Rotational and vibrational spectroscopy of diatomic molecules and Born–Oppenheimer approximation - One Line Questions

1. What is the zero-point energy of a harmonic oscillator? — 1/2 hν
2. Raman spectroscopy is another technique that probes vibrational modes. What is the primary requirement for a vibrational mode to be Raman active? — A change in polarizability during vibration
3. Which property must a diatomic molecule possess to exhibit pure rotational absorption or emission spectra? —
4. 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? — Approximately 2B
5. In rotational spectroscopy, the spectral lines are often referred to as: — Lines
6. For a diatomic molecule to be IR active, it must: — Undergo a change in dipole moment during vibration
7. What is the primary information obtained from rotational spectroscopy of diatomic molecules? — Internuclear distances (bond lengths)
8. The non-rigid rotor model accounts for which effect that is ignored in the rigid rotor model? — Centrifugal distortion
9. What type of molecular motion is primarily studied using rotational spectroscopy? — Changes in the overall rotation of the molecule
10. The rotational fine structure in vibrational spectra arises from: — Simultaneous changes in rotational energy levels
11. The spacing between adjacent rotational energy levels in a rigid rotor model increases with: — Increasing J
12. In the context of the Born–Oppenheimer approximation, what is assumed to be constant during electronic motion? — Nuclear positions
13. What is the combination of rotational and vibrational spectroscopy often referred to as? — Rotational-vibrational spectroscopy
14. The Born–Oppenheimer approximation is less accurate for molecules where: — Electronic states are close in energy (near degeneracy)
15. Microwave spectroscopy is primarily used to study: — Rotational transitions
16. 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? — Energy levels become more closely spaced at higher v
17. Which of the following diatomic molecules is IR active? — CO
18. Which of the following diatomic molecules is Raman active? — O2
19. If a diatomic molecule has a very weak bond (low force constant), its vibrational frequency will be: — Low
20. Which type of molecules can exhibit pure vibrational absorption or emission spectra? — Molecules with a changing dipole moment during vibration
21. The energy levels of a harmonic oscillator are equally spaced. What is the energy difference between adjacent levels? — hν
22. What is the typical energy range for rotational transitions in diatomic molecules? — Microwave region
23. What happens to the rigid rotor approximation when considering real diatomic molecules? — It predicts spectral lines that are too closely spaced
24. If a diatomic molecule has a large reduced mass, its rotational constant B will be: — Small
25. What is the typical energy range for vibrational transitions in diatomic molecules? — Infrared region
26. Which spectroscopic technique is most directly related to the vibrational energy levels of a diatomic molecule? — Infrared spectroscopy
27. The Born–Oppenheimer approximation allows for the separation of the molecular wavefunction into electronic and nuclear parts. This simplifies the calculation of: — Vibrational and rotational energy levels
28. What is the primary assumption of the Born–Oppenheimer approximation regarding the nuclei? — Nuclei are stationary relative to electrons
29. What is the vibrational frequency (ν) of a diatomic molecule related to? — Both the force constant (k) and the reduced mass (μ)
30. What additional transitions are allowed in vibrational spectroscopy due to anharmonicity, beyond the fundamental transition (Δv = 1)? — Both overtones and hot bands
31. What information can be obtained from the overtones observed in vibrational spectroscopy of diatomic molecules? — Information about the anharmonicity of the potential energy surface
32. Vibrational spectroscopy is used to study which type of molecular motion? — Oscillations of atoms around their equilibrium positions
33. Infrared (IR) spectroscopy is a technique that probes which type of molecular transitions? — Vibrational transitions
34. Centrifugal distortion causes spectral lines in rotational spectroscopy to be: — Shifted to lower frequencies
35. 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? — The centrifugal distortion constant
36. 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? — The rotational constant
37. The rotational constant B is inversely proportional to: — The reduced mass of the molecule
38. 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? — The vibrational frequency
39. The vibrational frequency ν is directly proportional to: — The square root of the force constant
40. The simplest model for molecular vibration is the harmonic oscillator. What is the potential energy function for a harmonic oscillator? — V(x) = 1/2 kx^2
41. For a rigid diatomic rotor, what is the rotational energy quantized in terms of? — Rotational quantum number (J)
42. Which approximation is fundamental to separating electronic, vibrational, and rotational motions in molecules? — Born–Oppenheimer Approximation
43. The P-branch in a rotational-vibrational spectrum corresponds to transitions where: — ΔJ = -1
44. The R-branch in a rotational-vibrational spectrum corresponds to transitions where: — ΔJ = +1
45. The Q-branch in a rotational-vibrational spectrum corresponds to transitions where: — ΔJ = 0
46. What is the selection rule for pure rotational transitions in a diatomic molecule? — ΔJ = ±1
47. What is the selection rule for vibrational transitions in a harmonic oscillator model? — Δv = ±1
48. 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? — Δv = ±1
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