So my knowledge of physics is limited to freshman physics where relativity and quantum mechanics (or atomic structure) were taught as two different things.
So, say a Hydrogen molecule travelling at half the speed of light - Is the e/m of the electrons the same ? Does the atomic radius change ? Does Lorentz transformation apply to atomic radii or is the change due to e/m or both ?
Neither charge nor mass is changed by motion at high speed, so neither is their ratio changed. Atomic radius isn’t as well-defined: An atom at rest is spherical, but one that’s moving past your at high speed will be squished flat in its direction of motion, so it won’t have a single “radius”. The circular cross-section will have the same radius, but it’ll be shorter than that from front to back.