Moon has no atmosphere:

At N.T.P. the root mean square velocity for hydrogen molecules and for oxygen molecules are nearly 1.92 km/sec and 0.48 km/sec respectively, for nitrogen slightly higher than this. These are much less than the escape velocity of 11.2 km/sec from the surface of the earth. For this reason, the earth’s atmosphere is retained. Although some leakage of hydrogen does take place due to the higher R.M.S. velocity of the hydrogen molecules. Thus there is an excess of oxygen and nitrogen in the earth’s atmosphere.

On the other hand, the escape velocity on the surface of the moon is just 2.38 km/sec. Therefore almost all the molecules of hydrogen have escaped out from the atmosphere of the moon, only a rare amount of molecules of oxygen, nitrogen and other gases have been left.