11. A transition is spectroscopically allowed if it obeys:
a. Wien’s displacement law
b. The law of conservation of energy only
c. The law of conservation of angular momentum only
d. Both the laws of conservation of angular momentum and energy

Spectroscopically allowed transitions in atomic and molecular spectroscopy follow strict selection rules derived from quantum mechanics. The correct answer to the question is d. Both the laws of conservation of angular momentum and energy.​

Option Analysis

Wien’s displacement law (option a) relates peak wavelength to temperature in blackbody radiation, not transition probabilities.​
Conservation of energy alone (option b) is necessary for any photon absorption/emission but insufficient, as many energy-matched transitions remain forbidden due to symmetry.​
Conservation of angular momentum alone (option c) governs changes in quantum numbers like Δl = ±1 or Δm_l = 0, ±1, but ignores energy matching required for spectral lines.​
Both laws together (option d) ensure viable transitions: energy conservation sets frequency (E = hν), while angular momentum rules (e.g., spin ΔS = 0, orbital parity changes) determine allowance.​

Selection Rules Overview

Allowed transitions produce intense spectral lines via electric dipole mechanisms.

• Energy conservation: Initial and final states differ by photon energy.​

• Angular momentum: ΔJ = 0, ±1 (no J=0 to J=0); ΔL = 0, ±1; ΔS = 0 for spin-allowed.​
  Forbidden transitions (spin, Laporte) occur weakly via higher-order processes.​​