Hydrogen atoms and other free radicals have been produced by gamma irradiation of a number of substances at 4.2\ifmmode^\circ\else\textdegree\fi{}K. Electron spin resonance was employed for detection and study of the free radicals within the solids at this temperature. It was found that strong electron spin resonance signals of H atoms could then be produced by dosages of ${10}^{6}$ r or less in ${\mathrm{H}}_{2}$O, HF, ${\mathrm{H}}_{2}$, and C${\mathrm{H}}_{4}$, but no H atom signals could thus be produced in HCl, ${\mathrm{H}}_{2}$S, N${\mathrm{H}}_{3}$, NaH, or LiH. The spacing of the hyperfine doublet was approximately 504 gauss for the H signals observed. An anomaly in the relative intensities of the H doublet for irradiated ${\mathrm{H}}_{2}$O was detected and attributed to spin-spin interaction with a second free radical. It is concluded that in HF and ${\mathrm{H}}_{2}$O the H atoms are formed from electron capture by the essentially ionic hydrogens rather than by removal of an electron from the molecule (ionization). Because this process does not require displacement of the atoms from their original sites in the lattice, it can take place in hard-frozen, rigid solids. In ${\mathrm{H}}_{2}$, C${\mathrm{H}}_{4}$, and similar substances the production of H atoms requires the breaking of covalent bonds. This process, although initiated by ionization, appears to require also the displacement of the H from its original site in the lattice.