given total charge Q uniformly distributes in an atomic nucleus with radius R.
If you mean the external electric potential due to the atomic nucleus then I believe the answer is exactly the same as the electric field for a point charge at the nucleus centre. So if you are a distance from the nucleus centre ( ) then the potential is
If you need to show this what you need to do is perform a volume integration in spherical coords. Your density is , and the distance to the volume element is . Then you want to evaluate
If we assume this integral is easy and gives the formula above.
I hope this is what you're after.