@@ -212,8 +212,8 @@ $g(E) \propto E^2$ ⇒ total energy is $T \times T^3$ ⇒ $C_V \propto T^3$.
#### Exercise 1: potassium
The Sommerfeld model provides a good description of free electrons in alkali metals such as potassium, which has a Fermi energy of 2.12 eV (data from Ashcroft, N. W. and Mermin, N. D., Solid State Physics, Saunders, 1976.).
1. Check the [Fermi surfaces](fermi_surfaces.md) in the attic. Explain why potassium and (most) other alkali metals can be described with the Sommerfeld model.
2. Calculate the corresponding Fermi temperature, Fermi wave vector and Fermi velocity.
1. Check the [Fermi surface database](fermi_surfaces.md) in the attic. Explain why potassium and (most) other alkali metals can be described with the Sommerfeld model.
2. Calculate the Fermi temperature, Fermi wave vector and Fermi velocity for potassium.
3. Why is the Fermi temperature much higher than room temperature?
4. Calculate the free electron density in Potassium.
5. Compare this with the actual electron density of Potassium, which can be calculated by using the density, atomic mass and atomic number of Potassium. What can you conclude from this?