1. Understanding Atoms Chapter 42

3. The Bohr Model – good but not perfect! For Hydrogen and “Hydrogenic” atoms predicts the Rydberg formula For Hydrogen and “Hydrogenic” atoms predicts the Rydberg formula R is the Rydberg constant for the element, Z is the atomic number (nuclear charge) and n & m are integers R is the Rydberg constant for the element, Z is the atomic number (nuclear charge) and n & m are integers Bohr Model fails hopelessly for Helium and most heavier atoms! Bohr Model fails hopelessly for Helium and most heavier atoms! go to spreadsheet

4. Fine Structure High resolution spectroscopy shows that the Balmer lines are multiplets! High resolution spectroscopy shows that the Balmer lines are multiplets!

5. Key Concepts… Energy solutions for SE can consist of combinations of radial and angular terms Energy solutions for SE can consist of combinations of radial and angular terms Conservation Laws help “set” the selection rules for atomic transitions Conservation Laws help “set” the selection rules for atomic transitions “Forbidden” transitions still occur but with very low probability. “Forbidden” transitions still occur but with very low probability.

6. Will that be one hump or two? Bohr model “n” (principal quantum number) represents energy level Bohr model “n” (principal quantum number) represents energy level QM “n” represents number of humps in the radial wavefunction QM “n” represents number of humps in the radial wavefunction

7. The radial – angular selection rules: n = energy level = maximum number of humps n = energy level = maximum number of humps l = orbital angular momentum ( l = 0,1,2, … n-1) l = orbital angular momentum ( l = 0,1,2, … n-1) m = z-component of angular momentum (-l, -(l-1)m, … (l-1),1) m = z-component of angular momentum (-l, -(l-1)m, … (l-1),1) m s = z-component of electron spin m s = z-component of electron spin

8. How to make atoms… The rules for n, n r, l and m s tell us how many different energy eigenfunctions exist for an atom The rules for n, n r, l and m s tell us how many different energy eigenfunctions exist for an atom Example 42.4 Example 42.4

9. Stern and Gerlach (SG) Link to fascinating historical account of the SG experiment – how a cheap cigar changed physics!

10. Using the “rules”

11. Photons Spin? Photons carry angular momentum – they are “spin-1 particles” All photons carry the same angular momentum: L = ±ћ Confirmed by number of ingenious experiments in the 1930s

12. Photon spin and allowed transitions… Photon’s are spin=1 particles (bosons) Photon’s are spin=1 particles (bosons) Electron transitions – to conserve angular momentum - are “l = ±1” transitions Electron transitions – to conserve angular momentum - are “l = ±1” transitions Transitions that violate the above rule are not strictly prohibited – they have a very low probability of occurrence Transitions that violate the above rule are not strictly prohibited – they have a very low probability of occurrence

13. Hydrogen and Multi-Electron Atoms HydrogenSodium

14. Metastable states and Forbidden or Auroral Transitions

15. Example questions… Practice with radial and angular parts use this applet Practice with radial and angular parts use this appletapplet