Q1(n). Photon–molecule interaction in rotating HCl

Answer in brief

The rotating permanent dipole of HCl is an oscillating dipole; when its frequency matches that of the radiation, the field exerts a torque: a photon is absorbed and J → J + 1.

Key points

• HCl has a permanent dipole moment, Hδ⁺–Clδ⁻, μ ≈ 1.1 D.
• As it rotates, the dipole component along any fixed direction varies as μ cos ωt: the rotating dipole is an oscillating dipole.
• At resonance (ν = rotational frequency) the field exerts a torque, energy is exchanged and the molecule absorbs (J → J + 1) or emits a photon.
• Gross selection rule: μ ≠ 0 (H₂, N₂, CO₂ are inactive); specific rule ΔJ = ±1, as the photon carries one unit ℏ of angular momentum.
• EJ = hcBJ(J + 1) ⇒ lines at ν̃ = 2B(J + 1); B = 10.44 cm⁻¹ gives lines at 20.9, 41.8, 62.6, 83.5 cm⁻¹ (far infrared).