Question on conjugated pi bonds

Question

1,2,3-butatri-ene is given, and the number of conjugated pi bonds is asked. The answer given is 2, but I am not sure how?

Answer 1

The molecule you refer to is an allene because it contains cumulative double bonds. It is linear. The double bonds are continuous without alternating single bonds between the double bonds. Because carbons 2 and 3 are sp hybridized and carbons 1 and 4 are sp² hybridized, carbons 2 and 3 must use different p orbitals to form the pi bonds with the outer carbons. The p orbitals on carbons 2 and 3 are perpendicular to the p orbitals on carbons 1 and 4. So, there are only two pi bonds in conjugation. The outer pi bonds are conjugated, but the center pi bond cannot participate in resonance because it is not in the same plane. Let me know if you need further clarification.