We have studied thermal mobility of atomic hydrogen in solid Xe using decomposition of water molecules as a source for hydrogen atoms. The formation of various isotopomers of HXeH and HXeOH is monitored at temperatures from 37 to 42 K by using infrared absorption spectroscopy, and the activation energy of this diffusion-controlled process is found to be similar to110 meV. Most importantly, the different mobility for hydrogen isotopes is demonstrated, H being faster than D, and the difference between the corresponding activation energies is estimated to be similar to4 meV. The electron paramagnetic resonance measurements of the thermal decay of H atoms and OH radicals show that the formation of HXeH and HXeOH is controlled by hydrogen mobility. The modeling of thermally activated jumps of hydrogen atoms in a relaxed Xe lattice agrees reasonably with experiment with respect to the isotopic effects but it underestimates the jump rate.