An Introduction to the Electronic Structure of Atoms and MoleculesProfessor of Chemistry / McMaster University / Hamilton, Ontario

Listed below are a number of equations which give the dependence of , and on the quantum numbers n, l and m. They refer not only to the hydrogen atom but also to any oneelectron ion in general with a nuclear charge of Z. Thus He^{+} is a oneelectron ion with Z = 2, Li^{+2} another example with Z = 3.
The average distance between the electron and the nucleus expressed
in atomic units of length is:

Note that
is proportional to n^{2} for l =
0 orbitals, and deviates only slightly from this for l ¹
0. The value of decreases
as Z increases because the nuclear attractive force is greater.
Thus for
He^{+} would be only one half as large as
for H.


