It is sometime difficult to project the effect of relativistic velocities on stable atoms. We can treat this theoretically within predefined limits, as is often done using special relativity, as a definition of the back ground conditions. But one must remember this does not represent the more complex real conditions an atom or object, moving with relativistic velocities would be subjected to. We just don't have a good real world reference.
The best we can do is to look at the solar or galactic winds. However, this does not provide an easily accessible data base, though it may exist. What I mean by this is that, those data references easily accessible talk about solar and cosmic winds in terms of the EM spectrum, which does not help us, and in terms of "ions". Keep in mind that a large portion of the ions being referred to are bare protons and alpha particles or bare helium nuclei. To be sure there are other ions present. I have seen reference to both oxygen and carbon ions. The problem is, that these ions could be anything from a bare nucleus to an atom missing one or more electrons.
The reason this is important to the issue you raise is that, if I understand you correctly you are asking how a relativistic velocity, in this case the speed of light, would affect matter, or atoms. We just don't have any practical data that supports any complex matter, meaning whole atoms, molecules or objects, moving at relativistic velocities, let alone the speed of light.
It seems likely from what we have observed that atomic structure, in practical real world conditions may not be stable at relativistic velocities. Our best information involving relativistic velocities, all seems to come from and involve ions and/or bare nuclei.
The only truely controlled conditions we have to judge this from originates within particle accelerators, and in those cases whole atoms are not involved in the relativistic velocities, except as stationary targets. We accelerate bare nucleons and nuclei, protons, neutrons, electrons and bare nuclei, not whole atoms.
The question you present, would seem to me only addressable as a thought experiment, where the background conditions are set and understood not to represent real world conditions.
Ask, how would this work in special relativity or a limited application of general relativity. How would it look from the prespective of Newtonian mechanics...?
But keep in mind that what you suggest as a starting point does not, at least to me, represent anything attainable in a real world environment. We just don't have any reliable information about what would happen to a clock or watch moving at the speed of light, under real world conditions.
We do know that both general relativity and special relativity, involve time dilation affects proportional to, once again.., an object's acceleration, location within a grabitational field and velocity. Will the clock remai a clock if it were moving AT the speed of light? Nobody knows, as we have yet to find a clock moving that fast.....
