Final answer:
The central bond in 1,3-butadiene is shorter than a regular single bond due to electron delocalization, which confers partial double bond character to that bond.
Step-by-step explanation:
The central bond of 1,3-butadiene is much shorter than a regular single bond because of electron delocalization within its conjugated system. In 1,3-butadiene, there is a conjugated system of alternating single and double bonds where the p-orbitals overlap allowing for the pi electrons to be delocalized across all four carbon atoms. This delocalization leads to a situation where the central bond exhibits partial double bond character, hence why it is shorter than a single bond that would normally result if the pi electrons were localized.
Comparing the molecular orbital (MO) picture of 1,3-butadiene to an isolated pi-bond example, we notice that the HOMO-LUMO energy gap is smaller in the conjugated system, characteristic of this delocalization. Furthermore, the conjugation affects the compound's reactivity and other physical properties, such as the fact that 1,3-butadiene absorbs UV light with a wavelength of 217 nm, which is indicative of its electronic structure.
It's important to differentiate this behavior from systems like butyne or benzene, where the structures and bonding differ. Butyne has a triple bond which leads to different chemical properties, and benzene, with its six-membered ring of delocalized electrons, has extraordinary stability.