Comparative radon investigations of two natural materials, crystalline apatite and amorphous oxide, are presented here. The radon retention in the apatite (sedimentary apatite) is more than 70% of the total radon formed in the solid matrix. The amorphous oxide (gel hydrothermal alteration) retains only 7% of radon. The nature of the material which plays an important role in the radon diffusion is confirmed by heat treatment. The major and interesting result of this heat treatment is increasing of crystallite size. This phenomenon induces improvement on radon retention ability. To study these properties one uses a structure band calculations based on the Linear Combinations of Orbital Atomic (LCAO) method convenient numerically for the ionic systems.