Question

1) Free electron model: (a) Show that the mean kinetic energy of one electron
in the quantum mechanical free electron model is 3/5 E F at T = 0 K.
(b) Calculate the Fermi energy and the mean kinetic energy for potassium
in electron volts. Use that K has a relative atomic mass of M = 39.1 u and a
density of 856 kg m^−3 . (c) Calculate the corresponding electron velocities.
(d) Calculate the density of states at the Fermi energy. How large is the
number of electrons in the “soft zone” of about 4kbT around the Fermi
energy at room temperature relative to the total number of electrons?
(e) Estimate the Thomas–Fermi screening length in potassium.

Chapter 6, Problem 1 from Solid State Physics: An Introduction 2nd edition

(Please answer parts a) - e), thank you very much!)

Answer 1