# Fermi Dirac / Maxwell Boltzmann Statistics, electron in metal at room temperature.

Ok so my question is as follows:

Can Maxwell Boltzmann statistics be used to describe electrons in a metal at room temperature?

I know that the Fermi Temperature in metals is about 10^4 K or something rather high, so does that mean that the metal / electron gas would need to be at a temperature of over 10^4K to be described by MB Statistics? So at room temp of about 300k

What about if the electrons were all replaced with something much heavier, say muons (approx 200x mass). What would you use then? My understanding is quantum gases occur at low temperatures / high densities (when the concentration is higher than the quantum concentration?) so does that mean the fermi temperature would be higher?

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the fermi temp is inversely proportiional to particl mass

well, as far as i know, its only at high temperature that fermi-dirac, bose-einstein and maxwell-boltzmann statistics amount to the same thing-if u look at some graph. and room temperature isn't high temperature, right? so maxwell boltzmann stats can't b used.
correct me if im wrong

No it can't. The electron density is too high and the Fermi Temp is on the order of a few thousand Kelvin. Thus, electrons are not excited far above the Fermi Temperature and there is a fairly well defined fermi surface that can be examined experimentally. There simply is not enough thermal scattering to get you to the maxwell-boltzmann limit.

well, as far as i know, its only at high temperature that fermi-dirac, bose-einstein and maxwell-boltzmann statistics amount to the same thing-if u look at some graph. and room temperature isn't high temperature, right? so maxwell boltzmann stats can't b used.
correct me if im wrong
It is appropriate to use MB statistics on an electron system when the probability of two electrons ever vying for the same state is extremely small. In other words if the effect of pauli-exclusion is insignificant. This is definitely not the case below the Fermi temperature where the vast majority of electrons are stuck in the first available state dictated by the pauli-exclusion principle. In fact this wouldn't even be valid on the surface of the sun, much less room temperature.

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