These
are the molecular orbitals, or electron probability clouds, that
a simple diatomic (two-atom) molecule can have. What can we say
about their energies, other than that half of the MO's are bonding
orbitals and half are antibonding? The energies all can be calculated
from molecular orbital theory and given numerical values, but we
can reach the same goal in our nonmathernatical treatment by recognizing
the significance of nodes in the wave functions. Other things being
equal, the greater the number of nodes in any wave, the higher the
energy. We have seen this principle before, but have not recognized
it explicitly. A high-frequency light wave has more nodes per unit
length (the wave returns to zero more often) than a low-frequency
one (see upper right). By the relationship E = hn,
higher frequency means higher energy. The same principle holds for
atomic orbitals (right): An s orbital is spherically symmetrical,
a p orbital has one nodal plane, and a d orbital has two nodal planes.
The energy within one n level accordingly increases from s to p
to d.