1. Hydrogen atom energy levels deBroglie and Bohr: 1. Wavelength comes from speed: 2. Integer wavelengths fit in orbit of size r 3. F = ma:

2. Light frequencies emitted/absorbed are given by initial and final electron energy levels

3. Bohr model incomplete 1. Assumes planar orbits, while atoms are more spherical 2. The electrons are not at a single distance r

4. Angular momentum in QM Classical: any L,  allowed L Quantum: L,  are quantized angular momentum magnitude l =0,1,2… angular momentum quantum number

5. Angular momentum in QM Quantum: the component of L along any axis measured is also quantized (call the measurement axis z): We can’t know the direction of L with precision angular momentum projection quantum number m = -l…l

6. Electron spin Besides orbital angular momentum, electrons have spin angular momentum

7. Quantum states in atoms Each electron quantum state is labeled by n,l,m,m s l can be 0 … n-1 In H-atom, energy depends only on n In all other atoms, there is more than one electron, and electron repulsion makes each electron’s energy depend on all the other electrons: so state energy depends on n,l,m,m s Kinetic energy is associated with wiggles ( more peaks and nodes) in the wavefunction, radially and angularly

9. Quantum Oscillator Masses (atoms) on “springs” Perfectly even spacing of levels

10. Quantum Oscillator “Ground state energy” is ½ hf. Half of that is KE. So “Zero point KE” here is 1/4 hf Wavelengths shorten at higher KE Wavefunctions “leak” beyond classical turning points

11. Quantum Oscillator You only get “back and forth” motion when the mass is in two or more n-states at once (superposition). So a quantum system can have an average energy between quantized energies, but the only energy you will ever measure is one of the quantized energies. See diagrams G, H: wikipedia

12. Play with superposition here http://phet.colorado.edu/en/simulation/bound-states

13. Light and quantum states Absorption

14. Light and quantum states Florescence, phosphorescence

15. Florescent minerals

16. Fluorescent shirts They appear brighter than other cloth because they don’t scatter light…they convert much of the visible spectrum into a single color

17. Lasers Lase: Light Amplification by Stimulated Emission

18. Lasers Need many atoms in excited state (“Population inversion”). Photons bouncing between mirrors stimulate emission of other photons that match their phase, direction.

19. Laser level diagram Need at least electron 3 levels, one of which is long- lived or “metastable” (as in flourescence)

20. Diode lasers Inject energetic electrons into semiconductors: light emitting diode or laser