# Formula Free Electron Gas in 3d Fermi temperature    Charge carrier density

## Fermi temperature

Unit
Fermi temperature is used to compare Fermi energy with thermal energy. Typical value is $$50 \, 000 \, \text{K}$$, which is well above the melting temperature of most elements. The Fermi temperature is related to the Fermi energy via the Boltzmann constant: $$T_{\text F} = \frac{E_{\text F}}{k_{\text B}}$$.

## Charge carrier density

Unit
Charge carrier density is the number $$N$$ of charges per volume $$V$$: $$n = N/V$$. Since the free Fermi gas is mostly used to describe the free electrons, $$n$$ gives the electron density.

## Mass

Unit
Mass of a particle of the Fermi gas. This can be for example the (effective) mass of the electron.

## Reduced Planck's constant

Unit
Action quantum is a physical constant (of quantum mechanics) and has the value: $$\hbar ~=~ \frac{h}{2\pi} ~=~ 1.054 \, 571 \, 817 \,\cdot\, 10^{-34} \, \text{Js}$$.

## Boltzmann Constant

Unit
This physical constant is often used in statistical physics and thermodynamics. It has the value: $$k_{\text B} ~\approx~ 1.380 \,\cdot\, 10^{-23} \, \frac{\text J}{\text K}$$.