinary magnet? Or is it an electromagnetic charge rather than a magnetic charge?
What is the difference between the momentum of waves and the movement, or temperature, of particles? Once again, thank you, I realize that this is a lot of questions for one thread. 
"Are you saying that the mass of a nucleus is greater than the mass of the protons and neutrons that compose it? The binding energy term adds mass?"
Exactly. Energy is mass. The mass of a battery increases when you charge it, even though no more particles are created. The mass of a rubber band increases when you stretch it, purely as a result of the increased elastic energy.
"When mass is converted to energy, is an entire particle converted?"
I think I’m correct in saying that no nuclear particles are converted to energy in fission. I’m certain none are converted in fusion. All the energy release comes from the binding energy.
"The thing that bugs me is that if fission involves a conversion of mass to energy, then shouldn’t fusion be the reverse?"
You’re right! If you fuse fairly heavy elements into even heavier elements, you would indeed need to put more energy in, because the resulting binding energy is greater.
The nulclear binding energy (per particle in the nucleus) of all the elements in order of atomic weight forms a U-shaped curve with iron at the minimum. So if you fuse elements lighter than iron into heavier elements still lighter than iron, you get energy out. If you fission elements heavier than iron into lighter elements still heavier than iron, you also get energy out. So long as you fission heavy elements and fuse light elements, you get energy.
I can answer part of the preceding. Up to iron, the mass of the nucleus is less than the sum of the masses of the constituent protons and neutrons and the energy of fusion is the energy released in their formation. Beyond iron, the mass of the nucleus is greater than that of the constituents and energy is released when they fission. Radioactive nucleuses are those for which this fission happens spontaneously. (There are radioactive nucleuses below iron; generally they have too large an imbalance between neutrons and protons.)
This raises the question of how the heavy elements form. They do not form in ordinary stars since it requires energy for them to form. They are formed inside supernovas at the point that they have collapsed because the mass of the star is too large to be supported by any kind of thermal or other pressure. This collapse releases gigantic amounts of gravitational potential energy and the star has to get rid of it quickly. The main way is by the release of stupendous quantities of neutrinos that travel through the star nearly without interaction. But the other way is by building transferric nucleuses. In particular, every atom of every element more massive than iron was formed in a supernova and then incorporated into the gas cloud that lead to our solar system. Any planetary system formed too early in the history of the universe would lack heavy elements. Actually, there would be only hydrogen and helium, which do not give a very interesting chemistry.
Not quite right but you’re getting closer. Let’s start with a stationary electric charge, like an electron. If another electric charge is introduced into the volume of space surrounding this charge, both of them will be acted upon by a force. If the charges are the same polarity the force will tend to push them apart. If the two charges are of opposite polarity the force will tend to pull them together. So far, no magnetic field has made an appearance, and the physics is purely descriptive. That is, we can describe how electric charges act but we don’t know on the most fundamental level why they act that way, they just do.
The force the charges “experience” at every point in the space depends on the property of the space known as the “electrical permittivity,” the inverse square of the distance between them and the product of the magnitudes of the two charges. There also exists, in the physics, a definition of what constitutes a unit electical charge. This force is what is called an “electric field.”
Now suppose the electric charge is put into motion. That motion of the charge is what is called an “electric current.” As soon as the charge starts to move at constant speed a magnetic field results. Again, the physics is descriptive and the fundamental reason why this happens is still not known. The magnetism of permanent magnetic material arises from the motion of the electric charges in the atoms of the material. The explanation of the process is quite complex and subtle and I really don’t understand it completely so I’ll leave it to someone who does.
I said above that the charge is moving at constant speed. To go from being stationary to moving at constant speed the charge must have been accelerated. And this brings in the electromagnetic field. During the time a charge is accelerating an electromagnetic field is generated that propagates at the speed of light away from the charge in a spherical volume around the charge. An electromagnetic field is an entity that will exert a force on electric chrges and magnetic poles that are in the field. And again, the physics is descriptive with the fundamental “why” being still a mystery.
