The most accurate to date determination of the frequency of the quantum states in the hydrogen atom has been determined to be Hz (Udem et al. 1997).
References
Udem, T.; Huber, A.; Gross, B.; Reichert, J.; Prevedelli, M.; Weitz, M.; and Hansch, T. W. "Hydrogen-Deuterium 1S-2S Isotope Shift and the Structure of the Deuteron." Phys. Rev. Let. 80, 468-471, 1997.
