The fundamental understanding of adsorption, absorption, diffusion, and permeation of hydrogen and its isotopes is of paramount importance in controlling the hydrogen-induced embrittlement and also very helpful in the selection of barrier materials, which can prevent the permeation of lighter gases. In view of that, we have performed a plane wave-based density functional theoretical calculation to investigate the interaction and dynamical behaviors of hydrogen and its isotopes in body-centered cubic Fe crystalline lattice. The activation barrier energy has been computed using nudge elastic band methods. Zero point energy was incorporated using phonon calculations to capture the isotope effects. The most favorable diffusion path of H atom was observed from one tetrahedral site to the nearest tetrahedral site. The calculated diffusion coefficients, rate constants, and permeability constants are found to be higher for H compared to its heavier isotopes D and T. Further, the diffusion and permeability coefficients of H, D, and T are found to increase with increase in the temperature. The present findings might help in the engineering design of tritium barrier materials.