Lecture 28 Hydrogen 3d, 4s and 4p 4s 3d 4p We can get some insight into the relative Energies of these three orbitals from the website:

Lecture 28 The periodic Table

Lecture 28 Atomic Radii See also:

Lecture 28 Combining angular momentum

Lecture 27 Energy splitting for 2 electrons in the 4p/4d states This corresponds to the case of two electrons in a 4p,4d level in which inner electrons are not providing any separation between the two; it considers only the interaction between these two electrons and relativity (only relevant to excited States of Helium or ions with only two electrons, not terribly realistic).

Lecture 28 Relativistic effects (S-O coupling, mass increase) f=2.46x10 15 Hz~ 2.5 PHz. Fine structure effects are on the order of ppm

P301 Exam II Review NO CALM QUESTION FOR FRIDAY!!! Exam Mechanics: Covers material from sections 5.2 thru 8.3 (but of course, some material from earlier sections may come in as well). 1 side of 8.5x11” formula sheet is allowed. It is not to be a general note sheet 4 questions with 9 parts (each worth 6 points) All have computational/short answer this time (no expt. descriptions). Tables from the inside front lay-out of the text will be provided. Exam will start at 11:10. Office Hours: Wednesday 2:30 to 3:30 (Forum) Thursday 4:00 to 5:00 ??? Friday 8:45 to 10:00 No office hours Friday afternoon.

P301 Exam I Review Important results/topics: Chapter 5 (4 lectures): Bragg’s law (as applied to particles) DeBroglie waves Fourier Analysis/ Wave packets /Group velocity Uncertainty Relations (position-momentum; time-energy) Wave-particle duality and the Copenhagen interpretation. Chapter 6 (5 lectures): Schrodinger Equation (time dependent and time-independent) Properties of wave functions and the application of boundary conditions. (e.g. problem 2 (7-38) on today’s assignment) Expectation values and the physical significance of  (x,t) Square wells (infinite and finite). Operators in quantum mechanics Confinement energy Quantum Simple Harmonic Oscillator Tunneling

P301 Exam I Review Important results/topics: Chapter 7 (3 lectures): Schrodinger Equation in spherical polar coordinates and angular/radial separation of variables Principal and Angular momentum quantum numbers Differences between the “Schrodinger” and “Bohr” hydrogen atom. Properties of the radial wave functions for hydrogen Selection rules (  l =+/-1,  m l =+/-1,  J=0,+/-1 (J:0->0 forbidden),  S=0. Zeeman effect Intrinsic spin and the Stern-Gerlach experiment Chapter 8 (3 lecutres): Pauli Exclusion principle Structure of the periodic table and the role played therein by inter- electron interactions (and radial wave function shapes) and Pauli. Angular momentum (magnitude and projection quantum numbers, uncertainty relations, etc.) Addition of Angular momenta Spectroscopic Notation Hund’s rules (especially number 1).

Examples Draw a sketch of the wave function for two lowest energy states in this potential (assuming that at least two exit) and emphasizing any features that are different for the two states. The wave function for a potential given by a delta-function (negative infinity at the origin, zero everywhere else) is given by Aexp(-|x|/a). What is the probability that the particle will be found at a distance greater than “a” from the origin? Nitrogen has atomic number 7, what electronic states would you expect to be occupied when a nitrogen atom is in its ground state, and what might you expect to be the lowest- lying excited state for this atom? {this is an example of a non- computational question that you could be asked}

(sort of) The K  x-ray line is actually a doublet (K  1, K  2 ) where the Difference between the two is quite small (20 eV out of 8keV for Cu for Instance). What is the origin of the energy splitting between these two lines and why are there two (and only two) lines? 5-