VI.

Quantum Theory

With the development of the quantum theory and its application to atomic structure by the Danish physicist Niels Bohr and other scientists, most of the detailed features of the periodic table have found a ready explanation. Every electron is characterized by four quantum numbers that designate its orbital motion in space. By means of the selection rules governing these quantum numbers and the exclusion principle of Wolfgang Pauli, which states that two electrons in the same atom cannot have all four quantum numbers the same, physicists can determine theoretically the maximum number of electrons required to complete each shell, confirming the conclusions inferred from the periodic table.

Further development of the quantum theory revealed why some elements have only one incomplete shell (namely, the outermost, or valence, shell), whereas others may have incomplete underlying shells as well. In the latter category is the group of elements known as the rare earth elements, which are so similar in properties that Mendeleyev had to assign all 14 to a single place in his table. The rare earth group includes the elements in the lanthanide series.