I decided to look up atoms in 4d and I found an interesting article that talks about why gravity and electromagnetism would have a 1/r potential in higher dimensions.
https://www.zarm.uni-bremen.de/fileadmi ... Macias.pdf
It talks about how when we assume that gravity and the force between two charges have a drop off of 1/r^(d-1) then stable orbits are in fact impossible but the only reason that we tend to assume a force of 1/r^(d-1) is because we assume that Maxwell's equations for electromagnetism, Newton's Field Equations, and Einstein's Field Equations would be the same in higher dimensions and try to extrapolate what effects they have on higher dimensions. It says though that Rutherford's Scattering Experiments seem to indicate that the 1/r potential is actually more fundamental than Maxwell's Equations for Electromagnetism so that in higher dimensions it would be Maxwell's Equations that are modified to fit the 1/r potential instead of the other way around. This means that in any number of dimensions the force between two charges is 1/r^2 instead of 1/r^(d-1). It also says that for Gravity we can assume a 1/r potential and modify Newton's field equations, and Einstein's Field Equations in order to get the 1/r potential for gravity which would also produce an inverse square law. This also means that there would be stable orbits in higher dimensions because the gravitational force between two masses is 1/r^2 in any number of dimensions instead of 1/r^(d-1). This seems to be saying that it is not only possible to adjust Maxwell's Equations as well as Newton's, and Einstein's Equations to produce stable orbits and stable atoms but that if there is the same kind of gravity, electromagnetism in higher dimensions then modifying Maxwell's Equations as well as Newton's, and Einstein's Equation is required.