The work (1913–14) of H. G. Moseley on the X-ray spectra of elements (see X ray) led to the present form of the periodic law. He found that the wavelength of the X-radiation of elements decreased with increasing atomic weight. However, the relationship was not a strict one. He assigned a new set of numbers, called atomic numbers, to the elements he had studied, so that there was a relation between the wavelength and the atomic number. The atomic number is the number of positive charges, or protons, contained in the atomic nucleus (see atom) or, equivalently, the number of negative charges, or electrons, outside the nucleus in a neutral atom. The periodic law can be explained on the basis of the electronic structure of the atom, which is believed to be the main factor underlying the chemical properties and many of the physical properties of the elements. In turn, the electronic structures of atoms have been successfully accounted for by the quantum theory.
In spite of its great success, the periodic system that had been introduced by Mendeleev had some discrepancies. Arranged strictly according to atomic weight, not all elements fell into their proper groups. Better arrangement could be made if the positions of certain neighboring couples were interchanged. For example, to suit the chemical order of the table, the inert gas argon (at. wt. 39.948) should come before the chemically active metal potassium (at. wt. 39.0983). Through Moseley's work, it was found that although the atomic number of an element is roughly half its atomic weight, the atomic weight does not always increase with increasing atomic number. The discrepancies occur just for those elements where Mendeleev's law failed. Based on atomic number, the periodic law now has no exceptions. Although all the missing elements in the periodic table have been found (with the aid of the periodic table itself), the table retains its usefulness to the chemist as a reliable check for disputed or uncertain data concerning some of the known elements.