The shells correspond to the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, ...).
In 1913, Niels Bohr proposed a model of the atom, giving the arrangement of electrons in their sequential orbits.
At that time, Bohr allowed the capacity of the inner orbit of the atom to increase to eight electrons as the atoms got larger, and "in the scheme given below the number of electrons in this [outer] ring is arbitrary put equal to the normal valency of the corresponding element".
"From the above we are led to the following possible scheme for the arrangement of the electrons in light atoms:"[3][4] The shell terminology comes from Arnold Sommerfeld's modification of the 1913 Bohr model.
During this period Bohr was working with Walther Kossel, whose papers in 1914 and in 1916 called the orbits "shells".
[5][6] Sommerfeld retained Bohr's planetary model, but added mildly elliptical orbits (characterized by additional quantum numbers ℓ and m) to explain the fine spectroscopic structure of some elements.
[8] The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies.
Moseley's work did not directly concern the study of electron shells, because he was trying to prove that the periodic table was not arranged by weight, but by the charge of the protons in the nucleus.
This led to the theory that electrons were emitting X-rays when they were shifted to lower shells.
[4][20][17] However, the electron shell development of Niels Bohr was basically the same theory as that of the chemist Charles Rugeley Bury in his 1921 paper.
Seeing this in 1925, Wolfgang Pauli added a fourth quantum number, "spin", during the old quantum theory period of the Sommerfeld-Bohr Solar System atom to complete the modern electron shell theory.
In particular, every set of five elements ( electric blue) before each noble gas (group 18, yellow) heavier than helium have successive numbers of electrons in the outermost shell, namely three to seven.
Sorting the table by chemical group shows additional patterns, especially with respect to the last two outermost shells.
The elements past 108 have such short half-lives that their electron configurations have not yet been measured, and so predictions have been inserted instead.