Forbidden transitions

Definition

Forbidden transitions refer to quantum mechanical transitions between energy levels that have very low probabilities of occurring due to selection rules. These transitions are typically associated with changes in quantum numbers that do not adhere to the allowed criteria set by conservation laws or symmetry principles, leading to their rarity in processes such as absorption and emission of light.

5 Must Know Facts For Your Next Test

1. Forbidden transitions often occur in systems where the selection rules are not satisfied, leading to very weak coupling between initial and final states.
2. These transitions can happen, but they typically require much longer timescales or higher intensities of external perturbations compared to allowed transitions.
3. In spectroscopic measurements, forbidden transitions can manifest as weak spectral lines, often seen in emission or absorption spectra of atoms and molecules.
4. Common examples of forbidden transitions include certain electronic transitions in multi-electron atoms and vibrational transitions in diatomic molecules.
5. Understanding forbidden transitions is crucial for interpreting phenomena like phosphorescence, where molecules remain excited for extended periods before returning to the ground state.

Review Questions

• How do selection rules impact the likelihood of forbidden transitions occurring in quantum systems?
  • Selection rules dictate which quantum mechanical transitions are allowed based on the changes in quantum numbers during the transition. Forbidden transitions violate these rules, resulting in significantly lower probabilities of occurrence. This means that while they can theoretically happen, the constraints imposed by selection rules make them rare compared to allowed transitions, affecting how systems interact with electromagnetic radiation.
• Discuss the significance of the transition dipole moment in relation to forbidden transitions and their observational characteristics.
  • The transition dipole moment is crucial in determining the probability of any transition between two quantum states. In the case of forbidden transitions, this moment is typically much weaker than that for allowed transitions, indicating lower interaction strengths with electromagnetic fields. Consequently, when observing spectra, forbidden transitions appear as weak lines that provide important information about molecular and atomic structure despite their rarity.
• Evaluate how understanding forbidden transitions can enhance our knowledge of phenomena like phosphorescence and its applications in modern technology.
  • Understanding forbidden transitions is key to explaining phosphorescence, where a molecule enters a long-lived excited state due to a forbidden transition. This process allows for delayed re-emission of light after excitation, which has significant applications in technology such as glow-in-the-dark materials and advanced display technologies. By studying these transitions, we can develop better materials and improve their efficiency in capturing and emitting light, thus broadening their practical applications.

Related terms

Selection rules: Guidelines that determine which transitions between quantum states are allowed or forbidden based on conservation laws and the symmetries of the system.

Transition dipole moment: A measure of the probability of a transition between two quantum states, reflecting how strongly the states interact with electromagnetic fields.

Perturbation theory: A mathematical approach used to find an approximate solution to a problem by starting from the exact solution of a related, simpler problem.