Rotational and vibrational spectroscopy of diatomic molecules and Born–Oppenheimer approximation - Question Bank
1. In rotational spectroscopy, the spectral lines are often referred to as:
2. What is the typical energy range for vibrational transitions in diatomic molecules?
3. What is the typical energy range for rotational transitions in diatomic molecules?
4. The Born–Oppenheimer approximation is less accurate for molecules where:
5. If a diatomic molecule has a large reduced mass, its rotational constant B will be:
6. If a diatomic molecule has a very weak bond (low force constant), its vibrational frequency will be:
7. What information can be obtained from the overtones observed in vibrational spectroscopy of diatomic molecules?
8. The vibrational frequency ν is directly proportional to:
9. The rotational constant B is inversely proportional to:
10. Microwave spectroscopy is primarily used to study:
11. Which spectroscopic technique is most directly related to the vibrational energy levels of a diatomic molecule?
12. The Born–Oppenheimer approximation allows for the separation of the molecular wavefunction into electronic and nuclear parts. This simplifies the calculation of:
13. What is the primary assumption of the Born–Oppenheimer approximation regarding the nuclei?
14. In a typical rotational-vibrational spectrum of a diatomic molecule (excluding the Q-branch for non-linear molecules), the P and R branches are often observed. What is the typical spacing between adjacent lines in these branches?
15. The Q-branch in a rotational-vibrational spectrum corresponds to transitions where:
16. The R-branch in a rotational-vibrational spectrum corresponds to transitions where:
17. The P-branch in a rotational-vibrational spectrum corresponds to transitions where:
18. The rotational fine structure in vibrational spectra arises from:
19. In the context of rotational-vibrational spectroscopy, transitions involve changes in both J and v quantum numbers. What is a common selection rule for the vibrational quantum number?
20. What is the combination of rotational and vibrational spectroscopy often referred to as?
21. Which of the following diatomic molecules is Raman active?
22. Which of the following diatomic molecules is IR active?
23. Raman spectroscopy is another technique that probes vibrational modes. What is the primary requirement for a vibrational mode to be Raman active?
24. For a diatomic molecule to be IR active, it must:
25. Infrared (IR) spectroscopy is a technique that probes which type of molecular transitions?
26. What additional transitions are allowed in vibrational spectroscopy due to anharmonicity, beyond the fundamental transition (Δv = 1)?
27. The anharmonicity of a molecular vibration means that the potential energy curve deviates from a perfect parabola. What is the consequence of anharmonicity on vibrational energy levels?
28. What is the zero-point energy of a harmonic oscillator?
29. The energy levels of a harmonic oscillator are equally spaced. What is the energy difference between adjacent levels?
30. What is the selection rule for vibrational transitions in a harmonic oscillator model?
31. What is the vibrational frequency (ν) of a diatomic molecule related to?
32. For a harmonic oscillator, the vibrational energy levels are quantized and given by E_v = (v + 1/2)hν, where v is the vibrational quantum number. What does ν represent?
33. The simplest model for molecular vibration is the harmonic oscillator. What is the potential energy function for a harmonic oscillator?
34. Which type of molecules can exhibit pure vibrational absorption or emission spectra?
35. Vibrational spectroscopy is used to study which type of molecular motion?
36. What is the primary information obtained from rotational spectroscopy of diatomic molecules?
37. Centrifugal distortion causes spectral lines in rotational spectroscopy to be:
38. In the non-rigid rotor model, the energy levels are typically expressed as E_J = BJ(J+1) - DJ^2(J+1)^2. What does the constant D represent?
39. The non-rigid rotor model accounts for which effect that is ignored in the rigid rotor model?
40. What happens to the rigid rotor approximation when considering real diatomic molecules?
41. The spacing between adjacent rotational energy levels in a rigid rotor model increases with:
42. What is the selection rule for pure rotational transitions in a diatomic molecule?
43. The energy levels of a rigid diatomic rotor are given by the expression E_J = BJ(J+1), where J is the rotational quantum number. What does the constant B represent?
44. For a rigid diatomic rotor, what is the rotational energy quantized in terms of?
45. Which property must a diatomic molecule possess to exhibit pure rotational absorption or emission spectra?
46. What type of molecular motion is primarily studied using rotational spectroscopy?
47. In the context of the Born–Oppenheimer approximation, what is assumed to be constant during electronic motion?
48. Which approximation is fundamental to separating electronic, vibrational, and rotational motions in molecules?