Bill Madden 559 2123

1. Bill Madden 559 2123

2.  = (4/3ħc) nem2 (Nm-Nn) (o-) 1 2 3 4 • Square of the transition moment nem2 • Frequency of the light  • Population difference (Nm- Nn) • Resonance factor - Dirac delta function (0) = 1

3. Fermi’s Golden Rule  = (4/3ħc) nem2 (Nm-Nn) (o-) 1

4. Take Home Message n*md  nm ~ d/dq Quantum Mechanics Matrix Mechanics Dirac Notation Quantum Mechanics Wave Mechanics Schrödinger Notation Classical Analogue Dipole moment change over motion …coordinate q

5. Take Home Message n*md  nm ~ d/dq ~ Quantum Mechanics Matrix Mechanics Dirac Notation Quantum Mechanics Wave Mechanics Schrödinger Notation Classical Analogue Dipole moment change over motion …coordinate q 

6.  = (4/3ħc) nem2 (Nm-Nn)(o-) 1 2 3 4 • Square of the transition moment nem2 • Frequency of the light  • Population difference (Nm- Nn) • Resonance factor - Dirac delta function (0) = 1

7. ABC Rotation of a Diatomic Molecule

8. For pure rotational transitions a molecule must have a permanent dipole moment

9. Observing the dipole change from the side i.e. the direction of propagation

10. dμ/dθ≠ 0

11. ∆N =? Selection Rules Harry Kroto 2004

12. (Nm- Nn) Nm-Nm

13. J 2J+1 e-∆E/kTNm/No F(J) 0 1 1.000 1.00 3.84 • 3 0.9812.94 7.69 • 50.9454.73 11.5 3 70.8936.25 15.4 • 90.8287.45 19.2 • 110.7548.29 23.1 • 13 0.6738.75 26.9 • 150.5908.85 30.8 • 170.5078.62 34.6 • 190.4288.13 38.4 • 22 0.355 7.46 42.3 • 230.288 6.62 46.1 • 250.230 5.75 50.0 Nm = No e-∆E/kT In the case of degenerate levels such as rotational levels eacj J level is 2J+1 degenerate we get Nm = Noe-∆E/kT

14. 0 1 2 3 4 5 6 7 J 0 2B 4B 6B 8B 10B 12B 14B 16B Boltzmann

15. http://en.wikipedia.org/wiki/Boltzmann_constant Boltzmann

16. J 2J+1 e-∆E/kT Nm/No F(J) 0 1 1.000 1.00 3.84 • 30.9812.94 7.69 • 50.945 4.73 11.5 3 70.8936.25 15.4 • 90.8287.45 19.2 • 110.7548.29 23.1 • 130.6738.75 26.9 • 150.5908.85 30.8 • 170.5078.62 34.6 • 190.428 8.13 38.4 • 22 0.3557.46 42.3 • 230.2886.62 46.1 • 250.2305.75 50.0 Nm = No e-∆E/kT In the case of degenerate levels such as rotational levels eacj J level is 2J+1 degenerate we get Nm = Noe-∆E/kT

17. 0 1 2 3 4 5 6 7 J 0 2B 4B 6B 8B 10B 12B 14B 16B Boltzmann

18. Boltzmann Population with Degeneracy

19. J 2J+1 e-∆E/kT Nm/No F(J) 0 1 1.000 1.00 3.84 • 3 0.981 2.94 7.69 • 5 0.945 4.73 11.5 • 7 0.893 6.25 15.4 • 9 0.828 7.45 19.2 • 11 0.754 8.29 23.1 • 13 0.673 8.75 26.9 • 15 0.590 8.85 30.8 • 17 0.507 8.62 34.6 • 19 0.428 8.13 38.4 • 22 0.355 7.46 42.3 • 23 0.288 6.62 46.1 • 25 0.230 5.75 50.0 Nm = No e-∆E/kT In the case of degenerate levels such as rotational levels each J level is 2J+1 degenerate we get Nm = No(2J+1)e-∆E/kT

20. 0 1 2 3 4 5 6 7 J 0 2B 4B 6B 8B 10B 12B 14B 16B Boltzmann

21. C≡O

22. CO Rotational Spectrum PROBLEM

23. Separation Vibration Rotation

24. ABC H Atom

25. H Atom Spectrum A

26. + - Positronium

27. n m Einstein Coefficients

28. H 21 cm Line Harry Kroto 2004