Geoscience Reference
In-Depth Information
•
l
, which represents the orbital angular momentum and
describes the number of possible angular momentum states.
Azimuthal quantum number,
Magnetic quantum number,
•
m
, where azimuthal represents the angular measurement in
a spherical coordinate system.
Spin quantum number,
•
s
. This number represents the intrinsic angular momentum.
It is important to note that matters are further complicated because for each principle quan-
tum number value (
n
) there are
n
- 1 values for
l
. In addition, when
s
is taken into con-
sideration for any quantum value
n
then there are a total of 2
n
2
states of the same energy
possible. This prohibition against more than one electron occupying the same quantum
energy state became known as the Pauli exclusion principle (Pauli,
1925
,
1926
; Massimi,
2005
).
1.2.1.3 Copenhagen Interpretation
The work of Louise de Broglie in
1923
linked wavelength, frequency, and momentum,
and de Broglie formulated the theory that any moving subatomic particle or object had an
associated wave. This theory saw the birth of wave mechanics (
mécanique ondulatoire
), a
mathematical unifying of the physics of energy (wave) and matter (particle). In 1925 an
explanation of the spin quantum number (the fourth parameter), which had been shown to
have two distinct possible values, was provided by the Dutch physicists George Uhlenbeck
and Abraham Goudsmit when they suggested that an electron, in addition to the angular
momentum of its orbit, could possess an intrinsic angular momentum. This property became
known as spin and explained the previously mysterious splitting of spectral lines observed
with a high-resolution spectrograph; this phenomenon is known as fine structure splitting.
In Copenhagen between 1925 and 1927, in an attempt to overcome the physical con-
straints and limitations of his theories, Bohr collaborated with the German physicists
Werner Heisenberg and Max Born and the Austrian physicist Erwin Schrödinger to develop
the use of abstract mathematical and theoretical formulations instead of physical empirical
experiments. This was an important shift in scientific thinking, the main thrust of which
was to explain the observations of everyday life and observation through mathematics, the
so-called 'matrix mechanics (Born et al.,
1925
; Born and Jordan,
1925
; Heisenberg,
1925
).
These models utilized matrices (rectangular array of numbers) to describe properties such
as momentum, energy, and position as opposed to ordinary numbers. In 1927, Heisenberg
published the uncertainty principle. The Heisenberg uncertainty principle gives an insight
into the nature of the quantum system itself and states that it is impossible to simulta-
neously know the momentum and position of a quantum object (e.g., electron) with perfect
accuracy. Furthermore, Heisenberg continued to show that the more precisely one property
is measured, the less precisely the other
can
be measured. The very act of observing a par-
ticle at any one point in time and space will change the behavior of that particle within the
quantum system. Therefore the uncertainty principle is not concerned about the limitations
of scientists or measurement techniques, but is a mere description of the nature of the quan-
tum system itself. Consequently, it is not possible to know the values of all of the properties
