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We consider hyperfine splitting of 1s and, in part, of 2s levels in lighthydrogen-like atoms: hydrogen, deuterium, tritium, helium-3 ion, muonium andpositronium. We discuss present status of precision theory and experiment forthe hfs intervals. We pay a special attention to a specific difference, D_{21}= 8 E_{hfs}(2s) - E_{hfs}(1s), which is known experimentally for hydrogen,deuterium and ^3He^+ ion. The difference is weakly affected by the effects ofthe nuclear structure and thus may be calculated with a high accuracy. Wecomplete a calculation of the fourth order QED contributions to this differenceand present here new results on corrections due to the nuclear effects. Ourtheoretical predictions appear to be in a fair agreement with availableexperimental data. Comparison of the experimental data with our examination ofD_{21} allows to test the state-dependent sector of theory of the hfsseparation of the 1s and 2s levels in the light hydrogen-like atoms up to10^-8.Comment: 12 pages, 1 figur

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Hyperfine structure of the ground and first excited states in light hydrogen-like atoms and high-precision tests of QED