(this
is arrived at by equating E=hf and E=mc2)9.2.6
Wave particle duality
Many
of light’s properties can be explained by considering it to be a transverse
wave motion. Reflection, refraction, diffraction, interference and polarisation
can all be satisfactorily explained. However the photoelectric effect poses
problems because it is necessary to attribute particle like properties to light
in order to explain this phenomena.
Note:
remember that the wave model and the particle model are exactly that – just
models which help us to explain the behaviour of light. Neither of them is a
literal description of what light is.
In
1924, in his PhD thesis Louis de Broglie wrote,
‘...
I assumed that the existence of waves and particles, perceived by Einstein in
1905 in respect of light in his theory of light quanta, should be extended to
all types of particle in the form of coexistence of a physical wave with a
particle incorporated in it....’
De Broglie was
suggesting that all matter should have both a wave and a particle
characteristic. Other than light there was no experimental work to justify this-
it was pure speculation. He suggested that the wavelength of all matter was
given by the relation
(this
is arrived at by equating E=hf and E=mc2)
where r
= mv, the particle’s momentum
This
equation was confirmed by experiments carried out on electron diffraction by
Davisson and Germer in 1927.
When
an electron is accelerated through a pd V the work done on the electron is eV.
If the energy gained by the electron is entirely kinetic, then
and
thus
from which it can be
shown that
It
can thus be shown that the wavelength of an electron accelerated through a pd of
100V will be approximately 1.2 x 10-10m. This is approximately the
same value as the wavelength of X-rays, which can be diffracted by metal
crystals. Thus metal crystals ought to be able to diffract electrons too.
In
1927 Davisson and Germer showed that a beam of electrons directed at a metal
crystal produced a diffraction pattern similar to an X ray diffraction pattern.
In the same year George Thomson (son of J.J) showed that a beam of electrons
directed at a thin polycrystalline metal foil produced a diffraction pattern of
rings. An X ray beam directed at the foil produced the same pattern.
Thus
de Broglie was proved correct. Particles do have a wave-like nature.
Using a similar
set up to Young’s slits, but using electrons instead of light it is possible
to obtain an interference pattern similar to that produced by light except that
the fringes are about 1000 times closer together.
The
easiest interpretation is that half the electrons arrive at each slit and
interference occurs between these two sets of electrons. This is a false
interpretation.
It
is found that if the intensity of the electron beam is reduced until only one
electron at a time is released, the interference pattern still occurs. It can be
concluded from this result that each electron interferes with itself and
therefore each electron actually passes through both slits. By considering the
electron as a particle this explanation appears highly implausible but if one
considers it’s wave-like nature then the explanation does become more
plausible.
Light
is made up of photons each of which travels in a specific direction. Since
interference requires coherent sources, and since the arrival of individual
photons or electrons at a slit is random, for coherence to occur then each
photon or electron must interfere with itself. Thus when considering the
interference of light one must accept that each photon passes through each slit
and interferes with itself.
After
passing through the double slits it is impossible to predict which direction
each individual electron or photon will travel in. However it is possible to
predict the probability of an electron arriving at a specific point on the
screen. Thus the central point of a bright fringe indicates a high probability
of finding an electron (or photon) and the central part of a dark fringe
indicates a low probability.