How the nuclear binding energy gives mass to the nucleus?

In summary, the conversation discusses the concept of nuclear binding energy and its relationship to high-energy particle collisions. The example provided shows how kinetic energy can be converted into rest mass, and the theory of quantum field explains this phenomenon. The conversation also mentions that the theory is not incomplete and that mathematics is necessary for understanding quantum mechanics.
  • #1
HakimPhilo
77
10
Hello everybody! :wink:
I have some difficulties concerning the concept of nuclear binding energy.
First, look at this example:
http://www.freeimagehosting.net/newuploads/jtefo.png
In the first case, the two protons have big energy. But this energy is not changing it's weight. And in the second case, when they collided, the energy that they contained transformed to new particles, so more mass.
But in the nuclear binding energy, when this energy converts into mass?

Thank you in advance...∞ :happy:
 
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  • #2
The example seems to be one of particle production rather than nuclear binding energy.

On the left side, the initial (rest?) mass is 0.3 unit, and on the right side one has 9 tracks, which are ostensibly particles and the total rest mass is now 1 unit. So the unknown or unspecified kinetic energy has been transformed into rest mass. It's not clear if the new particles are stable however.
 
  • #3
Yes, but my question is when the energy of the proton converts to mass an how? We are speaking about the nuclear-binding energy.
 
  • #4
For high-energetic particle collisions, nuclear binding energy is not relevant. You convert the kinetic energy of particles to mass of new particles.

"How": quantum field theory. It just happens, and theories can calculate the probabilities. There is no fundamental "reason" or "process" why/how it happens.
 
  • #5
mfb said:
For high-energetic particle collisions, nuclear binding energy is not relevant. You convert the kinetic energy of particles to mass of new particles.

"How": quantum field theory. It just happens, and theories can calculate the probabilities. There is no fundamental "reason" or "process" why/how it happens.
We know that it happens but then the theory is incomplete since it can't explain how it happens.
 
  • #6
The theory is not incomplete.
It is physics, not philosophy.
The theory can give you a model "how" it happens, it does not care if it is "real" (whatever that means).
 
  • #7
HakimPhilo said:
We know that it happens but then the theory is incomplete since it can't explain how it happens.
Every theory has axioms. Plane geometry says that two lines meet in a point, but it's meaningless to pose the question "how" they do. That fact does not make plane geometry incomplete.

In this case we have an initial state A and a final state B, both with the same energy but with different particles having different masses. There is a term in the Hamiltonian that connects state A with state B, and therefore Schrodinger's Equation tells us there's a probability per unit time that A will evolve into B.

You may consider this to be mathematical and unintuitive, but mathematics is necessary for an understanding of quantum mechanics.
 

Related to How the nuclear binding energy gives mass to the nucleus?

1. How does nuclear binding energy give mass to the nucleus?

The mass of a nucleus is a result of the sum of the masses of its individual protons and neutrons. However, according to Einstein's famous equation E=mc^2, energy and mass are equivalent and can be converted into each other. In a nuclear reaction, some of the mass is converted into energy, and this released energy is known as nuclear binding energy. This energy is what gives mass to the nucleus.

2. What is nuclear binding energy?

Nuclear binding energy is the amount of energy required to split or break apart a nucleus into its individual protons and neutrons. It is also the amount of energy released when these particles come together to form a nucleus. This energy is what holds the nucleus together and is responsible for the stability of atoms.

3. How does nuclear binding energy affect the stability of the nucleus?

The higher the nuclear binding energy, the more stable the nucleus is. This is because a higher binding energy means that it takes more energy to break apart the nucleus, making it more difficult for radioactive decay to occur. Elements with a higher number of protons and neutrons tend to have a higher binding energy, making them more stable.

4. How is nuclear binding energy calculated?

Nuclear binding energy is calculated using the mass defect, which is the difference between the mass of an atom and the sum of the masses of its individual protons and neutrons. This mass difference is then multiplied by the speed of light squared (c^2) to determine the amount of binding energy released.

5. What is the relationship between nuclear binding energy and nuclear power?

Nuclear binding energy is the driving force behind nuclear power. In nuclear power plants, the energy released from splitting atoms (nuclear fission) is used to generate electricity. This energy is a result of the conversion of a small amount of mass into energy, and it is the high nuclear binding energy of certain elements, such as uranium, that makes this process possible.

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