Flashcards on Molecular Spectroscopy: Fundamentals and Applications
Molecular Spectroscopy: Fundamentals and Applications Guide
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Vibrational Spectroscopy
22 cards
Card 1
Question: What types of vibrational motions occur in polyatomic molecules?
Answer: Bends, symmetric stretches, and asymmetric stretches.
Card 2
Question: What is the harmonic approximation for the potential energy V(x) of a diatomic bond near equilibrium?
Answer: V(x) ≈ 1/2 kf x^2, where kf is the force constant and x = R − Re.
Card 3
Question: What does a large force constant (kf) indicate about a bond?
Answer: A stiff bond that is difficult to displace and has a sharply curved potential energy.
Card 4
Question: How is the effective mass (meff) for a diatomic vibration defined?
Answer: meff = m1 m2 / (m1 + m2). For identical atoms m1 = m2 = m, meff = m/2; if m1 ≫ m2 then meff ≈ m2.
Card 5
Question: Write the expression for the vibrational energy levels (quantized) of a harmonic oscillator.
Answer: Eν = (ν + 1/2) ħω where ν = 0,1,2,... and ω = sqrt(kf / meff).
Card 6
Question: How is the vibrational term value Gν (in wavenumbers) defined?
Answer: Gν = Eν / (hc) = (ν + 1/2) ṽ where ṽ = ω / (2πc).
Card 7
Question: What is the gross selection rule for infrared (IR) activity in a vibrational transition?
Answer: The electric dipole moment must change upon the change in vibrational state (Δμ ≠ 0).
Card 8
Question: Do molecules need a permanent dipole moment to be IR active?
Answer: No. A molecule does not require a static dipole moment; the dipole moment must change during vibration.
Card 9
Question: Give the specific selection rule for vibrational transitions in the harmonic approximation.
Answer: Δν = ±1 (Δν = +1 corresponds to absorption; Δν = −1 to emission).
Card 10
Question: Why are most molecules in the vibrational ground state at room temperature?
Answer: Because kT ≈ 200 cm^−1, so thermal energy is small compared with typical vibrational energies and population of ν>0 is low (Boltzmann distribution).