Numbers
So Quantum far, we are aware of three integer quantum numbers for atoms: the principal (n > 0),
the angular (0 l < n), and the magnetic (-l m l ). It was subsequently shown that
there must be a fourth quantum number bearing a separate resonance of the electron itself
when it exists apart from the atom as a particle-like entity. It is called the spin quantum
number and given the unfortunate symbol ms. This quantum number is not an integer and
can have one of only two values regardless of the situation: + or . You will be
expected to be able to distinguish valid sets of quantum numbers (n, l, m , ms) from
invalid ones using the rules above. For instance, the set (0, 2, -3, 1) actually has four fatal
flaws: n cannot be zero; l cannot be greater than n; the magnitude of m cannot be greater
than l; and ms must be either or -. Each set of distinct quantum numbers represents a
distinct electron in a given atom. Two cannot have the same numbers as their resonances
would cancel out. This is called the Pauli exclusion principle.
l
l
l
Even though these numbers were found by the excitation to higher and higher energies of
the electron in the hydrogen atom, they describe the possible component resonances of
the electrons in all atoms. Chemistry texts often take the time to describe orbitals of
electrons in atoms, but usually fail to mention that these are simply the regions of wave
function resonance (anti-nodes) for the standing waves that compose the atoms, that give
them their unique chemical characteristics. Virtually everything with which you will ever
interact the has properties it does because of these resonance patterns.
The principal quantum number occurs in the classical radius of the atom. This is the mean
distance of the strongest resonance zone from the nucleus for any give shell. The values n
= 1, 2, 3, . . . correspond to the shells K, L, M, . . .. For the moment, we will not care
about these capital letters, only the numbers. The angular quantum number is said to
specify the subshell. The values l = 1, 2, 3, 4, 5, . . . have been given the subshell
designations s, p, d, f, g, . . .. The first four stand for sharp, principal, diffuse, and
fundamental, but then the decision was made to simply start following the alphabet after
f. The first subshell (l=0) of the fourth shell (n=4) is thus identified by the label 4s. Every
s subshell has an overall spherical geometry and (doing the math) holds up to two
electrons. Every p orbital is barbell-shaped and holds six. Every d orbital, which holds up
to ten electrons, is either clover-shaped or else like a barbell with a donut around it. The f
orbitals hold up to 14 electrons and are still more complicated. These numbers determine
the shape of the period table. Rearranged slightly, it looks like the image below:
f (14 elements)
Lanth anides
Actinides
d (10 element s)
p (6 elements)
3d transitions
4d transitions
5d transitions
6d transitions
B C N O F Ne
Al S i P S C l Ar
Ga G e As Se Br Kr
I n Sn Sb T e I X e
Tl Pb Bi Po A t Rn
(Elem. 113 118)
s (2 elements)
H
He
Li
Be
Na
Mg
K
Ca
Rb
Sr
Cs
Ba
Fr
Ra
No t y e t fo u n d
n=1
n=2
n=3
n=4
n=5
n=6
n=7
n=8
n=9