The Photoelectric Effect
Albert Einstein was awarded the Nobel Prize in 1921 for his discovery of the linear relationship between the wavelength of light and the energy of the ejected electron in the photoelectric effect.
Einstein's prediction was a very small part of his 1905 paper that hypothesized radiation could best be understood as coming in discrete quanta of energy E = hν. Einstein wondered how an outgoing spherical radiation field could possibly collect itself together instantaneously to be absorbed by a single atom. Einstein wrote:
The wave theory of light, which operates with
continuous spatial functions, has worked well in
the representation of purely optical phenomena
and will probably never be replaced by another
theory. It should be kept in mind, however, that
the optical observations refer to time averages
rather than instantaneous values. In spite of the
complete experimental confirmation of the theory
as applied to diffraction, reflection, refraction,
dispersion, etc., it is still conceivable that the
theory of light which operates with continuous
spatial functions may lead to contradictions
with experience when it is applied to the phenomena of emission and transformation of light.
It seems to me that the observations associated
with blackbody radiation, fluorescence, the
production of cathode rays by ultraviolet light,
and other related phenomena connected with the
emission or transformation of light are more
readily understood if one assumes that the energy
of light is discontinuously distributed in space.
In particular, the photoelectric effect showed discontinuous discrete light quanta, though it was doubted until the Compton Effect in 1923.
In accordance with the assumption to be considered here, the energy of a light ray spreading
out from a point source is not continuously
distributed over an increasing space but consists
of a finite number of energy quanta which are
localized at points in space, which move without
dividing, and which can only be produced and
absorbed as complete units.
We therefore arrive at the conclusion: the
greater the energy density and the wavelength
of a radiation, the more useful do the theoretical
principles we have employed turn out to be; for
small wavelengths and small radiation densities,
however, these principles fail us completely.
[W]e further conclude that: Monochromatic radiation of low density (within the
range of validity of Wien's radiation formula)
behaves thermodynamically as though it consisted of a number of independent energy quanta.
Thermodynamically, radiation behaves like a gas.
Light cannot be spread out continuously in all directions
if the energy is absorbed as a unit that ejects a photo-electron.
[T]he energy of a light ray spreading
out from a point source is not continuously
distributed over an increasing space but consists
of a finite number of energy quanta which are
localized at points in space, which move without
dividing, and which can only be produced and
absorbed as complete units.
The usual conception, that the energy of light
is continuously distributed over the space
through which it propagates, encounters very
serious difficulties when one attempts to explain
the photoelectric phenomena,
Why did Bohr not see in 1913, or Einstein point out to him, that when an electron in an atom absorbs or emits energy, the jumping electron is accompanied by a single light quantum?
According to the concept that the incident
light consists of energy quanta..., however, one can conceive of the ejection
of electrons by light in the following way. Energy
quanta penetrate into the surface layer of the
body, and their energy is transformed, at least in
part, into kinetic energy of electrons. The simplest
way to imagine this is that a light quantum
delivers its entire energy to a single electron; we
shall assume that this is what happens.
According to the concept that the incident
light consists of energy quanta of magnitude
Rβν/N, however, one can conceive of the ejection
of electrons by light in the following way. Energy
quanta penetrate into the surface layer of the
body, and their energy is transformed, at least in
part, into kinetic energy of electrons. The simplest
way to imagine this is that a light quantum
delivers its entire energy to a single electron; we
shall assume that this is what happens...
If the derived formula is correct, then ... when
represented in Cartesian coordinates as a function
of the frequency of the incident light, must
be a straight line whose slope is independent of
the nature of the emitting substance.
As far as I can see, there is no contradiction
between these conceptions and the properties of
the photoelectric effect observed by Herr Lenard.
If each energy quantum of the incident light,
independently of everything else, delivers its
energy to electrons, then the velocity distribution
of the ejected electrons will be independent of the
intensity of the incident light; on the other hand
the number of electrons leaving the body will,
if other conditions are kept constant, be proportional
to the intensity of the incident light.
Einstein greatly expanded his light-quantum hypothesis in a presentation at the Salzburg conference in September, 1909. He argued that the interaction of radiation and matter involved elementary processes that are not
reversible, a deep insight into the
irreversibility of natural processes. While incoming spherical waves of radiation are mathematically possible, they are not practically achievable. Nature appears to be
asymmetric in time. He speculates that the continuous electromagnetic field might be made up of large numbers of light quanta - singular points in the field that superimpose to create the wavelike behavior.
Consider the laws governing the production of secondary cathode radiation by X-rays. If primary cathode rays impinge on a metal plate P1, they produce X-rays. If these X-rays impinge on a second metal plate P2, cathode rays are again produced whose speed is of the same order as that of the primary cathode rays.
As far as we know today, the speed of the secondary cathode rays depends neither on the distance between P1 and P2, nor on the intensity of the primary cathode rays, but rather entirely on the speed of the primary cathode rays. Let's assume that this is strictly true. What would happen if we reduced the intensity of the primary cathode rays or the size of P1 on which they fall, so that the impact of an electron of the primary cathode rays can be considered an isolated process?
In his remarks after the talk, Johannes Stark confirmed that he had observed a single X-ray that traveled as far as ten meters and ejected a similar energy electron from P2.
If the above is really true then, because of the independence of the secondary cathode rays' speed on the primary cathode rays' intensity, we must assume that an electron impinging on P1 will either cause no electrons to be produced at P2, or else a secondary emission of an electron whose speed is of the same order as that of the initial electron impinging on P1. In other words, the elementary process of radiation seems to occur in such a way that it does not scatter the energy of the primary electron in a spherical wave propagating in every direction, as the oscillation theory demands.
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