Atomic radii are determined via construction of dependences between dissociation energies of homonuclear diatomic molecules, on the one hand and linear and volume fractions of the overlap area of spherical atoms, on the other hand. The procedure is accompanied by checking out whether the obtained radii satisfy the conditions of periodicity and correlation to atomic refractions and ionization energies and is completed by comparison of the radii with those derived from the wave functions of Clementi and Roetti (1974). There is an excellent coincidence of the radii of /7-elements if the theoretical ones are restricted by a defmite level of electron density. There is an unambiguous dependence of the cohesion energy on the volume fraction of the overlap area with particular trends for mono-, di- and tri-valent elements. These results support the idea that atoms tend to retain their volumes in homonuclear molecules. The most reliable explanation is repulsion of moving electrons. In crystals, the valence electrons of neighboring atoms have a smaller possibility to escape each other. It would lead to a greater distortion of their volumes and shape. However, there is also a quite satisfactory dependence between sublimation energy and atomic overlap volume fraction. Thus, atoms really exist in homonuclear substances due to their interpermeability. This property does not strongly violate the one of the basic principles of quantum chemistry - indistinguishability of electrons. It assumes that electron exchange has a rather small probability.