(4) Find the Fermi energy of lithium Er, the Fermi temperature TF, and the speed of wF of the fastest free electrons.

(a) If EF equals Eo, calculate the Fermi probability of a state being occupied at E=E₂+kT. (b) If EF equals Ev, determine the probability of a state being empty at E=E,-kT. (c) Find the probability that an energy level is occupied by an electron when the state is positioned above the Fermi level by 5kT. (d) Determine the probability that an energy level is occupied by an electron when the state is positioned above the Fermi level by 10kT. Utilize Fermi-Dirac statistics with a temperature of T=300K.

Grüneisen parameter for silicon The silicon crystal (diamond structure) has the following properties at 500 K. The lattice parameter (a) = 0.5440 nm, thermal expansion coefficient (a) = 3.6x106 K-', and the bulk modulus is about the same as that at room temperature (K = 99 GPa). The Debye temperature of Si is 625 K. At room temperature (300 K) its density is 2.33 g cm³, and its lattice constant is 0.5430 nm. Calculate the Grüneisen parameter at 500 K and compare with its value at room temperature in Table 1. Is 3 constant?

Copper metal can be well-described by assuming that the electrons inside are free, with a den- sity ne = 8.47 × 1028 m-³. Calculate the Fermi energy EF.