The Photo-electric effect:

 

                          The Nobel Prize was won in 1905 by Albert Einstein for his description of the photo-electric effect. The main elements of which were as follows. In 1887 Hertz had found that the irradiation of a spark gap with ultra violet at high voltage applied across it facilitates spark discharge in air , that is , discharge takes place at greater gaps than in the absence of radiation. Subsequently it was found that light focused on a light sensitive coating could produce an electric current to flow in a metal plate placed a small distance from it which was  connected to a circuit. The apparatus was as follows. (a) the light source (b) light sensitive material (c) metal plate connected to a circuit in which a galvanometer is present which can measure the current flow.  When the light sensitive material was irradiated with light electrons were ejected from its surface and traveled to the metal plate  (b) causing a current to flow.

                       If this flow of current was calculated using Maxwell’s theory of electromagnetic radiation it should have resulted in there being  an increase in the flow of current which was dependent only on the intensity of the impinging light  regardless of its frequency.  However it was soon observed that the intensity of the light had little to do with the amount of current which flowed it was dependent instead on the frequency of the light source. Thus even a highly intense light source of say infra-red light would not cause a current to flow even if the intensity was increased , while ultra violet light of moderate intensity would immediately cause the current to flow the amount of current increasing linearly with the intensity of the light.

          All attempts to explain these properties on the basis of wave-theory failed. Then in 1905 Albert Einstein demonstrated that the laws of the photoelectric effect can be explained on the  basis of quantum theory.

            An electron can leave the surface of any body , for example of a metal , only if it’s kinetic energy is equal to or exceeds the wok function. Let the radiation falling on the surface of the metal consist of photons with an energy h/f  . The electrons near the surface of the metal absorb the photons penetrating into the metal , acquiring their energy. The interaction of the radiation with the substance in this case consisting of an enormous number of elementary acts in each of which one electron completely absorbs one quantum (photon.) If the magnitude of the quantum exceeds the work function , the electron is able to leave the metal. The major part of the quantum’s energy is spent on the work function , the remainder comprising the electron’s kinetic energy.

             Amazingly , and not surprisingly , considering the circumstances , Einstein was wrong  .

            Einstein’s mistake was in attributing the intensity of  the light to the eigen qualities of the photon , in reality the two are completely unrelated or distinct.  Thus Einstein’s photo-electric equation:

        hf = W + ½(mv^2max)

 

Is correct but the definition of  frequency is wrong because it confuses frequency with the eigen value of the photon treating both terms as being interchangeable which they are not.

            The frequency of a photon and its eigen energy value are two completely distinct but related phenomenon . If we take a 1W. ultraviolet light emitting diode and point it at a light emitting screen , it should make no difference whether the screen is  1cm away form the source or 10m. away the electrons should continue to be emitted with the same force.  This does not happen , as the distance between the source and the screen increases the number of scintillations die of rapidly , however calculations show that the number of photons which should reach the screen remains large , if we assume  that the diode is emitting about 10 ¹⁹ photons/ sec. Then over a distance of 10 m. from the source there should be at least 10 ¹⁸  photons reaching the screen   over an area of 1m. , why are the scintillations so limited since according to your theory the diode is emitting photons of the same eigen  energy and they are reaching the screen in such large numbers ( i.e.10¹² photons per millimeter ), surely the number of scintillations should not reduce so drastically ?   The answer is that the intensity of the photons has reduced to an extent that they lack the power to impart to free electrons the necessary energy equal to the work function required to eject them from the metal’s surface. Now hold on a minute you say , we have been through all this before and we know that it not the intensity but the frequency of the impingent light which is the causative factor.  But as I see it , it is  the combined factors of  the  eigen energy value of the photon  its intensity and frequency  when taken together which are the causative factor. In order to understand this we have to re-define the terms : First of all frequency represents the interval between one photon and the next arriving at the destination , these photons might all be from different origins being emitted from different electrons , in which case the intensity of the incident  light will be slight . The intensity is frequency when applied to photons present in a single line of force . So intensity means the number of photons per line of  force , notice that here the frequency remains the same but the intensity is greater because they are all arranged in a single line of force and will therefore all be absorbed at the same point. . Now as the wave propagates further from the source the intensity (i.e number of  photons per line of force , is reduced. ) while the eigen energy values of the photon remains the same. The photoelectric effect has little to do with independent eigen values and everything to do with the  intensity of those eigen values.  If we extend this theory to the photoelectric effect it would mean that the  electron undergoes continuous excitation in order to reach the level of energy required by the work function for it to be ejected from the metal surface. This can only be provided by a series of photons hitting the same electron in rapid succession (i.e photons from a single line of force. )   So once we re-define frequency to mean the number of photons of a certain energy arriving  at a certain time interval and separate this from the actual eigen value we are making progress.  Thus an electron absorbing a single photon of a certain eigen value will immediately re-emit a photon of the same eigen value , that eigen value has nothing to do with the frequency with which that particular photon is emitted. If the electron is continuously excited at the correct  energy level then it will emit photons of  a particular eigen value at a particular frequency ( i.e ., so many photons per second. )

Returning to the experiment referred to earlier of an ultra violet light emitting  diode , it is now easy to see that the eigen value has little to do with the photoelectric effect and frequency and intensity has everything to do with it.