The paper presents two modern versions of the periodic system of chemical elements by D.I. Mendeleev. Both variants contain in their structure a zero period in which the electron, proton and neutron are located, that is, this period does not contain chemical elements, but contains these three elementary particles – the constituent parts of any atom. According to the authors, an electron neutrino (electron antineutrino) should be located behind the zero period, and the photon completes the lower layer of the periodic table. From the photon to the universal Planck length, the scale of as yet unknown particles is realized in the range from 10-18 to 10-35m. Another feature of the proposed tables is the arrangement of lanthanides and actinoids in a perpendicular plane to the existing matrix. Moreover, in the second variant, the triad tables can also be located in a perpendicular plane. All quantum numbers corresponding to the proposed two variants of the periodic table are interrelated with fundamental constants of nature, for example, with such as the fine structure constant, the ratio of the mass of a proton to the mass of an electron, Feigenbaum constants, direct F and inverse f numbers of the golden proportion, the number 𝜋, etc. It is shown for the first time that the square of the product of the first and second Feigenbaum constants approximately coincides with the value of the inverse of the fine structure constant and the ratio F/f and with the limiting value of the orbital quantum number l.