"Bead Guns" are a staple of science fiction. Conceptually, it is a short rail-gun that fires a tiny bead* at a significant fraction of the speed-of-light.
If the 14.5mm Soviet anti-tank (and GPU round) is the practical maximum amount of recoil for a man-fired weapon, then a 1.0mm aluminum-oxide bead will have the same momentum (equal-and-opposite creating the recoil) when fired at 0.1C. The upside is that it will have approximately twenty-eight thousand times as much kinetic energy as the 14.5mm round.
The momentum deposition of the impact on the target is not as straightforward as it first appears. After all, it has no more momentum than the 14.5mm Soviet. What caves-in and destroys armor is the fact that the bead's energy is converted to heat when it impinges on the armor and the vaporized (plasma, actually) armor creates inward momentum as it explodes outward.
One technical problem that is usually overlooked by Sci-Fi writers is that the energy in the bead rapidly converts to heat as it travels through the atmosphere. Without some "tunneling" strategy, the only way to ensure a bead actually makes it to the target is to fire a great number of them in rapid succession. That causes recoil problems and tends to launch the person shooting the rail-gun into low-earth orbit.
Fortunately, for every problem there are usually multiple solutions.
The most elegant solution is to "drill" through the atmosphere with a 85nm (on earth**), short-wave length UV laser before launching the bead.
85nm is the wavelength associated with the energy required to ionize N2. N2 is approximately 75% (by mass) of earth's atmosphere. A sufficiently powerful enough of a laser will superheat the air along the path and cause it to explode outward, much like the passage of lightning. Appropriately timed, a bead can be fired down the tube of near-vacuum and thus avoid the problem of vaporizing enroute.
I hope this treatise has been helpful as we all tinker in our basements during Covid times.
*"Bead" morphs to something entirely different when translated from Standard Galactic back into Archaic American English. "B", as everybody knows, translates into "30". The remaining characters translate into -06.
Based on this rudimentary linguistic analysis, we can look forward to major advances in propellants and sabot technologies in the future.
**Other planets require different laser wavelengths if the primary component of the atmosphere is something other than Nitrogen.