TRB PG Assistant - Rotational and vibrational spectroscopy of diatomic molecules and Born–Oppenheimer approximation Online Test (MCQ Quiz)

1. Which approximation is fundamental to separating electronic, vibrational, and rotational motions in molecules?

A) Virial Approximation B) Born–Oppenheimer Approximation C) Hartree-Fock Approximation D) Slater Approximation

2. In the context of the Born–Oppenheimer approximation, what is assumed to be constant during electronic motion?

A) Electronic energy B) Nuclear positions C) Molecular volume D) Electron spin

3. What type of molecular motion is primarily studied using rotational spectroscopy?

A) Changes in electron distribution B) Changes in bond lengths and angles C) Changes in the overall rotation of the molecule D) Changes in nuclear spin states

4. Which property must a diatomic molecule possess to exhibit pure rotational absorption or emission spectra?

A) A permanent dipole moment B) A non-zero quadrupole moment C) An induced dipole moment D) No dipole moment

5. For a rigid diatomic rotor, what is the rotational energy quantized in terms of?

A) Vibrational quantum number (v) B) Rotational quantum number (J) C) Electronic quantum number (n) D) Magnetic quantum number (m)

6. 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?

A) The force constant of the bond B) The reduced mass of the molecule C) The rotational constant D) The vibrational frequency

7. What is the selection rule for pure rotational transitions in a diatomic molecule?

A) ΔJ = ±1 B) ΔJ = ±2 C) Δv = ±1 D) ΔJ = 0, ±1

8. The spacing between adjacent rotational energy levels in a rigid rotor model increases with:

A) Decreasing J B) Increasing J C) Increasing rotational constant B D) Decreasing rotational constant B

9. What happens to the rigid rotor approximation when considering real diatomic molecules?

A) It becomes more accurate at higher J values B) It predicts spectral lines that are too closely spaced C) It predicts spectral lines that are too widely spaced D) It is always perfectly accurate

10. The non-rigid rotor model accounts for which effect that is ignored in the rigid rotor model?

A) Centrifugal distortion B) Anharmonicity C) Electronic transitions D) Nuclear spin coupling

11. 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?

A) The centrifugal distortion constant B) The vibrational frequency C) The dipole moment D) The reduced mass

12. Centrifugal distortion causes spectral lines in rotational spectroscopy to be:

A) Shifted to higher frequencies B) Shifted to lower frequencies C) Unchanged in frequency D) Split into multiple lines

13. What is the primary information obtained from rotational spectroscopy of diatomic molecules?

A) Bond strengths B) Molecular geometry C) Internuclear distances (bond lengths) D) Electronic configurations

14. Vibrational spectroscopy is used to study which type of molecular motion?

A) Rotation of the entire molecule B) Translation of the molecule C) Oscillations of atoms around their equilibrium positions D) Changes in electronic energy levels

15. Which type of molecules can exhibit pure vibrational absorption or emission spectra?

A) Homonuclear diatomic molecules only B) Heteronuclear diatomic molecules only C) Molecules with a changing dipole moment during vibration D) All diatomic molecules

16. The simplest model for molecular vibration is the harmonic oscillator. What is the potential energy function for a harmonic oscillator?

A) V(x) = kx B) V(x) = 1/2 kx^2 C) V(x) = kx^3 D) V(x) = e^(-kx)

17. 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?

A) The rotational frequency B) The vibrational frequency C) The electronic frequency D) The fundamental frequency

18. What is the vibrational frequency (ν) of a diatomic molecule related to?

A) Only the masses of the atoms B) Only the force constant of the bond C) Both the force constant (k) and the reduced mass (μ) D) The electronic configuration

19. What is the selection rule for vibrational transitions in a harmonic oscillator model?

A) Δv = ±1 B) Δv = ±2 C) Δv = 0, ±1 D) Δv = ±1, ±2, ±3, ...

20. The energy levels of a harmonic oscillator are equally spaced. What is the energy difference between adjacent levels?

A) hν B) 1/2 hν C) 2hν D) 0

21. What is the zero-point energy of a harmonic oscillator?

A) 0 B) hν C) 1/2 hν D) kT

22. 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?

A) Energy levels become more widely spaced B) Energy levels become more closely spaced at higher v C) Energy levels become equally spaced D) The zero-point energy increases significantly

23. What additional transitions are allowed in vibrational spectroscopy due to anharmonicity, beyond the fundamental transition (Δv = 1)?

