The excitation of molecules and materials by light involves the interaction of photons with the electronic structure of the molecules or materials. This interaction can result in the absorption or emission of photons at specific wavelengths, which is a fundamental aspect of photochemistry and photophysics. The quantum mechanics principles behind this phenomenon can be explained through the following concepts:1. Energy levels and transitions: Molecules and materials have discrete energy levels associated with their electronic, vibrational, and rotational states. When a photon interacts with a molecule or material, it can be absorbed if its energy matches the energy difference between two energy levels. This process promotes the molecule or material from a lower energy state to a higher energy state, known as an excited state. Conversely, when a molecule or material in an excited state relaxes back to a lower energy state, it can emit a photon with energy equal to the energy difference between the two states.2. Selection rules: Quantum mechanics imposes certain restrictions on the allowed transitions between energy levels, known as selection rules. These rules determine the probability of a transition occurring and are based on the conservation of angular momentum and other quantum numbers. As a result, only specific wavelengths of light can be absorbed or emitted by a given molecule or material, leading to the characteristic absorption and emission spectra observed in photochemistry and photophysics.3. Wave-particle duality: Photons exhibit both wave-like and particle-like properties, as described by the wave-particle duality principle in quantum mechanics. The wave-like nature of photons allows them to interact with the electronic structure of molecules and materials, while their particle-like nature enables them to carry discrete amounts of energy during absorption and emission processes.4. Born-Oppenheimer approximation: In quantum mechanics, the Born-Oppenheimer approximation is used to separate the electronic and nuclear motions in molecules. This approximation allows chemists to study the electronic structure and energy levels of molecules independently of their vibrational and rotational states. This simplification is crucial for understanding the absorption and emission of photons in photochemistry and photophysics.5. Franck-Condon principle: The Franck-Condon principle states that electronic transitions in molecules occur much faster than nuclear motions. As a result, during an electronic transition, the nuclear positions of the molecule remain essentially unchanged. This principle helps explain the vibrational structure observed in absorption and emission spectra, as the overlap between the vibrational wavefunctions of the initial and final states determines the intensity of the spectral lines.In summary, the excitation of molecules and materials by light and the resulting absorption or emission of photons at specific wavelengths can be understood through various quantum mechanics principles, including energy levels and transitions, selection rules, wave-particle duality, the Born-Oppenheimer approximation, and the Franck-Condon principle. These concepts provide the foundation for the study of photochemistry and photophysics.