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

2. Dr. Jie ZouPHY 13712 Outline The quantum model of the hydrogen atom The wave functions for hydrogen

3. Dr. Jie ZouPHY 13713 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.

4. Dr. Jie ZouPHY 13714 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.

5. Dr. Jie ZouPHY 13715 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

6. Dr. Jie ZouPHY 13716 Relationship among the three quantum numbers

7. Dr. Jie ZouPHY 13717 Atomic shell and subshell notations

8. Dr. Jie ZouPHY 13718 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.

9. Dr. Jie ZouPHY 13719 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:

10. Dr. Jie ZouPHY 137110 Hydrogen atom in its ground state The charge of the electron is extended throughout a diffuse region of space - Electron cloud

11. Dr. Jie ZouPHY 137111 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.

12. Dr. Jie ZouPHY 137112 Example: The ground state of hydrogen Calculate the most probable value of r for an electron in the ground state of the hydrogen atom.

13. Dr. Jie ZouPHY 137113 Homework Chapter 42, P. 1393, Problems: #19, 20.