Comparing Silver Electron Spacing & Free-Electron Model

[bobred]

Homework Statement

Compare the electron spacing of silver (0.26 nm) to the estimate for mean free path calculated earlier (52 nm), explain the discrepancy in terms of Pauli's free-electron model of conductivity.

Homework Equations

The Attempt at a Solution

I would say this is down to the exclusion principle. The translational energies are spread out across a great range as only two electrons can occupy a given translational energy state.
Am I on the right track.

Thanks

 

[mark726]

for your question. Yes, you are on the right track. In Pauli's free-electron model of conductivity, electrons are treated as a gas of free particles that can move independently. The exclusion principle states that no two electrons can occupy the same quantum state simultaneously. In the case of silver, the electron spacing is much smaller than the mean free path because the electrons are tightly packed together in the metal. This means that the electrons are constantly interacting with each other, leading to collisions and scattering, which in turn reduces the mean free path of the electrons. Therefore, the discrepancy between the electron spacing and mean free path in silver can be attributed to the exclusion principle and the interactions between electrons in the metal.