1 / 44

Rotational Spectroscopy of Linear Molecules

Explore the far infrared spectrum of the diatomic molecule CO to measure line frequencies accurately, determine the Bo value for rotational transitions, and calculate the bond length in Ångstroms. The analysis involves rotational spectroscopy of linear molecules, deriving formulas for Bo, and investigating energy levels and selection rules for transitions.

andreabush
Download Presentation

Rotational Spectroscopy of Linear Molecules

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. This is the far infra red spectrum of the diatomic molecule CO. It is due to absorption by pure rotational transitions of this molecule. Measure the line frequencies as accurately as possible and thus determine the Bo value and from this calculate a bond length in Å.

  2. This is the far infra red spectrum of the diatomic molecule CO. It is due to absorption by pure rotational transitions of this molecule. Measure the line frequencies as accurately as possible and thus determine the Bo value and from this calculate a bond length in Å. I = μro2μ = m1m2/(m1+m2) Io (uÅ2) = 16.863/ Bo(cm-1) Assume C has mass 12.0 and O mass 16.0

  3. This is the far infra red spectrum of the diatomic molecule CO. It is due to absorption by pure rotational transitions of this molecule. Measure the line frequencies as accurately as possible and thus determine the Bo value and from this calculate a bond length in Å. I = μro2μ = m1m2/(m1+m2) Io (uÅ2) = 16.863/ Bo(cm-1) Assume C has mass 12.0 and O mass 16.0 NB The subscript o indicates that Bo, Io and ro are for the v=0 vibrational state

  4. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  5. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  6. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  7. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  8. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  9. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  10. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  11. Rotational Spectroscopy of Linear Molecules J 7 56B 6 42B 2B 4B 6B 8B 10B 12B… 5 30B 4 20B 3 12B 2 6B 1 2B 0

  12. J+1 J Harry Kroto 2004

  13. J+1 J Harry Kroto 2004

  14. J+1 BJ(J+1) J Harry Kroto 2004

  15. B(J+1)(J+2) J+1 BJ(J+1) J Harry Kroto 2004

  16. B(J+1)(J+2) J+1 BJ(J+1) J F(J) = 2B(J+1) Harry Kroto 2004

  17. Rotational Spectroscopy of Linear Molecules J 7 56B 14B 6 42B 2B 4B 6B 8B 10B 12B… 12B 5 30B 10B 4 20B 8B 3 12B 6B 2 6B 4B 1 2B 0 2B

  18. B(J+1)(J+2) J+1 BJ(J+1) J F(J) = 2B(J+1) Harry Kroto 2004

  19. Absorption B(J+1)(J+2) J+1 BJ(J+1) J F(J) = 2B(J+1) Harry Kroto 2004

  20. 5 10 J= 12 15 20B Harry Kroto 2004

  21. Line separations 2B Harry Kroto 2004

  22. J=5 J=15 20B Line separations 2B Harry Kroto 2004

  23. Rotational Spectroscopy of Linear Molecules J 7 56B 14B 6 42B 12B 5 30B 10B 4 20B 8B 3 12B 6B 2 6B 4B 1 2B 0 2B

  24. 23.065 cm-1 20 21 22 23 24 25

  25. 60 61 62 63 64 65

  26. 61.35 ±cm-1 60 61 62 63 64 65

  27. 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B Harry Kroto 2004

  28. 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 Harry Kroto 2004

  29. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 B = 16.863/ I I = 16.863/ B Harry Kroto 2004

  30. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 B = 16.863/ I I = 16.863/ B I = 8.76 uA2 I =  r2 Harry Kroto 2004

  31. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 B = 16.863/ I I = 16.863/ B I = 8.76 uA2 I =  r2  = m1m2/(m1+m2) = 16x12/28 = 6.86 Harry Kroto 2004

  32. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 B = 16.863/ I I = 16.863/ B I = 8.76 uA2 I =  r2  = m1m2/(m1+m2) = 16x12/28 = 6.86 8.76/6.86 = 1.277 = r2 Harry Kroto 2004

  33. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 B = 16.863/ I I = 16.863/ B I = 8.76 uA2 I =  r2  = m1m2/(m1+m2) = 16x12/28 = 6.86 8.76/6.86 = 1.277 = r2 r = 1.277½ = 1.130 Ǻ (1.128 acc B value 1.921) Harry Kroto 2004

  34. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 B = 16.863/ I I = 16.863/ B I = 8.76 uA2 I =  r2  = m1m2/(m1+m2) = 16x12/28 = 6.86 8.76/6.86 = 1.277 = r2 r = 1.277½ = 1.130 A (1.128 acc B value 1.921) Harry Kroto 2004

  35. 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

  36. B(J+1)(J+2) – D(J+1)2(J+2)2 J+1 BJ(J+1) – DJ2(J+1)2 J F(J) = 2B(J+1) – 4D(J+1)3 Harry Kroto 2004

  37. Far infrared rotational spectrum of CO 5 10 J= 12 15 20B 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 ( 50/3.85 = 12.99 = 13 so line at 50cm-1 is J=12 B = 16.863/ I I = 16.863/ B I = 8.76 uA2 I =  r2  = m1m2/(m1+m2)= 16x12/28 = 6.86 8.76/6.86 = 1.277 = r2 r = 1.277½ = 1.130 A (1.128 acc B value 1.921) Harry Kroto 2004

  38. 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 ( Harry Kroto 2004

  39. J= 12 61.5 cm-1 23.0 cm-1 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 50/3.85 = 12.99 = 13 so line at 50cm-1 is J=12 Harry Kroto 2004

  40. 5 10 15 Line separations 2B Approximately 61.5 – 23 = 38.5 cm-1 = 20B 2B = 3.85 B = 1.925 cm-1 ( 50/3.85 = 12.99 = 13 so line at 50cm-1 is J=12 Harry Kroto 2004

More Related