The center of mass of a hydrogen atom can be calculated based on the relative masses of its constituents, the proton and the electron. Given that a proton is approximately 1837 times heavier than an electron, we can assume that the mass of the proton is much greater than that of the electron.
Since the center of mass is determined by the distribution of masses, in the case of a hydrogen atom, the center of mass will be very close to the position of the proton. The electron's mass is negligible compared to the proton, so its contribution to the center of mass is practically negligible.
Therefore, the center of mass of a hydrogen atom is located very close to the position of the proton.