材料物理course-4-question and anwser 1.pptVIP

Exercise Class 1 * * Balmer series Ans: 13.6 eV Ans: n from 1 to 4 E1=-13.6eV, E4=-0.85eV ?E=E4-E1=12.8eV Solution of the Schrodinger wave equation, which includes a potential function Epot, are only possible for quantized eigenvalues. The solution is the wave function ?. The wave function ? is used for probability calculations. All four quantum numbers (n,l,ml,mz) of two electrons within an atom cannot be equal. At least one of them must differ. The Schrodinger equation is solved for an electron in a box (the metal) with constant potential energy Epot=0. The solution shows that the energy of the electron is quantized Where k=(kxkykz) is the wavevector of the matter wave of the electron. E and kxkykz are quantized. The number of occupied energy levels = number of atoms times the valence number. The Pauli principle is valid for electrons. Hence much higher energy levels are occupied than that which a Boltzman distribution would have indicated. The upper limit of the electron energy of the free electrons is the Fermi energy EF. The work function is the energy required to release the most energetic free electrons from the metal surface. Define the wavevector and give its relationship to the eigenfunction of the free electron in one dimension Wavevector is a vector in the direction of the wave motion: With the magnitude Give the kinetic energy of a free electron as a function of the wavevector. Illustrate the function graphically. Is the curve continuous? The curve is not continuous. It consists of numerous close and discrete energy levels, because kx is quantized. Ans: 4.3 eV Define the Fermi factor and show graphically how it depends on temperature. Give the expressions of the Fermi distribution of energies in the electron gas, i.e. the densities of available and occupied energy state as a function of the electron energy. Why is the mass of the electron designated m* instead of m? m* = effective mass of an electron in the interior of the metal ? m for an electron