A new method and devices for cooling of atomic hydrogen up to the values less than 100 µK aimed for the development of the optical frequency standard with significantly improved parameters (Δν/ν£1 x 10-16) is discussed. The method exploits the unique properties of atomic hydrogen such as atomic hydrogen does not condense at temperatures as low as 20µK and can not be heated by IR radiation in the absence of atom-wall collisions. Therefore, the most efficient and well-known gas cooling technique can be employed, namely, the adiabatic expansion of the volume occupied by the gas. This approach is used in a cryogenic gas expansion machine. It is suggested to use the adiabatic expansion of the volume of the magnetic atomic trap containing atomic gaseous hydrogen for embodiment of this idea.