De Broglie's idea, as stated previously, was that electrons were both
particles and waves, ie. particles traveling in a sinuous path. A series
of experiments seemed to confirm his assumption.
In the double-slit experiment, a candle shines light at a wall
with two holes in it. Light, being composed of waves, begins at the left
and propagates toward the slits. Upon reaching them, the waves begin anew.
The two daughter waves interfere at some points along the waves, and are
in phase at other points. The resulting picture on the final wall has
regions of low intensity or amplitude, where the waves canceled out. Other
areas are of higher amplitude, where the waves were strengthened.
If particles were shot through the double-slits instead of waves, one
would not expect an interference pattern. There would be
regions behind each hole where the particles ended up the most .
So curious scientists decided to shoot electrons in the double-slit experiment
to
see what would happen. It turned out that electrons formed an interference
pattern! Electrons were in fact waves. Similar results were
observed with other sub-atomic particles: protons, neutrons, positrons.
There seemed to be a symmetrical pattern in the structure of these particles..
In some situations, they behaved like particles. Other times, they acted
just like waves. This property of matter is termed wave-particle
duality.
Max Born later clarified that the waves represented the probability
that a particle was at some position in time. The electrons in the double-slit
experiment were particles with unknown position as they traveled from the
source to the final wall. Instead of acting as real particles, the probability
waves canceled and strengthened each other, meaning that electrons were more
likely to be at certain places than other.
The wave-particle duality allowed quantum mechanics to further develop.
Erwin Schrödinger introduced his wave equation based on the duality and Planck's
quantum theory. Schrödinger's wave equation , with
multi-variable differential calculus, allowed the probability waves to be
tracked throughout time. It formed the base of wave mechanics, which were may be
used to derive the concepts of energy eigenstates, quantum mechanical tunneling
and scattering, wave packet dispersion, and particle bound states. Most
importantly, the equation successfully explained atomic orbitals, atomic
interactions, and molecular bonds.
One major puzzle in nuclear physics in the early twentieth century was
the alpha decay of radioactive nuclei. Alpha particles consist of two p
rotons and two neutrons. When a nucleus decays through alpha radiation,
it emits an alpha particle and a new nucleus (element) results. Scientists
treated the nucleons as regions of differing potentials, ie. the nuclei
was an area of positive voltage while the neighboring spaces were neutral.
According to classical mechanics, it was unthinkable that a wave-particle
could pass through such a potential step. The wave would supposedly only
bounce back from the step, unable to penetrate the barrier and escape
from the nucleus. Alpha decay, in terms of classical physics, was impossible.
However, Schrödinger's wave equation marvelously explained the phenomena.
When one applies the equation to a potential step, as in the nucleus,
it is found that waves may in fact pass through the potential barrier.
A small portion of these waves, as position-probability waves, enters the
forbidden zone. This is interpreted to mean that there is a small probability
that an alpha particle may escape the nucleus as radiation.
This process is called tunneling.
One major puzzle in nuclear physics is the puzzle of alpha decay.
In the decay of Uranium, physcists had measured the energy of the alpha particle that was thrown out of the nucleus and found it to be aobut 4 MeV (eV is an electron-volt).
This amount of energy is coorisponding to the energy levels of an atom.
Normally processes involving nucleus requires more energy than those
envolving electrons.
This figure is Gamow's original application of quantum tunnelling or
otherwise known as alpha decay. Alpha particles are unusually stable, so one can consider them as existing in a nuclear potential due to all the other particles in the nucleus. It is clear that it is possible for
an alpha particle to tunnel out of the nucleus causing it to decay.
This is a plot for the binding energy per nucleon corresponding to
mass number A, which is the total number of nucleons in the nucleus. Nucleon is
the combination of both proton and neutrons.
