"Sea" of electrons in metals

Brock

Is it a "floating" sea of electrons in metals? meaning they are not restricted to a spot relative to the atoms, but they just "float" around as long as it's in the metal, and the charge is almost perfectly level throughout the metal. (I doubt it would be absolutly entropicly level)

Arn't electrons pulled by gravity? So a metal pole being held up vertically would stay there because the atoms are "locked" into place with relation to eachother, but the floating electrons are not, so would they fall to the bottom edge of the pole? This effect might be very very small because the entropy of the charge forces would be much stronger then gravity.

Ariste

To your first question, yes, I think they do just 'float' around in the metal.

As for your second question, I'm pretty sure that gravity is so insignificant as to be meaningless on the atomic scale. The other forces (electromagnetic, strong nuclear, weak nuclear) are many orders of magnitude stronger. So no, the electrons will not 'fall' to the bottom of the pole. If they did, you'd get shocked every time you touched a pole ;)

olgranpappy

In this case you are right since the two energy scales that should be compared are the typical
energies of free electrons in the fermi sea versus typical gravitational potential energies. Thus we are comparing a number on the order of 10 eV (typical fermi energy) to the number
[tex]
m_e g h
[/tex]
where h is the height.

In order for the gravitational potential energy to be comparable one would need
[tex]
h \approx 10000 \textrm{meters}
[/tex]

If, on the other hand, we were talking about a free gas of, say, air molecules instead of electrons, then we would compare to kT (much less than typical E_f usually) and find a height of much less. That's why one does have to take gravitational potential energy into account in the thermodynamics of air in the atmosphere, for example... but for the case of electrons in a rod one can safely ignore gravity except in the case of a very very very long rod.

Cheers.

Gokul43201

This is only true within a Jellium model where the fixed positive charge is assumed to be uniformly distributed. In reality, the charge density is different depending on whether you are near a lattice site or far from it (i.e., since the underlying potential is not invariant under continuous spatial translations, neither should you anticipate the resulting charge density to be).

See also:
Bloch states
Nearly free electron approximation
Tight binding model

Brock

Thanks. I wounder if spinning a star shaped (or anything that comes to points on the outer radious) piece of metal, at extremely fast rmp would cause a voltage difference from the centre of the spin to the outer edge of the spin. Or are the other forces that keep the electrons still far too stronge to overcome? Well ofcourse there would be some voltage, though maybe unmeasureably small.

olgranpappy

that's an interesting question, but again I think that the frequency would have to be quite high indeed to observe any effect.

Gokul43201

I'd imagine that would take tangential velocities comparable to the Fermi velocity (~10⁶ m/s) before you notice much change in the charge density.