have the extra complication of the electrical interaction between the
two electrons, rather than being able to imagine everything in terms
of an electron moving in a static field of force created by the nucleus
alone.
Despite all this, it turns out that we can get a surprisingly good
description of many-electron atoms simply by assuming the elec-
trons can occupy the same standing-wave patterns that exist in a
hydrogen atom. The ground state of helium, for example, would
have both electrons in states that are very similar to then= 1
states of hydrogen. The second-lowest-energy state of helium would
have one electron in ann= 1 state, and the other in ann= 2 states.
The relatively complex spectra of elements heavier than hydrogen
can be understood as arising from the great number of possible com-
binations of states for the electrons.
A surprising thing happens, however, with lithium, the three-
electron atom. We would expect the ground state of this atom to
be one in which all three electrons settle down inton= 1 states.
What really happens is that two electrons go inton= 1 states, but
the third stays up in ann= 2 state. This is a consequence of a new
principle of physics:The Pauli Exclusion Principle
Two electrons can never occupy the same state.^12There are twon= 1 states, one withsz= +1/2 and one with
sz = − 1 /2, but there is no thirdn= 1 state for lithium’s third
electron to occupy, so it is forced to go into ann= 2 state.
It can be proved mathematically that the Pauli exclusion prin-
ciple applies to any type of particle that has half-integer spin. Thus
two neutrons can never occupy the same state, and likewise for two
protons. Photons, however, are immune to the exclusion principle
because their spin is an integer.Deriving the periodic table
We can now account for the structure of the periodic table, which
seemed so mysterious even to its inventor Mendeleev. The first row
consists of atoms with electrons only in then= 1 states:
H 1 electron in ann= 1 state
He 2 electrons in the twon= 1 states
The next row is built by filling then= 2 energy levels:
Li 2 electrons inn= 1 states, 1 electron in ann= 2 state
Be 2 electrons inn= 1 states, 2 electrons inn= 2 states...
O 2 electrons inn= 1 states, 6 electrons inn= 2 states
F 2 electrons inn= 1 states, 7 electrons inn= 2 states
Ne 2 electrons inn= 1 states, 8 electrons inn= 2 states
938 Chapter 13 Quantum Physics