tron in the valence band over the range E,- 2kT eV< beng emply by an el E< E. 3.35 The probability that a state at E. + kT is occupied by an electron is equal to the prob- ability that a state at E, - kT is empty. Determine the position of the Fermi energy | level as a function of E, and Ey. 3.36 Six free electrons exist in a one-dimensional infinite potential well of width a = 12 Å. Determine the Fermi energy level at T = 0 K. 3.37 (a) Five free electrons exist in a three-dimensional infinite potential well with all three widths equal to a = part (a) for 13 electrons. 3.38 Show that the probability of an energy state being occupied AE above the Fermi energy is the sáme as the probability of a state being empty AE below the Fermi level. 3.39 (a) Determine for what energy above EF (in terms of kT) the Fermi-Dirac probability function is within 1 percent of the Boltzmann approximation. (b) Give the value of the probability function at this 3.40 The Fermi energy level for a particular material at T trons in this material follow the Fermi-Dirac distribution function. (a) Find the probability of an electron occupying an energy at 5.80 eV. (b) Repeat part (a) if the temperature is increased toT = 700 K. (Assume that EF is a constant.) (c) Determine the temperature at which there is a 2 percent probability that a state 0.25 eV below the Fermi level will be empty of an electron. 12 Å. Determine the Fermi energy level at T= 0 K. (b) Repeat energy. = 300 K is 5.50 eV. The elec- 5.41 The Fermi energy for copper at T = 300 K is 7.0 eV. The electrons in copper follow the Fermi-Dirac distribution function. (a) Find the nrohahility of an energy lexel at

3 The Fermi-Dirac distribution provides the fraction of electrons that can be found for a given electron energy and temperature of the material. Silicon is a widely use semiconductor for computer processors and GPUs, with a band gap of 1.11 eV at room temperature (293 K). a) What is the Fermi energy of Silicon at room temperature? b) Calculate the electron concentration (total number of electrons) at 0.6 eV above the fermi level (in the conduction band) of one mol of silicon (each silicon atom contributes 4 electrons).

Q2 part c

4. Calculate the potential energy of the system of Na* and CI ions when they are at a distance of 4Å.