I have a number of titanium atoms. I'm trying to find the total electron energy of this. I know that one formula is

Total Electron Energy = (3/5) * (Number of Electrons) * (Fermi Energy)

but I don't know what the Fermi Energy of titanium is even after quite a bit of research. Is there any other way to find the total electron energy of titanium given just the number of atoms?


The formula you mention is for the energy of a free electron model. That's an idealized model for very weakly interacting electrons in the molecular structure of solids. This model in turn relates to the Fermi Gas model. That link to Wikipedia's page on the Fermi Gas goes into more detail on the derivation of the theory and related results.

The Fermi Energy is given by :

$$E_F=\frac{\hbar ^2}{2m_e}\left(\frac{3\pi^2N}{V}\right)^{\frac 2 3}$$

Where $N$ is the number of particles and $V$ is the volume occupied.

I would point out that this model, although useful, does not give the full picture and is probably best thought of as giving you an order of magnitude for the total energy value you want.

  • $\begingroup$ For the particles, is it the number of electrons? atoms? Also, if this model does not give the full picture, do you know a better one to serve the purpose? $\endgroup$
    – Undefined
    Mar 12 '21 at 3:26
  • $\begingroup$ @Undefined Sorry for the confusion. It should be the total number of valence electrons. I think it's 4 (per atom) for Titanium. What model is appropriate depends on what you want to do. I'd suggest reading Wikipedia's page on Solid State Physics which has some info on alternative models and those links will have even more links to more detail and models. $\endgroup$
    – StephenG
    Mar 15 '21 at 13:16

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