1. 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
Harry Kroto 2004

2. 5 10
J= 12 15
20B
Harry Kroto 2004

3. 20B
23.0 cm-1
61.5 cm-1
Line separations 2B
Harry Kroto 2004

4. 20B 23.0 cm-1 61.5 cm-1 Line separations 2B
61.5 – 23 = cm-1 = 20B
Harry Kroto 2004

5. 20B 23.0 cm-1 61.5 cm-1 Line separations 2B
61.5 – 23 = cm-1 = 20B
2B = B = cm-1
Harry Kroto 2004

6. Determine the bond length of the CO5 10 15
Homework
Determine the bond length of the CO
in A (Angstroms) and nm
B (cm-1) = / I (UA2)
I =  r  = m1m2/(m1+m2)
Assume U of C =12 and O = 16
Note 1A = 0.1nm
Harry Kroto 2004

7. Harry Kroto 2004

8. 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
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

9. 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
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

10. 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
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

11. 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 (
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

12. 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

13. 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
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

14. 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

15. Radiotelescope in Canada
Harry Kroto 2004

16. 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

17. 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

18. 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

19. 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

20. 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

21. Radiotelescope in Canada
Harry Kroto 2004

22. Black clouds and stars in space -Taurus
Harry Kroto 2004

23. Harry Kroto 2004