GATE PH: Atomic and Molecular Physics

Atomic and Molecular Physics in GATE PH tests hydrogenic spectra, fine structure, electron spin, LS coupling, term symbols, selection rules, rotational and vibrational spectra, Raman scattering, and basic magnetic resonance. The exam often uses a spectrum spacing or a term symbol to test a compact calculation.

Core rules and concepts

• Hydrogen energy levels: E_n = -13.6 eV/n². Fine structure includes relativistic correction, spin-orbit coupling, and the Darwin term.
• LS coupling gives term symbols in the form 2S+1L_J. Hund's rules order the terms for a given electron configuration.
• Electric-dipole selection rules: Δl = ±1, Δm_l = 0, ±1, and ΔS = 0 in LS coupling. For rotational transitions, ΔJ = ±1.
• Rigid-rotor energies: E_J = BJ(J+1), where B = ħ²/(2I). The absorption lines are spaced by 2B in wavenumber.
• Vibrational levels: E_v = (v + ½)ħω. Raman scattering involves a change in polarisability and follows different selection rules from infrared absorption.

Worked example

For a rigid diatomic rotor with rotational constant B = 10 cm⁻¹, the energy levels are E_J = BJ(J+1). The transition from J to J+1 has wavenumber ν = B[(J+1)(J+2) - J(J+1)] = 2B(J+1). Adjacent lines are separated by 2B = 20 cm⁻¹. This spacing is independent of J in the rigid-rotor approximation.

Traps that cost marks

• Using the electron mass instead of the reduced mass for molecular rotation.
• Forgetting that ΔJ = ±1 for pure rotational absorption.
• Misreading the term symbol: the superscript is 2S+1, not the number of electrons.
• Confusing infrared-active and Raman-active vibrational modes.