A) Overtones (Δv = 2, 3, ...) B) Hot bands (transitions originating from excited vibrational states) C) Both overtones and hot bands D) No additional transitions are allowed

24. Infrared (IR) spectroscopy is a technique that probes which type of molecular transitions?

A) Rotational transitions B) Vibrational transitions C) Electronic transitions D) Nuclear magnetic resonance transitions

25. For a diatomic molecule to be IR active, it must:

A) Be homonuclear B) Have a permanent dipole moment C) Undergo a change in dipole moment during vibration D) Have a high vibrational frequency

26. Raman spectroscopy is another technique that probes vibrational modes. What is the primary requirement for a vibrational mode to be Raman active?

A) A change in dipole moment during vibration B) A change in polarizability during vibration C) A permanent dipole moment D) A significant electronic transition

27. Which of the following diatomic molecules is IR active?

A) H2 B) O2 C) CO D) N2

28. Which of the following diatomic molecules is Raman active?

A) HCl B) CO C) O2 D) HI

29. What is the combination of rotational and vibrational spectroscopy often referred to as?

A) Electronic spectroscopy B) Vibronic spectroscopy C) Rotational-vibrational spectroscopy D) Nuclear spectroscopy

30. 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?

A) Δv = ±1 B) Δv = ±2 C) Δv = 0 D) Δv = ±1, ±2, ...

31. The rotational fine structure in vibrational spectra arises from:

A) Changes in electronic states B) Changes in vibrational energy levels C) Simultaneous changes in rotational energy levels D) Changes in nuclear spin

32. The P-branch in a rotational-vibrational spectrum corresponds to transitions where:

A) ΔJ = +1 B) ΔJ = -1 C) ΔJ = 0 D) ΔJ = ±1

33. The R-branch in a rotational-vibrational spectrum corresponds to transitions where:

A) ΔJ = +1 B) ΔJ = -1 C) ΔJ = 0 D) ΔJ = ±1

34. The Q-branch in a rotational-vibrational spectrum corresponds to transitions where:

A) ΔJ = +1 B) ΔJ = -1 C) ΔJ = 0 D) ΔJ = ±1

35. 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?

A) Approximately 2B B) Approximately B C) Approximately 4B D) Approximately 0.5B

36. What is the primary assumption of the Born–Oppenheimer approximation regarding the nuclei?

A) Nuclei are stationary relative to electrons B) Nuclei are in constant motion C) Nuclei have quantized vibrational motion D) Nuclei have quantized rotational motion

37. The Born–Oppenheimer approximation allows for the separation of the molecular wavefunction into electronic and nuclear parts. This simplifies the calculation of:

A) Nuclear spin states B) Electronic energy levels C) Vibrational and rotational energy levels D) All molecular properties

38. Which spectroscopic technique is most directly related to the vibrational energy levels of a diatomic molecule?

A) Microwave spectroscopy B) Infrared spectroscopy C) UV-Visible spectroscopy D) Nuclear Magnetic Resonance spectroscopy

39. Microwave spectroscopy is primarily used to study:

A) Electronic transitions B) Vibrational transitions C) Rotational transitions D) Nuclear transitions

40. The rotational constant B is inversely proportional to:

A) The force constant of the bond B) The reduced mass of the molecule C) The dipole moment of the molecule D) The electronic configuration

41. The vibrational frequency ν is directly proportional to:

A) The square root of the reduced mass B) The square root of the force constant C) The inverse square root of the reduced mass D) The inverse square root of the force constant

42. What information can be obtained from the overtones observed in vibrational spectroscopy of diatomic molecules?

A) Precise bond lengths B) Information about the anharmonicity of the potential energy surface C) The rotational constant D) The electronic ground state energy

43. If a diatomic molecule has a very weak bond (low force constant), its vibrational frequency will be:

A) High B) Low C) Unchanged D) Zero

44. If a diatomic molecule has a large reduced mass, its rotational constant B will be:

A) Large B) Small C) Unchanged D) Zero

45. The Born–Oppenheimer approximation is less accurate for molecules where:

A) Electronic states are widely separated B) Electronic states are close in energy (near degeneracy) C) The molecule is very small D) The molecule has strong covalent bonds

46. What is the typical energy range for rotational transitions in diatomic molecules?

A) Infrared region B) Visible region C) Microwave region D) Ultraviolet region

47. What is the typical energy range for vibrational transitions in diatomic molecules?

A) Microwave region B) Infrared region C) Visible region D) X-ray region

48. In rotational spectroscopy, the spectral lines are often referred to as:

A) Band heads B) Lines C) Peaks D) Signals

Rotational and vibrational spectroscopy of diatomic molecules and Born–Oppenheimer approximation - Online Test

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