Free Proton verses Nucleus Proton rest mass

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SUMMARY

The rest mass of a free proton is definitively 938.272 MeV in the center of momentum frame where its momentum is zero. When considering a proton within a Uranium atom, the rest energy associated with it remains the same unless it undergoes β+ decay, which transforms it into a neutron. The concept of "rest energy inside a proton" is misleading, as a proton within a nucleus is not completely at rest due to the presence of kinetic energy. The mass of the proton does not change when it is bound within the nucleus compared to its free state.

PREREQUISITES
  • Understanding of nuclear physics concepts, particularly binding energy
  • Familiarity with the principles of mass-energy equivalence
  • Knowledge of β+ decay and its implications on nucleon transformations
  • Basic grasp of the structure of atomic nuclei, specifically Uranium
NEXT STEPS
  • Research the concept of binding energy in atomic nuclei
  • Study the process and implications of β+ decay in nuclear reactions
  • Explore the principles of mass-energy equivalence as outlined by Einstein's theory
  • Investigate the differences between free and bound nucleons in various elements
USEFUL FOR

This discussion is beneficial for nuclear physicists, students studying atomic structure, and anyone interested in the energy dynamics of protons within atomic nuclei.

Albertgauss
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The energy associated with the mass of a free proton in the center of momentum frame where the proton’s momentum is zero is 938.272 (with more decimals).

What is the rest energy of a single proton inside a Uranium atom? (It could be any other radioactive or fissionable element but I took something common for an example). That is, if I subtracted out the binding energy and all other forms of energy for the proton while inside the atom, how much energy would be left that would only be associated with the rest mass of the proton while it is inside the nucleus?

I know there are calculations where the total mass of the nucleus is less than the mass of its individual nucleons if the masses of the individual nucleons were summed together. This missing energy goes into forming the binding energy of the atom. But these calculations deal with all the nucleons as a system, whether separated into individual particles or all together in the nucleus. I want to compare the energy associated with the p = 0 rest mass of a separated single proton to the p = 0 rest mass of a single proton in the nucleus.
 
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Albertgauss said:
I want to compare the energy associated with the p = 0 rest mass of a separated single proton to the p = 0 rest mass of a single proton in the nucleus.
It should be the same unless the bound proton transforms into a neutron through β+ decay.
 
"Rest energy inside a proton" is a problematic concept because a proton inside a nucleus is not "at rest" (without kinetic energy) in any frame. The mass is the same inside a nucleus.
 
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