Account for the fact that C₂-C₃ bond length in 1,3 butadiene is shorter than expected value.

C2-C3 bond length is shorter than the expected value due to resonance in 1,3 butadiene. There are two resonance structures possible for this. The other one is not too stable but it does contribute towards the hybrid. You can draw and see.

IN 1,3 BUTADIENE THERE IS CONJUGATION BETWEEN THE PHI BOND BETWEEN C1-C2 AND C3-C4 SO DUE TO RESONANCE THE SINGLE BOND BETWEEN C2-C3 HAS PARTIAL DOUBLE BOND CHARACTER AND SINGLE BOND CHARACTER SO THE BOND LENGTH BETWEEN C2 C3 IS GREATER THAN A CARBON CARBON DOUBLE BOND AND HAS A LESSER BOND LENGTH THAN A CARBON CARBON SINGLE BOND