The property that the elements in each column of the representative elements series of the periodic table have in common is: number of valence electrons.
An atom can be defined as the smallest unit comprising of matter that forms all chemical elements. Thus, atoms are basically the building blocks of matters and as such determines or defines the structure of a chemical element.
Generally, atoms are typically made up of three distinct particles and these are protons, neutrons and electrons.
Periodic table is an organized tabular array of all the chemical elements arranged in order of increasing atomic number (in rows).
Valence electrons can be defined as the number of electrons present in the outermost shell of an atom. Valence electrons are used to determine whether an atom or group of elements found in a periodic table can bond with others. Thus, this property is typically used to determine the chemical properties of elements.
In the periodic table, chemical elements that are having the same number of valence electrons are found in the same column.
This ultimately implies that, all the chemical elements such as Hydrogen, Sodium, etc., with one (1) valence electrons in their outermost shell (S-orbital) are found in the first (1st) column of the periodic table.
In conclusion, property that the chemical elements in each column of the representative elements series of the periodic table have in common is number of valence electrons.
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