We have a reference system in a conducting coil . Our reference velocity is the velocity of current(electrons).

Why the spacing between the nuclei is smaller than if we take as reference system with reference velocity the velocity of nuclei?

Length contraction decreases the dimensions of the nuclei , not making smaller the spacing between the nuclei.

Why the spacing between the nuclei is smaller than if we take as reference system with reference velocity the velocity of nuclei?

Length contraction decreases the dimensions of the nuclei , not making smaller the spacing between the nuclei.

What is the context of this question? What are you trying to do, learn, or analyze?

How do you know the velocity of the electrons? You said something about a coil, so aren't the electrons traveling in circles?

Are you asking about a

What is the velocity of the nuclei?

The circle is a bit hard for me for that reason to discuss further. But, if you have a long line of electrons moving at a steady velocity, then that electric current creates a magnetic field. If you move at the same velocity in the same direction, then those electrons appear stationary and what you see and can measure is an electric field instead of a magnetic field. This effect was understood before special relativity. Maxwell wrote his equations and came up with this conclusion. For this reason, he went to Faraday, his scientific friend, who is laughed at by other physicists when Faraday made a conjecture that the speed of light was constant, and told Faraday that is conjecture was correct. That is from Maxwell's equations, you could actually compute the speed of light.

Maxwell's equations and michelson-morley experiment were part of the reasons that led Einstein to make the constant speed of light a postulate 4 special relativity.