In this work, we report on electron spin resonance studies of H atoms stabilized in solid H₂ films at temperature 0.1 and 0.7 K and in a magnetic field of 4.6 T. We produced H atoms by two different techniques: bombarding H₂ films by 0.1 keV electrons generated during an rf discharge run in the sample cell or exposing H₂ films to a flux of 5.7 keV electrons released during tritium decay. We observed a faster H atom accumulation in the films made of H₂ gas with a small initial ortho-H₂ content (0.2-3%) as compared with those made from the gas with a higher initial ortho-H₂ admixture. The accumulation rate difference was about 70% for the samples exposed to high energy electrons and about an order of magnitude for the samples bombarded by low-energy electrons. We propose possible explanations for the observed behavior.