# Free Proton verses Nucleus Proton rest mass

• B
• Albertgauss
In summary, the rest energy of a single proton inside a Uranium atom, or any other radioactive or fissionable element, is 938.272 (with more decimals). This energy would only be associated with the rest mass of the proton while it is inside the nucleus, after subtracting out the binding energy and other forms of energy. The total mass of the nucleus is less than the sum of its individual nucleons, with the missing energy going into forming the binding energy of the atom. However, this calculation deals with all the nucleons as a system, whether separated or together in the nucleus. The energy associated with the p = 0 rest mass of a separated single proton is expected to be the same as that of a single
Albertgauss
Gold Member
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.

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.

stoomart

## 1. What is the difference between free proton and nucleus proton rest mass?

The free proton refers to a proton that is not bound to any other particles, while the nucleus proton refers to a proton that is part of an atomic nucleus. The rest mass of a proton is the mass that it has when it is at rest.

## 2. Why is there a difference in rest mass between free proton and nucleus proton?

The difference in rest mass between free proton and nucleus proton is due to the strong nuclear force. This force is responsible for binding protons and neutrons together in the nucleus, and it decreases the rest mass of a nucleus proton compared to a free proton.

## 3. How is the rest mass of a proton measured?

The rest mass of a proton is measured using mass spectrometry, which involves accelerating protons in an electric field and then measuring the curvature of their path in a magnetic field. The amount of curvature is directly proportional to the mass of the proton.

## 4. What is the rest mass of a proton?

The rest mass of a proton is approximately 1.6726219 × 10^-27 kilograms or 938.272 MeV/c^2 (megaelectronvolts per speed of light squared). This value is very close to the rest mass of a neutron, which is approximately 1.6749274 × 10^-27 kilograms or 939.565 MeV/c^2.

## 5. How does the rest mass of a proton affect its behavior in a particle accelerator?

The rest mass of a proton affects its behavior in a particle accelerator as it determines the amount of energy required to accelerate the proton to a certain speed. As the proton's speed approaches the speed of light, its mass increases due to relativistic effects, making it more difficult to accelerate. This is why higher energy accelerators are needed to study particles with larger rest masses.

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