1 / 35

m 1

Rigid Diatomic molecule. m 2. m 1. I = r 2  = m 1 m 2 /(m 1 +m 2 ). Harry Kroto 2004. Rigid Diatomic molecule. m 2. m 1. I = r 2  = m 1 m 2 /(m 1 +m 2 ). B (MHz) = 505391/I (u Å 2 ) B (cm -1 ) = 16.863/I (u A 2 ). Harry Kroto 2004.

rlindholm
Télécharger la présentation

m 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Rigid Diatomic molecule m2 m1 I = r2 = m1m2/(m1+m2) Harry Kroto 2004

  2. Rigid Diatomic molecule m2 m1 I = r2 = m1m2/(m1+m2) B (MHz) = 505391/I (u Å 2) B (cm-1) = 16.863/I (u A2) Harry Kroto 2004

  3. Rotational Spectroscopy of Linear Molecules Harry Kroto 2004

  4. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) Harry Kroto 2004

  5. Rotational Spectroscopy of Linear Molecules J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 0 Harry Kroto 2004

  6. Rotational Spectroscopy of Linear Molecules J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 1 2B 0 Harry Kroto 2004

  7. Rotational Spectroscopy of Linear Molecules J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 2 6B 1 2B 0 Harry Kroto 2004

  8. Rotational Spectroscopy of Linear Molecules J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  9. Rotational Spectroscopy of Linear Molecules J J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  10. Rotational Spectroscopy of Linear Molecules J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 5 30B 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  11. Rotational Spectroscopy of Linear Molecules J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 6 42B 5 30B 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  12. Rotational Spectroscopy of Linear Molecules J 7 56B J BJ(J+1) 0 0 1 2B 2 6B 3 12B 4 20B 5 30B… 6 42B 5 30B 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  13. Harry Kroto 2004

  14. Rotational Spectroscopy of Linear Molecules J 7 56B F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 6 42B 5 30B 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  15. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 0 Harry Kroto 2004

  16. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 1 2B 0 Harry Kroto 2004

  17. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 2 6B 1 2B 0 Harry Kroto 2004

  18. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  19. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  20. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  21. Rotational Spectroscopy of Linear Molecules F(J) = BJ(J+1) 0 2B 6B 12B 20B 30B… F(J) = 2B(J+1) 2B 4B 6B 8B 10B 12B… 6 42B 5 30B 4 20B 3 12B 2 6B 1 2B 0 Harry Kroto 2004

  22. Rotational Spectroscopy Harry Kroto 2004

  23. Nuclear Energies H + H E(r) Chemical Energies Rotational levels 0 r  Harry Kroto 2004

  24. Rotational Spectra Linear Molecules E = ½I2 Rigid Diatomic molecule Angular velocity  m2 m1 • I = r2 • = m1m2/(m1+m2) Harry Kroto 2004

  25. Rigid Diatomic molecule Angular velocity  m2 Rotational Energy Linear Diatomic Molecules E = ½I2 m1 • I = r2 • = m1m2/(m1+m2) Harry Kroto 2004

  26. A Classical Description > E = T + V E = ½I2 V=0 B QM description > the Hamiltonian H J  = E J  H = J2/2I C Solve the Hamiltonian > Energy Levels F (J) = BJ(J+1) D Selection Rules > Allowed Transitions J =±1 E Transition Frequencies > F B(J+1) F Intensities > THE SPECTRUM J Analysis > Pattern recognition; assign J numbers H Experimental Details > microwave spectrometers I More Advanced Details: Centrifugal distortion, spin effect J Information obtainable: structures, dipole moments etc Harry Kroto 2004

  27. Rotational Spectra Linear Molecules E = ½I2  J2/2I (J = I ) E = ½ mv2  p2/2m (p = mv) H = J2/2I (Note V= 0) Harry Kroto 2004

  28. Rotational Spectra Linear Molecules E = ½I2  J2/2I (J = I ) E = ½ mv2  p2/2m (p = mv) H = J2/2I (Note V= 0) Harry Kroto 2004

  29. H = J2/2I J J2J  = ħ2 J(J+1) E(J) = (ħ2/2I) J(J+1) F(J) = B J(J+1) B = ħ2/h2I MHz B = ħ2/hc2I cm-1 J J2J  J*J2 Jd Harry Kroto 2004

  30. A Classical Description > E = T + V E = ½I2 V=0 B QM description > the Hamiltonian H J  = E J  H = J2/2I C Solve the Hamiltonian > Energy Levels F (J) = BJ(J+1) D Selection Rules > Allowed Transitions J =±1 E Transition Frequencies > F B(J+1) F Intensities > THE SPECTRUM J Analysis > Pattern recognition; assign J numbers H Experimental Details > microwave spectrometers I More Advanced Details: Centrifugal distortion, spin effect J Information obtainable: structures, dipole moments etc Harry Kroto 2004

  31. H = J2/2I J J2J  = ħ2 J(J+1) E(J) = (ħ2/2I) J(J+1) F(J) = B J(J+1) B = ħ2/h2I MHz B = ħ2/hc2I cm-1 J J2J  J*J2 Jd Harry Kroto 2004

  32. H = J2/2I J J2J  = ħ2 J(J+1) E(J) = (ħ2/2I) J(J+1) F(J) = B J(J+1) B = ħ2/h2I MHz B = ħ2/hc2I cm-1 J J2J  J*J2 Jd Harry Kroto 2004

  33. H = J2/2I J J2J  = ħ2 J(J+1) E(J) = (ħ2/2I) J(J+1) F(J) = B J(J+1) B = ħ2/h2I MHz B = ħ2/hc2I cm-1 J J2J  J*J2 Jd Harry Kroto 2004

  34. H = J2/2I J J2J  = ħ2 J(J+1) E(J) = (ħ2/2I) J(J+1) F(J) = B J(J+1) B = ħ2/h2I MHz B = ħ2/hc2I cm-1 J J2J  J*J2 Jd Harry Kroto 2004

More Related