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

$$ n $$ Unit $$ \frac{1}{\mathrm{m}^3} $$

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

$$ m $$ Unit $$ \mathrm{kg} $$

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

Reduced Planck's constant

$$ \hbar $$ Unit $$ \mathrm{Js} $$

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

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

You must have JavaScript enabled to use this form.

Give feedback

Hey! I am Alexander, the physicist and author here. It's important to me that you are satisfied when you come here to get your questions answered and problems solved. But since I don't have a crystal ball, I depend on your feedback. That way I can eliminate mistakes and improve this content so that other visitors can benefit from your feedback.

How satisfied are you?

Very nice!

If there is anything you would like to see improved, please send me a message below. I would be very happy if you support the project.

Hmm...

Would you mind telling me what you were missing? Or what you didn't like? I take every feedback to heart and will adapt and improve the content.

What's the trouble?

Do not be disappointed, I can certainly help you. Just send me a message what you actually wanted to find here or what you don't like. I really take your feedback seriously and will revise this content. If you are very disappointed, explain your concern in the feedback and leave your email and I will try to help you personally.