Well, in nuclear processes, generally binding energy alone is converted, due to something called conservation of baryon number. What that means is that you have to have the same number of (protons+neutrons) at the end as you did at the beginning. But if we broaden our scope, then there can certainly be cases where an entire particle is converted to energy: this is what happens in matter-antimatter reactions, for example. Pieces of a particle don’t really do this: either you lose the entire thing, or else you lose a binding energy type term (as in fission or fusion), or else you change from one kind of particle to another. In doing that latter, you create particles different from electrons, protons, and neutrons.
Ah, okay. A magnet has two poles, north and south. This is a fundamentally different beast than electric charge. David Simmons has already explained much about this, so I’ll hope his explanation is good enough! Like him, I don’t really want to touch the issue of permanent magnets.
Let’s pretend relativity doesn’t exist for a moment, because it introduces some complications here, okay? Then for particles, momentum is just some particular combination of things (mass*velocity) that happens to be conserved. The explanation of WHY momentum is conserved is non-trivial at best and probably won’t help you any.
Now, we have processes where waves interact with particles and make the particles move. If a particle was just sitting there and starts moving merrily along all of a sudden, this apparently violates conservation of momentum. Big no-no. The way out of this is to start wondering about momentum in the wave itself. And if you work through the formulae, you’ll find that sure enough, the wave DOES carry momentum. How this can be is confusing, of course, because a wave doesn’t really have a mass. Nevertheless, it does have energy, it does have momentum, and so on. These are hard (or impossible, maybe) to visualize, but it’s also true. As I said, it’s easier if you think about things like light waves as being bundles of photons, but even classically (where we don’t have photons), light waves still carry momentum.
matt, thank you- you understand my questions very well. However, I have trouble comprehending how energy adds mass. I realize energy can be converted to mass, but while it exists as energy how does it increase the mass of a nucleus? I thought that energy, at least in the form of light, had no mass. So it must somehow affect the protons and the neutrons in the nucleus to increase their mass? If one could remove the protons and neutrons from a nucleus while leaving the strong force intact, would the strong force have mass?
In light of matt’s post I take this to mean that the mass of a nucleus is less than the sum of the masses of the nucleuses that were fused to form it. Since they are becoming more stable by becoming closer to iron, the strong force uses less energy to hold the nucleus together, and the excess energy is released.
Are neutrinos particles that are created from energy that have different mass/energy than protons, neutrons, and electrons?
Alright! This is what I was really interested in. However, doesn’t this contrast with:
Do nuclear reactions (fission and fusion) involve a conversion of mass to energy, or not? The answer seems to be no, but I am still puzzled by the underlined statement.
David Simmons, let me get this straight. An electric charge is a charged particle, like an electron. An electric field is two charged particles within range of each other. An electric current is the movement of an electric charge, and when this movement is constant it is a magnetic field. And an electromagnetic field is created while an electric charge is accelerating.
gr9rguy, it seems to me that the momentum of light really shows its particle nature rather than its wave nature. This transferring of momentum from light to particles is how it was shown that light acts as a particle as well as a wave, right?
I thank everyone so much for your patience and kindness.
No no, it’s easier to think of momentum in light if you think about photons, but it’s not necessary to do so. Classical electromagnetism has no photons at all, and the light waves still carry momentum. It’s just hard to understand.
Concerning my underlined statement, the idea is this: the mass of a nucleus really is not the same as the sum of the masses of the neutrons and protons; it includes also binding energy. In neither fission nor fusion do you change the overall number of these particles. You get energy out because the binding energy is different for different nuclei, and this is reflected in the fact that in both fission and fusion, the overall “mass” will change, if by that you mean the sum of the mass of the various nuclei.
Oh, I hate trying to explain this kind of thing! Umm… Think of it this way: before your fission reaction, you’ve got M protons, N neutrons, and a nucleus with a total mass that’s
Mmass[sub]proton[/sub]+Nmass[sub]neutron[/sub]+mass[sub]binding energy[/sub].
