Nuclear fusion- Is this right?

[eightsquare]

In the fusion of hydrogen to give helium, some protons get converted into neutrons. As a proton and neutron have no electrostatic force of repulsion between them, the potential energy between the two protons is released in the form of gamma rays(ultimately). Also part of the energy is used to create the neutron(which has more mass than the proton). Ultimately, as a helium nucleus has two neutrons instead of protons, the energy released in this reaction is potential energy as the electrostatic potential energy is reduced.
Is this correct?

EDIT: If there is no conversion of a proton into a neutron, how is energy released(Second stage of P-P chain for example?)

 

[SteamKing]

All is revealed here:

http://en.wikipedia.org/wiki/Proton–proton_chain_reaction

 

[eightsquare]

I made a mistake in the 'EDIT' part of my first post. I know that the potential energy at the end of fusion is less than the energy before fusion, but I don't understand how. Everywhere I'm reading the mass of the fused nucleus is less than the mass of the individual nucleons. As the elementary particles have fixed rest mass, I'm assuming the potential energy is converted into energy. Could you tell me the potential interactions before and after the reaction and which potential is 'lost'?
The rest mass cancels on both sides. On the reactants side we have a lot of kinetic energy and increasing electrostatic potential energy. After the reaction we have high electrostatic potential energy and low strong nuclear potential. I have a feeling the energy released has something to do with the transition of strong nuclear potential from low(due to distance) to high to low again(once the nucleons are close)?

 

[SteamKing]

I don't know what you mean by 'potential energy' of a nucleus. Are you perhaps referring to the Coulomb force which repels particles of like charge from one another?

Anywho, this article delves into fusion a little more further:

http://en.wikipedia.org/wiki/Nuclear_fusion

The energy emitted in the various fusion reactions comes from a decrease in the binding energy as two nuclei are fused together. The binding energy is related to the strong nuclear force, which overcomes the Coulomb force at very small distances, and allows nuclei which contain more that a single proton to exist.

 

[sophiecentaur]

I don't know what you mean by 'potential energy' of a nucleus. Are you perhaps referring to the Coulomb force which repels particles of like charge from one another?

Anywho, this article delves into fusion a little more further:

http://en.wikipedia.org/wiki/Nuclear_fusion

The energy emitted in the various fusion reactions comes from a decrease in the binding energy as two nuclei are fused together. The binding energy is related to the strong nuclear force, which overcomes the Coulomb force at very small distances, and allows nuclei which contain more that a single proton to exist.

I think he means the net potential - including the effects of all forces - where there is attraction and repulsion to keep the nucleons 'separated' by a specific (classical) distance. The potential well.

 

[eightsquare]

"Because the nuclear force is stronger than the Coulomb force for atomic nuclei smaller than iron and nickel, building up these nuclei from lighter nuclei by fusion releases the extra energy from the net attraction of these particles."

I don't get what this means(excerpt from the Wikipedia article).
When nucleons are close together, there is electrostatic repulsion but the nucleons stay together nevertheless because of the strong force. Even if the nucleus is stable, the electrostatic repulsion is there, its only overridden by the strong nuclear force. I don't get what the article means by 'releases the extra energy from the net attraction of particles". For example I'm gravitationally attracting the chair below me, but there is no energy released. Also, the concept of 'binding energy' seems pretty vague to me. If the nucleons are bound more tightly, why should energy be released?

 

[eightsquare]

I read a rubber band analogy for this on some site. Is the energy released due to conversion of kinetic energy into gamma rays, etc.? I mean when the strong nuclear force takes over these nucleons start accelerating towards each other. When they fuse is it their kinetic energy that becomes gamma rays, etc.?

 

[SteamKing]

You can do further research on the topic of nuclear physics. It will take a lot of this to answer all your questions.
Here are a couple of articles illustrating the concept of binding energy:

http://en.wikipedia.org/wiki/Nuclear_binding_energy

http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html

 

[eightsquare]

I've read all those articles.

Here's a quote from Wikipedia-

"If one must inject energy to separate a system of particles into its components, then the initial weight is less than that of the components after they are separated. In the latter case, the energy injected is "stored" as potential energy, which shows as the increased mass of the components that store it. This is an example of the fact that energy of all types is seen in systems as mass, since mass and energy are equivalent, and each is a "property" of the other."

