Fermi Gas Model: Energetic Degeneration & the Pauli Exclusion Principle

In summary, the fermi gas model assumes a 3D potential well with "energetic degeneration" for each three index "nx, ny, nz". However, this assumption does not hold true for a real nucleus because the potential well is not a cube. This leads to the question of why there are only two particles for each state in the image, which is due to the simplification of a 1D potential well.
  • #1
lukka98
30
1
Potential-functions-used-in-the-Fermi-gas-model-of-the-nucleus-as-well-as-some-model_Q320.jpg

In the fermi gas model, there is assumption that there is a 3D potential well, but there is "energetic degeneration" for each three index "nx, ny, nz".
Now the problem is with that image, if there is degeration, for some level En there may be 10 distinctive state with same energy, so there is 20 proton and 20 neutron for Pauli exclusion in that state, why in the image there are only two particle for each state?

Is because is a 1D potential well, just for simplify?

thanks
 
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  • #2
It's a very simplified sketch, and the real potential well is not a cube so treating x,y,z independently isn't working in a real nucleus.
 

1. What is the Fermi Gas Model?

The Fermi Gas Model is a theoretical model used to describe the behavior of a large number of particles, such as electrons, in a system. It assumes that the particles are non-interacting and obey the laws of quantum mechanics.

2. What is energetic degeneration in the Fermi Gas Model?

Energetic degeneration refers to the fact that in the Fermi Gas Model, particles can have the same energy level. This is due to the Pauli Exclusion Principle, which states that no two particles can occupy the same quantum state simultaneously.

3. How does the Pauli Exclusion Principle affect the Fermi Gas Model?

The Pauli Exclusion Principle plays a crucial role in the Fermi Gas Model. It dictates that particles with half-integer spin, such as electrons, cannot occupy the same quantum state. This leads to the formation of energy levels and energetic degeneration in the model.

4. What is the significance of the Fermi energy in the Fermi Gas Model?

The Fermi energy, also known as the Fermi level, is the highest energy level that is occupied by electrons in a system at absolute zero temperature. It is a crucial parameter in the Fermi Gas Model as it determines the behavior of the system, such as its electrical and thermal conductivity.

5. How does the Fermi Gas Model explain the properties of metals?

The Fermi Gas Model is often used to explain the properties of metals, such as their electrical and thermal conductivity. This is because metals have a high density of free electrons, which can be described by the Fermi Gas Model. The model also explains why metals are good conductors of electricity and heat due to the high mobility of the free electrons.

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