Afterwards, you’ve got multiple nuclei that between them still have M protons and N neutrons. Now you have a total mass that’s
Mmass[sub]proton[/sub]+Nmass[sub]neutron[/sub]+mass[sub]binding energy, different[/sub] + mass[sub]boom[/sub].
Overall mass is conserved. Now mass[sub]boom[/sub] gets converted to energy. Does that make sense?
Yes, I understand that less binding energy is required when nuclei (sorry about using nucleuses) fuse or fiss (?) to become closer to carbon. However, how does binding energy have mass? Binding energy is not a particle, right? Binding energy is energy and I thought that energy does not have mass, even though it can be converted to mass.
JFMichael: One way to look at it that might help is that mass and potential energy are exactly the same thing. I mean this literally. Mass and potential energy are two different terms which refer to exactly the same physical quantity. The units used to measure this quantity from a “mass” or “energy” perspective, which are kilograms and joules in the SI system, differ by a factor of exactly c[sup]2[/sup]. The reason light has no mass, by the way, is that all of its energy is kinetic rather than potential.
(There is also the concept of relativistic mass which is equal to total energy, potential plus kinetic, but it is rarely used and isn’t important here.)
I’ll try to explain binding energy in slightly different terms. The binding energy of a collection of particles is almost always negative. The reason is that if an object made of particles has a negative mass change from binding together, it will require an addition of energy to split up the object into its component particles. On the other hand, if a collection of particles has a positive mass change, it will release energy in the process of splitting into its individual particles. This will usually happen spontaneously. All known elements have a negative binding energy, which means that the mass of a nucleus is less than the total mass of the protons and neutrons constituting the nucleus. This makes sense when you realize that the particles lose potential energy from sticking together, and mass and potential energy are the same thing.
The important factor when determining whether or not a nuclear reaction will release energy is the binding energy per nucleon. This is just the binding energy of the nucleus divided by the total number of protons and neutrons in the nucleus. By convention, binding energy is always given as positive when the mass change is negative. It is understood that this amount is actually subtracted to find the total mass/energy of the system.
Iron has the largest binding energy per nucleon of all elements; elements that are either higher or lower on the periodic table have a steadily decreasing binding energy per nucleon as you get farther away from iron. This means that if two elements lower than iron fuse to form another element lower than iron, the total binding energy will be greater than before. Binding energy is negative mass, so an increase in binding energy causes a reduction in mass; the extra mass (energy) is radiated away from the new nucleus. Similarly, if an element heavier than iron splits into two new nuclei, both still heavier than iron, the total binding energy will be increased, so energy is released from the reaction.
Ah, I see the confusion. No, binding energy does have mass too. It’s all really a confusion about what mass means, but you can see that this is true by looking up the mass, say, of the carbon 12 atom and the mass of the hydrogen 2 atom.
The carbon 12 atom has 6 protons, 6 neutrons, and 6 electons, and one mole of [sup]12[/sup]C weighs 12.000000 grams. [sup]2[/sup]H has 1 proton, 1 neutron, and 1 electron, but weighs 2.014 g/mol. The reason the carbon isn’t exactly 6 times heavier is that the binding energy is different, so the mass is also different.
We’re getting close now.
Actually an electron is the fundamental unit of electric charge. So electric charge in general is an accumulation of one or more unit electron charges.
An electric field is the force between two electric charges.
A constant velocity moving charge is not a magnetic field. A constant velocity moving charge produces a magnetic field that encircles the path of the moving charge. Incidently, a magnetic field is the force that magnetic poles exert on each other or on a magnetic material.
Almost there. The field is the force divided by the charge that’s feeling it. If I have one charge all by itself, there’s still an electric field around it, even though the field isn’t doing anything. If I now bring in another charge, it’ll feel a force from the field of the first charge. The size of the force the second particle feels depends both on the field and on the amount of the second charge.