Chapter Outline Single Particle SE for H-atom Angular Moment QN H-atom Atomic Orbitals Atomic Orbitals & Spectroscpy Multielectron Systems

Single Particle Under Central Force The Hamiltonian No dependence on direction – spherically symmetric PE depends only on position: Single Particle Under Central Force Reduced mass: Approximate as a single particle system with the massive proton being fixed Enter H-atom We have a 2 particle system with 1 proton & 1 electron

Getting our DiffEq SE for H-atom

Isolating R(r) & Y(,) SE for H-atom

We get to our l QN when we apply Angular Moment & QNs

H Atomic s & Orbitals Getting to En Hydrogen Atomic s Now for R(r) First few  with Z = atomic # H Atomic s & Orbitals Now for R(r)

Recall the QNs The Atomic Orbitals

The Atomic Orbitals Radial Distribution Plots Nodes: location where the probability is zero S-Orbitals The max for 1s is located at a0 P-orbitals m = 0 for –pz orbital m =  1 for px & py orbitals The Atomic Orbitals d-Orbitals are similar

Skip!!! For now

Multi-electron Systems The Problem Multi-electron Systems We can solve it exactly for 1 e- systems We cannot get an analytic solution for more than 1 e- We will discuss approximate/numeric solutions in Ch 8