QB_PH_SEC6_013: Molecular Spectroscopy

The Franck-Condon principle in molecular electronic spectroscopy is based on the physical approximation that

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Born-Oppenheimer Context**: Electronic and nuclear motions separate due to the large mass ratio $M_{\text{nucleus}} / m_e \gg 10^3$. 2. **Time Scale Hierarchy**: - Electronic rearrangement: $\tau_{\text{elec}} \approx 10^{-16} - 10^{-15}\text{ s}$ - Nuclear vibrational period: $\tau_{\text{vib}} \approx 10^{-13}\text{ s}$ 3. **Franck-Condon Principle**: Since $\tau_{\text{elec}} \ll \tau_{\text{vib}}$, an electronic transition occurs virtually instantaneously relative to nuclear motion. The nuclei do not significantly alter their positions or momenta during the transition. 4. **Graphical Consequence**: Transitions are represented by vertical lines on potential energy curves. The transition intensity is proportional to the square of the overlap integral of the vibrational wavefunctions (Franck-Condon factor): $|\int \psi_{v'}^* \psi_{v''} dR|^2$. 5. **Conclusion**: Option (A) is the authentic physical statement.