[gaze]

Links [1] and [3] are wrong, and link [2] is correct but has nothing to do with this discussion. Link [1] is so full of errors it isn't even worth discussing. The pingpong ball analogy is wrong--it's all wrong. Link [3] commits the sin of ascribing single-electron behavior to parameters extracted from the Drude model. This is a semiclassical analogy and worked essentially thanks to units.

Here's the link you're looking for. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/Fermi.html . Two electrons can't occupy the same state. In a metal of finite size, the momentum spectrum becomes quantized. Two electrons can occupy each k-state, one for spin up, one for spin down. Considering an empty metal, we can insert electrons one by one. They will find their lowest energy by packing into a sphere in k-space. Electrons inside the sphere have no states to scatter into, and there are no electrons occupying states outside the sphere. This means that only electrons on the surface of this sphere participate in conduction. The radius of this sphere is called the Fermi wavevector, and converting to units of velocity you get the Fermi velocity. All electrons participating in conduction travel at approximately the fermi velocity... at room temperature plus or minus a tiny fraction of a percent.

[ethn]

Drift velocity has everything to do with the discussion, which is why you brought it up.

I’m familiar with Pauli exclusion principle I’ve worked on real semiconductors.

Your last point is wrong, everything else you said is correct but it remains irrelevant since it does not contradict what was said. Both links are correct.

As you know the net fermi velocity of a fermion is 0. The directional velocity resulting from an electric field on an electron, the fermi velocity which becomes directional due to net flow, is the drift velocity. Which is what we care about.

You can do a simple experiment with NMR to measure the speed of electrons. Indeed they’ve done it and it corresponds to the “wrong calculations”.[1]

Edit: Good resource [2] to help you understand the difference between those two velocities:

> However, the drift velocity of electrons in metals - the speed at which electrons move in applied electric field - is quite slow, on the order of 0.0001 m/s, or .01 cm/s. You can easily outrun an electron drifting in a metal, even if you have been drinking all night and have been personally reduced to a very slow crawl.

> To summarize, electrons are traveling in metals at the Fermi velocity vF, which is very, very fast (106 m/s), but the flux of electrons is the same in all directions. That is, they are going nowhere fast. In an electric field, a very small but directional drift velocity is superimposed on this fast random motion of valence electrons.

[1] https://physics.aps.org/story/v17/st4

[2] https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/...

[gaze]

> All electrons participating in conduction travel at approximately the fermi velocity... at room temperature plus or minus a tiny fraction of a percent.

> Your last point is wrong

> To summarize, electrons are traveling in metals at the Fermi velocity vF

your own quote. come on. I have a phd in this shit.

[ethn]

Many people on HN have a PhD in similar fields but that isn't relevant, though it's the smart people here that give us these thoughtful conversations on HN.

No one has disagreed with it, I explicitly agreed with you on the existence of Fermi velocity. I don't have the ability to downvote, but you were downvoted because you mentioned the fermi velocity in contradiction to electron flow even though it is the drift velocity that is pertinent in the original context of electricity (which requires a non-net zero velocity).