I've been asked to estimate the number of electrons in a metal, and the number of electrons available for conduction. I don't want to use proper Fermi-Dirac or anything, I just want an easy way to estimate it.

So for number of electrons, that easy enough: $$ n_e=\frac{\rho_e}{V} $$ where $n_e$ is the number of electrons, $\rho_e$ the density and $V$ the volume.

I know how to find density of states and all that, but that's working out the answer, not really "estimating".

put on hold as off-topic by Jon Custer, Kyle Kanos, Emilio Pisanty, glS, JMac Aug 13 at 14:39

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  • 1
    I’m not your dude, and I’m not interested in doing your homework. Since you know how to do it properly, one might suppose you would know how to estimate it. So do the back of the envelope estimate. – Jon Custer Aug 9 at 15:09
  • I don't know a way to estimate the occupancy * dos over de, with de being the whole cb. I cant even imagine how that would be estimated. I feel like I may have forgot something from way at the beginning, and I cant find anything – tgmjack Aug 9 at 15:13
  • Is the conduction band empty, full, or somewhere in between? – Jon Custer Aug 9 at 15:17
  • depends on the metal / temperature etc. the question is as simple as ive asked it. no real details given. just "estimate the number of e available for conduction" – tgmjack Aug 9 at 15:21
  • If it is a metal, the conduction band is neither full nor empty. – Jon Custer Aug 9 at 15:22