Heisenberg, in conjunction with the Austrian physicist Erwin Schrödinger, agreed
with the de Broglie concept that the electron is bound to the nucleus in a manner
similar to a standing wave. They developed the complex equations that describe
the wave-mechanical model of the atom. The solution of these equations gives
specific wave functions called orbitals. These are not related at all to the Bohr
orbits. The electron does not move in a circular orbit in this model. Rather, the
orbital is a three-dimensional region around the nucleus that indicates the
probable location of an electron but gives no information about its pathway. The
drawings in Figures 8a and 8b are only probability distribution representations of
where electrons in these orbitals might be found.
Quantum Numbers and the Pauli Exclusion Principle
Each electron orbital of an atom may be described by a set of four quantum
numbers in the wave-mechanical model. These numbers give the position with
respect to the nucleus, the shape of the orbital, its spatial orientation, and the spin
of the electron in the orbital.
TIP
The principal quantum number refers to the principal energy level: 1, 2, 3, and so on. The
angular momentum quantum number refers to shape.Principal
quantum
number
(n) 1, 2, 3,
4, 5, etc.
The values
of n = 1, 2,
3...This number refers to average distance of the orbital from the
nucleus. 1 is closest to the nucleus and has the least energy. The
numbers correspond to the orbits in the Bohr model. They are
called energy levels.Angular
momentum
(ℓ)
quantum
number
s, p, d, f
(in order of
increasing
energy)