# Nitrogen with shortest bond length in histidine?

The question asks what nitrogen in the ring of histidine has the shortest bond length.

I was thinking that since it has resonance, the initial thought of the nitrogen with the $$\pi$$ bond is incorrect. However, I imagine the resonance structure shown in the figure below makes the greatest contribution to the resonance hybrid. Therefore making my first guess correct. The question also asks for a single line of reasoning so I am confused how to present my thinking concisely.

It is correct that the $$\ce{N}$$ with the double bond has a localized lone pair, because of its $$sp^2$$ hybridization, due to which the lone pairs are in the same plane as ring, and hence not conjugated.
However, the other $$\ce{N}$$ is clearly in conjugation, hence, if you draw the $$5$$ possible resonance structures, you would notice that each bond in the ring is a double bond for exactly $$2$$ of them. However, since there is a positive charge on electronegative $$\ce{N}$$ in all of them except the one you have drawn, this structure would have maximum contribution. Thus, the shortest bond length indeed would be the one you've shown as a double bond in your figure, although in reality it would have bond order $$<2$$ due to resonance.