Final answer:
The configurational change from all-trans-lycopene to 13-cis-lycopene is detectable in a UV-vis spectrum at a particular wavelength, which is influenced by its conjugated pi system and the resulting electronic transitions. Extended conjugation causes absorption in the visible spectrum, allowing the detection of cis/trans isomerization events.
Step-by-step explanation:
The configurational change from all-trans-lycopene to 13-cis-lycopene, catalyzed by I2 (iodine), can be observed in a UV-vis spectrum due to the molecule's extended system of conjugated pi bonds. The specific wavelength at which this configurational change can be detected is dependent on the electronic transitions that take place within lycopene's structure. Such molecules have a smaller HOMO-LUMO (Highest Occupied Molecular Orbital - Lowest Unoccupied Molecular Orbital) gap, leading to light absorption in the visible spectrum as opposed to the UV region.
In general, conjugated compounds like all-trans-lycopene with numerous conjugated double bonds absorb light at longer wavelengths. The alteration from a trans configuration to a cis configuration, as seen in lycopene, may result in a new peak on the UV-vis spectrum corresponding to the shift in the conjugated system. The exact wavelength for the cis peak has to be determined experimentally, as it is influenced by the extent of conjugation and the resulting electronic transitions of that particular isomer. However, for demonstration, beta-carotene, not to be confused with lycopene but also a compound with an extended conjugated pi system, absorbs in the blue region, causing a compound like it to appear orange because of the transmitted red-yellow wavelengths. Since the absorption occurs in the visible rather than UV region, we can infer an analogous trend for lycopene.