Is this correct: In a hot gas, the particles have very high kinetic energy and also potential energy. Due to the mass energy equivalence, this means they have more mass. When they fuse together to form a larger nucleus, the potential energy and the kinetic energy of the particles is less(kinetic energy being zero) in this configuration. Consequently the mass is less and this lost mass is converted to energy.

 

[eightsquare]

In exothermic chemical reactions when electrons move to a lower potential they release energy. If localized temperatures exceed a certain limit the particles even start radiating in the visible wavelength. Nuclear fusion is basically a similar process for nucleons like electrons in the previous example. The difference being nucleons release much more energy. I know the process. My question all along is what are the forces and potentials involved that are less after fusion. In chemical reactions the electrostatic potential is less. I wanted the analogous potentials for fusion.

 

[Nugatory]

I've read all those articles.

Is this correct: In a hot gas, the particles have very high kinetic energy and also potential energy. Due to the mass energy equivalence, this means they have more mass. When they fuse together to form a larger nucleus, the potential energy and the kinetic energy of the particles is less(kinetic energy being zero) in this configuration. Consequently the mass is less and this lost mass is converted to energy.

Yes for the potential energy, no for the kinetic energy. Usually we calculate the mass change in a nuclear reaction as if all the massive particles involved are at rest; that makes it clear how much energy was released in the fusion process itself. In any case, the initial kinetic energy is usually insignificant compared with the potential energy released in the fusion.

 

[eightsquare]

@Nugatory: Thanks for clarifying that. Just tell me if this overall picture is correct:
Like electrostatic potential is converted into heat in chemical reactions, fusion reactions convert strong nuclear potential into heat. Even though the electrostatic potential increases as the protons come close together, the nuclear potential decreases much faster.

 

[Khashishi]

Sounds good to me. The strong force is stronger than the electromagnetic force for small nuclei like deuterium. As you get to larger and larger nuclei, the Coulomb forces get larger and larger compared to the strong forces, so very heavy nuclei like uranium are unstable.

 

[eightsquare]

Thanks. I have a couple more questions. First, a quote from Resnick and Halliday's 'Fundamentals of Physics'.
"It takes a few eV to remove an electron from an atom, but it takes a few million eV to remove a nucleon. That is why nuclear fusion releases so much more energy than chemical reactions."
My question is, if the strong force is only about a 100 times stronger than the EM force why does it take so much energy to separate a nucleon?
And secondly, if uranium nucleus is unstable because the EM force beats the strong force due to the strong force's short range, why doesn't the nucleus fly apart immediately? Why do we need bombard it with a neutron to accelerate the process? I would think that work was done to bring it into this position, so as soon as the work is removed the nucleus should fly apart.

 

[Khashishi]

In a heavy nucleus, the strong force is still stronger than the Coulomb force, but the strong potential is weaker than the Coulomb potential. The potential is the force integrated over distance, and the Coulomb force acts over a longer distance. It's energetically favorable for an alpha particle (a helium-4 nucleus) to escape from a uranium nucleus, but it has to first get over a large activation energy.
In the picture, the top represents the potential of a stable nucleus. The nucleons are trapped in the well on the left, which is the strong potential. The bottom represents and unstable nucleus. The nucleons are somewhat trapped by the strong potential, but they can sometimes tunnel out and release stored Coulomb energy.

Chemical reactions only involve electrons and nuclei. The Coulomb force between the electron and the nucleus is much weaker than the Coulomb force between two protons in the nucleus, which is still weaker than the strong force in many scenarios.

 

[eightsquare]

Ok great. So here's a final picture. When two light nuclei fuse, their electromagnetic potential increases but their strong nuclear potential decreases much more rapidly, releasing a lot of stored energy. For an unstable nucleus, although the strong force is stronger if an activation energy is overcome then when the nucleus splits the electromagnetic potential decreases much faster than the strong potential increases, hence releasing energy. Nuclei like uranium can still however be formed, because though it takes energy to form the nucleus(strong potential doesn't decrease as fast as electromagnetic potential increases) and there is no energy release after the formation of the nucleus, the strong force is still stronger than the em force and holds the nucleus together.