Modes of molecular vibrations MCQs With Answer

Introduction

The concept of molecular vibrations is central to Modern Pharmaceutical Analytical Techniques, especially infrared (IR) and Raman spectroscopy used for drug characterization, polymorph identification, impurity profiling, and solid-state analysis. This blog provides carefully designed MCQs on modes of molecular vibrations for M. Pharm students, covering normal modes, stretching and bending types, selection rules, Hooke’s law, isotope effects, group vs fingerprint regions, anharmonicity, Fermi resonance, and Raman–IR complementarity. Each question targets conceptual clarity and application in pharmaceutical analysis, enabling students to connect vibrational behavior with spectral features. Work through the set to strengthen your grasp of how vibrations translate into spectral signatures that drive evidence-based decisions in modern pharmaceutics.

Q1. For a non-linear molecule with N atoms, the total number of normal vibrational modes is:

• 3N − 6
• 3N − 5
• 2N − 3
• N − 1

Correct Answer: 3N − 6

Q2. For a linear molecule with N atoms, the total number of normal vibrational modes is:

• 3N − 6
• 3N − 5
• 2N − 2
• N

Correct Answer: 3N − 5

Q3. The total number of vibrational modes expected for CO₂ at the fundamental level is:

• 2
• 3
• 4
• 6

Correct Answer: 4

Q4. Which of the following is an out-of-plane bending vibration for a CH₂ group?

• Scissoring
• Rocking
• Wagging
• Symmetric stretching

Correct Answer: Wagging

Q5. A diatomic molecule exhibits which type(s) of vibrational motion?

• Stretching only
• Bending only
• Stretching and bending
• No vibrational motion

Correct Answer: Stretching only

Q6. Which vibrational mode of CO₂ is IR inactive but strongly Raman active?

• Symmetric stretch
• Asymmetric stretch
• Degenerate bending
• Overtone of bending

Correct Answer: Symmetric stretch

Q7. The primary selection rule for IR activity is that the vibrational motion must cause a:

• Change in polarizability
• Change in dipole moment
• Change in rotational constant only
• Change in nuclear spin

Correct Answer: Change in dipole moment

Q8. The primary selection rule for Raman activity is that the vibrational motion must cause a:

• Change in dipole moment
• Change in polarizability
• Change in magnetic moment
• Change in nuclear quadrupole coupling

Correct Answer: Change in polarizability

Q9. According to the diatomic harmonic oscillator model, the fundamental vibrational frequency (ν) in wavenumbers is proportional to:

• ν ∝ √(μ/k)
• ν ∝ kμ
• ν ∝ (1/2πc) √(k/μ)
• ν ∝ (1/2πc) √(μ/k)

Correct Answer: ν ∝ (1/2πc) √(k/μ)

Q10. Replacing ¹⁶O with ¹⁸O in a carbonyl group typically causes the C=O stretching band to:

• Shift to lower wavenumber (red shift)
• Shift to higher wavenumber (blue shift)
• Remain unchanged
• Disappear due to selection rules

Correct Answer: Shift to lower wavenumber (red shift)

Q11. The IR fingerprint region is generally defined as:

• 4000–3000 cm⁻¹
• 3000–2000 cm⁻¹
• 2000–1500 cm⁻¹
• 1500–500 cm⁻¹

Correct Answer: 1500–500 cm⁻¹

Q12. The “group frequency” region in IR spectra is typically considered to be:

• 4000–1500 cm⁻¹
• 1500–500 cm⁻¹
• 500–100 cm⁻¹
• 2000–500 cm⁻¹

Correct Answer: 4000–1500 cm⁻¹

Q13. Conjugation of a carbonyl group (C=O) with a C=C bond most commonly:

• Increases the C=O stretching frequency due to higher force constant
• Lowers the C=O stretching frequency due to π-electron delocalization
• Eliminates the C=O stretch by symmetry
• Has no effect on the C=O stretching frequency

Correct Answer: Lowers the C=O stretching frequency due to π-electron delocalization

Q14. Which statement about vibrational overtones is most accurate?

• They occur at exact integer multiples of the fundamental and are very intense
• They arise due to anharmonicity and appear at approximate multiples with lower intensity
• They are forbidden in both IR and Raman spectroscopy
• They occur only in Raman spectra

Correct Answer: They arise due to anharmonicity and appear at approximate multiples with lower intensity

Q15. Fermi resonance in vibrational spectroscopy refers to:

• Splitting of rotational lines in a vibrational band
• Interaction between a fundamental and a nearby overtone/combination band of the same symmetry
• Resonance Raman enhancement near electronic absorption
• Coupling of translational and rotational motions

Correct Answer: Interaction between a fundamental and a nearby overtone/combination band of the same symmetry

Q16. The bending vibration of a linear molecule like CO₂ is best described as:

• Non-degenerate
• Doubly degenerate
• Triply degenerate
• Forbidden in both IR and Raman

Correct Answer: Doubly degenerate

Q17. The number of normal vibrational modes expected for benzene (C₆H₆) is:

• 24
• 30
• 36
• 12

Correct Answer: 30

Q18. Which functional group typically shows two bands in the 3300–3500 cm⁻¹ region due to symmetric and asymmetric N–H stretching?

• Primary amine (–NH₂)
• Secondary amine (–NH–)
• Tertiary amine (–N–)
• Nitro group (–NO₂)

Correct Answer: Primary amine (–NH₂)

Q19. The CH₂ rocking vibration in long-chain hydrocarbons typically appears near:

• 720 cm⁻¹
• 1450 cm⁻¹
• 1720 cm⁻¹
• 2250 cm⁻¹

Correct Answer: 720 cm⁻¹

Q20. The mutual exclusion rule (no mode is both IR and Raman active) applies to molecules that are:

• Polar
• Ionic
• Centrosymmetric (possessing an inversion center)
• Linear only

Correct Answer: Centrosymmetric (possessing an inversion center)

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