Vibrational Spectra: IR and Raman Spectroscopy: 20 MCQs

Q1. Which equation gives the vibrational frequency of a bond modelled as a harmonic oscillator?

Q2. How many vibrational modes does a non-linear molecule with $N$ atoms have?

Q3. Which statement correctly describes the IR selection rule?

Q4. Which region of an IR spectrum is most useful for matching an unknown compound to a known one?

Q5. Which pair of functional groups gives stretches in the $1600$–$1800\ \text{cm}^{-1}$ region?

Q6. Which statement about stretching and bending modes is correct?

Q7. Which of the following is a bending mode?

Q8. Which technique is complementary to IR because it detects vibrations that do not change the dipole moment?

Q9. For a molecule with $N$ atoms, the number of vibrational modes is $3N - 6$ if non-linear and $3N - 5$ if linear.

Q10. A C–H stretch appears near $3000\ \text{cm}^{-1}$. The corresponding C–D stretch appears at about $2200\ \text{cm}^{-1}$. What is the main reason for the shift?

Q11. Carbon dioxide is a linear molecule with $N = 3$. How many vibrational modes does it have?

Q12. The symmetric stretch of $\text{CO}_2$ is silent in the IR spectrum. Why?

Q13. A student runs an IR spectrum of an aqueous sample and finds the spectrum dominated by water absorption. Which technique would be a better choice?

Q14. Why do vibrational levels of a real molecule crowd together at higher energy?

Q15. A small peak appears at roughly twice the frequency of a strong fundamental. What is it most likely to be?

Q16. A molecule has two oscillators sharing a central atom with similar frequencies. What effect does this produce in the spectrum?

Q17. A molecule with 4 atoms exhibits a vibrational spectrum. Calculate the number of vibrational modes it has if it is non-linear. What does this imply about the types of vibrations present?

Q18. Given the vibrational frequency equation $$ u = \frac{1}{2\pi}\sqrt{\frac{k}{\mu}}$$, if the force constant $k$ of a bond is doubled while the reduced mass $\mu$ remains constant, how does the frequency change?

Q19. In a Raman spectrum, a peak appears at a frequency corresponding to a combination band of two vibrational modes. If the fundamental frequencies of these modes are $1000\ ext{cm}^{-1}$ and $1500\ ext{cm}^{-1}$, what is the expected frequency for the combination band?

Q20. A student observes that a certain vibrational mode is absent in the IR spectrum but present in the Raman spectrum. What can be concluded about the nature of this vibrational mode?