Dr. Jie ZouPHY 13711 Chapter 42 Atomic Physics (cont.)

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Presentation transcript:

Dr. Jie ZouPHY Chapter 42 Atomic Physics (cont.)

Dr. Jie ZouPHY Outline The quantum model of the hydrogen atom The wave functions for hydrogen

Dr. Jie ZouPHY The quantum model of the hydrogen atom Difficulties with Bohr theory: Many of the lines in the Balmer and other series of hydrogen are not single lines at all. Splitting of spectral lines when atoms are placed in a strong magnetic filed. Need a full quantum model involving the Schrödinger equation to describe the hydrogen atom.

Dr. Jie ZouPHY The quantum model of the hydrogen atom General strategy: Solving the Schrödinger equation for the hydrogen atom The three-dimensional time-independent Schrödinger equation: Formal procedure for solving the problem: The potential energy function for the hydrogen atom: Substitute U(r) into the Schrödinger equation and find the appropriate solutions to the equation satisfied by appropriate boundary conditions.

Dr. Jie ZouPHY Results for a Hydrogen atom Three different quantum numbers for each allowed state of the hydrogen atom ( ): Principal quantum number, n: The energies of the allowed states for the hydrogen atom depend only on n, Orbital quantum number, l Orbital magnetic quantum number, m l

Dr. Jie ZouPHY Relationship among the three quantum numbers

Dr. Jie ZouPHY Atomic shell and subshell notations

Dr. Jie ZouPHY Example: The n=2 level of Hydrogen For a hydrogen atom, determine the number of allowed states corresponding to the principal quantum number n = 2, and calculate the energies of these states.

Dr. Jie ZouPHY The wave functions for Hydrogen Wave function in the ground state 1s: Radial probability density function P(r) = 4  r 2 |  | 2. For the hydrogen atom in its ground state:

Dr. Jie ZouPHY Hydrogen atom in its ground state The charge of the electron is extended throughout a diffuse region of space - Electron cloud

Dr. Jie ZouPHY Example: Probabilities for the electron in hydrogen Calculate the probability that the electron in the ground state of hydrogen will be found outside the first Bohr radius, a 0.

Dr. Jie ZouPHY Example: The ground state of hydrogen Calculate the most probable value of r for an electron in the ground state of the hydrogen atom.

Dr. Jie ZouPHY Homework Chapter 42, P. 1393, Problems: #19, 20.