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We have measured the isothermal buildup of the atomic-hydrogen (T and D) concentration inside solid T{sub 2} and D-T from 1.3 to 10 K. The atoms are produced by the {beta} decay of tritium. Measurements were made using adiabatic slow-passage electron-spin-resonance (ESR) techniques. The atom concentration increases with time and does not saturate for the duration of our experiments ({gt}2000 min). The atom concentration increases with decreasing temperature, and reaches values over 0.2% below 3 K. Using a simple analysis we find (1) the atomic recombination coefficients, (2) the production rate of trapped atoms that are visible with ESR, (3) the atomic diffusion coefficients, and (4) the trapping energy for atoms in the solid. Finally, we have observed that in D-T the number of D atoms is equal to the number of T atoms, while in HD+2%T{sub 2} the number of H atoms is greater than the number of D atoms.