In the framework of the Thomas-Fermi (statistical) model of neutral heavy atoms, in this paper we investigate the electronic structure of the atoms from the Mendeleyev table, namely the order of filling with electrons of various sub-shells of a shell. Because exact solutions of the Thomas-Fermi equation do not exist, we will use three new approximate solutions, compatible with the boundary conditions. By means of an old and, in the same time, well-known method, we investigate the distribution of the electrons according to their angular momentum, that is to say, we calculate the minimum value of the atomic number Z for which the filling of s- , p-, d- and f-state is possible in atoms. For one of these trial functions (with a good confidence - in our opinion), the deduced values of the atomic number Z, at which a given value of orbital angular momentum (quantum number l ) can appear, are in enough good agreement with the reality.