184 The Poetry of Physics and The Physics of Poetry
determines its angular momentum or the eccentricity of its elliptical
orbit, m that determines the orientation of its orbital plane and ms that
determines the orientation of its spin. The number n is an integer, which
does not exceed 7; l is an integer ranging from 0 to n – 1; m is an integer
with 2l + 1 values that range from –l to +l and ms = ±1/2.
All electrons are identical. There is no way of distinguishing one
electron from another. If an electron from an atom was removed and
replaced by another electron with the same quantum numbers the atom
would be identical. The principle of indistinguishability applies to all the
other elementary particles in addition to the electron. There is no way of
distinguishing one proton from another or one neutron from another.
Two photons with the same frequency are identical.
In 1925, Pauli discovered on the basis of his study of the energy
levels of various atoms that no atom could contain two electrons with
the same quantum numbers. Thus, for example, two electrons in an
atom with the same values of n, l and m would be obliged to have
their spins aligned in opposite directions, i.e., ms = +1/2 and –1/2. It
would be impossible to introduce into this atom a third electron with
the same value of n, l, and m as the first two. The electron would
be excluded by the Pauli exclusion principle. The Pauli exclusion
principle also explains the regularities of the periodic table of chemical
elements.
In 1871, the Russian chemist Mendeleeff proposed a classification
scheme of the chemical elements. He found that if he ordered the
chemical elements by their atomic mass or weight the elements with
similar chemical properties recurred periodically at more or less regular
intervals. He constructed a table of the elements by increasing the atomic
weight such that elements with similar chemical properties appeared in
the same column. He left certain entries blank, which he predicted would
be filled by elements that had not yet been discovered. He also described
the chemical properties these missing chemical elements would possess
on the basis of the chemical properties of the other elements in its
column. The discovery of these elements displaying the properties
predicted by Mendeleeff dramatically demonstrated the validity of his
scheme. The x-ray work of Mosely in which he determined the nuclear
charge of each element helped to refine the Mendeleeff classification
scheme. For example, it explained why Argon, with atomic weight 39.9
but atomic number 18 comes before potassium with atomic weight 39.1
but atomic number 19.