1. This is the far infra red spectrum of the diatomic molecule CO
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. I = μro2 μ = m1m2/(m1+m2) Io (uÅ2) = 16.863/ Bo(cm-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.
I = μro2 μ = m1m2/(m1+m2) Io (uÅ2) = / Bo(cm-1)
Assume C has mass and O mass 16.0

3. I = μro2 μ = m1m2/(m1+m2) Io (uÅ2) = 16.863/ Bo(cm-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.
I = μro2 μ = m1m2/(m1+m2) Io (uÅ2) = / Bo(cm-1)
Assume C has mass 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 MoleculesJ 7
56B 6
42B 2B 4B 6B 8B
10B
12B… 5
30B 4
20B 3
12B 2 6B 1 2B

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

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

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

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

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

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

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

12. J+1 J
Harry Kroto 2004

13. J+1 J
Harry Kroto 2004

14. J+1
BJ(J+1) J
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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 MoleculesJ 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 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

21. 5 10
J= 12 15
20B
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22. Line separations 2B
Harry Kroto 2004

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

24. Rotational Spectroscopy of Linear MoleculesJ 7
56B
14B 6
42B
12B 5
30B
10B 4
20B 8B 3
12B 6B 2 6B 4B 1 2B 2B

26. cm-1

28. 61.35 ±cm-1

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

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

31. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1
B = / I I = / B
Harry Kroto 2004

32. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1
B = / I I = / B
I = 8.76 uA I =  r2
Harry Kroto 2004

33. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1
B = / I I = / B
I = 8.76 uA I =  r2
 = m1m2/(m1+m2) = 16x12/28 = 6.86
Harry Kroto 2004

34. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1
B = / I I = / B
I = 8.76 uA I =  r2
 = m1m2/(m1+m2) = 16x12/28 = 6.86
8.76/6.86 = = r2
Harry Kroto 2004

35. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1
B = / I I = / B
I = 8.76 uA I =  r2
 = m1m2/(m1+m2) = 16x12/28 = 6.86
8.76/6.86 = = r2
r = 1.277½ = Ǻ ( acc B value 1.921)
Harry Kroto 2004

37. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1
B = / I I = / B
I = 8.76 uA I =  r2
 = m1m2/(m1+m2) = 16x12/28 = 6.86
8.76/6.86 = = r2
r = 1.277½ = A ( acc B value 1.921)
Harry Kroto 2004

38. 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

39. 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

41. Far infrared rotational spectrum of CO J= 12 15 20B10
Far infrared rotational spectrum of CO
J= 12 15
20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Approximately 61.5 – 23 = 38.5 cm-1 = 20B
2B = B = cm-1 (
50/3.85 = = 13 so line at 50cm-1 is J=12
B = / I I = / B
I = 8.76 uA2 I =  r2
 = m1m2/(m1+m2)= 16x12/28 = 6.86
8.76/6.86 = = r2
r = 1.277½ = A ( acc B value 1.921)
Harry Kroto 2004

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

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

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