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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.

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m 1

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  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

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