Periodic system of elements in the form in which it exists today is just a convenient form of presentation of the late XIX early XX centuries. It does not fit into the Unified System of combinatorial evolution, adaptation and selection. It is in no way affiliated with the fundamental concept of nature - symmetry. It does not allow clear and easy to determine the accuracy of the experimental data for the nuclei of atoms and ions and their electron shells in general. In this work, an attempt was made to consider a set of atomic nuclei as a combination of a proton and a neutron with repetitions. Constructed a new form of chemical elements. On the example of the first twenty elements analyzed ionization energy of atoms. On the basis of previously made representations on unitary symmetry derived equation - conservation laws. It is shown that a significant number of data for the ionization energies of atoms were measured not accurately enough.