It means that if the elements are arranged in order of increasing atomic numbers, the elements with similar properties appear after regular intervals.
Moseley’s view appears to be correct, because atomic mass of an element is due to the mass of protons and neutrons present in nucleus. Since nucleus is located well within the atom and is shielded by electrons, it cannot interact with the reagent and hence cannot effect the chemical properties. Actually it must be the electrons which interact with the reagent because electrons are exposed to environment. Thus the properties of an atom depends the atomic number not on atomic mass.
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