The highest occupied molecular orbital of a molecule is abbreviated as the HOMO. The lowest unoccupied molecular orbital in a molecule is called the LUMO. Experimentally, one can measure the difference in energy between the HOMO and LUMO by taking the electronic absorption (UV-visible) spectrum of the molecule. Peaks in the electronic absorption spectrum can be labeled as p2p9p2p*, s2s9s2s*, and so on, corresponding to electrons being promoted from one orbital to another. The HOMO-LUMO transition corresponds to molecules going from their ground state to their first excited state. (c) The electronic absorption spectrum of the N2 molecule has the lowest energy peak at 170 nm. To what orbital transition does this correspond?

Verified step by step guidance

1. Identify the type of electronic transition that occurs in the N2 molecule when it absorbs light at 170 nm.
2. Understand that the lowest energy peak in the electronic absorption spectrum corresponds to the HOMO-LUMO transition.
3. Recall that the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) are involved in the transition from the ground state to the first excited state.
4. Determine the nature of the orbitals involved in the HOMO-LUMO transition for the N2 molecule, which typically involves \\pi \, \text{to} \, \\pi^* \, \text{or} \, \\sigma \, \text{to} \, \\sigma^* \, \text{transitions}.
5. Conclude that the transition at 170 nm corresponds to the HOMO-LUMO transition, likely involving a \\pi \, \text{to} \, \\pi^* \, \text{transition} \, \text{in} \, \text{the} \, \text{N}_2 \, \text{molecule}.

Key Concepts

HOMO and LUMO

The Highest Occupied Molecular Orbital (HOMO) is the highest energy orbital that contains electrons in a molecule, while the Lowest Unoccupied Molecular Orbital (LUMO) is the lowest energy orbital that is empty. The energy difference between these two orbitals is crucial for understanding electronic transitions, as it determines the energy required for an electron to be excited from the HOMO to the LUMO.

Electronic Absorption Spectrum

An electronic absorption spectrum is a graphical representation of the wavelengths of light absorbed by a molecule as electrons transition between energy levels. Peaks in this spectrum indicate specific electronic transitions, such as from the HOMO to the LUMO, and the position of these peaks can provide information about the energy levels of the molecular orbitals involved.

Orbital Transitions

Orbital transitions refer to the movement of electrons between different molecular orbitals, typically from a lower energy orbital to a higher energy one. In the context of the question, the transition from the HOMO to the LUMO corresponds to the absorption of a photon, which promotes an electron to a higher energy state, and is fundamental in understanding the electronic properties of molecules.