Observations are reported of the ground state hyperfine resonance of hydrogen atoms stored in a 5 cm. diameter bottle coated with frozen molecular hydrogen. Dephasing of the hyperfine resonance while the atoms are adsorbed produces frequency shifts which vary by a factor of two over the temperature range 3.7 K to 4.6 K and radiative decay rates which vary by a factor of five over this range. The magnitudes and temperature dependences of the frequency shifts and decay rates are consistent with a non-uniform distribution of surface adsorption energies with mean about 38(8) K, in agreement with theoretical estimates for a smooth surface. Extrapolation of the 30 nanosec. mean adsorption times at 4.2 K predicts very long adsorption times for H on H2 below 1 K. Studies of level population recovery rates provide evidence for surface electron spin exchange collisions between adsorbed atoms with collision duration long compared to the hyperfine period, suggesting that the atoms are partially mobile on the surface. The lowest rates observed for level population recovery set a lower limit of about 500 atom-surface collisions at 4.2 K without recombination