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Frontiers in Optics

The Classical Electrodynamics Approach To Explain The Photoelectric Effect And The Photoelectric Emission

BingXin Gong

Published Jan 1, 2005• 0 citations
Publisher

Abstract

By re-analyzing the photoelectric effect, the limitations of Einstein’s photon hypothesis are identified and the relation between the photoelectron’s kinetic energy and the circular frequency of the incident light is reinterpreted using classical electrodynamics.
DOI
10.1364/fio.2005.jwa14

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According to an entropy approach and by reviewing the similarity between laws characterizing the flow of heat and electric charges, electric charges were defined as electromagnetic waves that possess an electrical potential or simply as ionized photons. Accordingly, the flow of electrons was defined as a simultaneous flow of particulate energy and wave energy. Such definitions led to clear the confusions of duality properties of electrons and light waves, conflicts in the SI system of units and to explain the difference between the calculated drift speed of electrons and the speed of electricity or charges in conductors. However, Einstein considered the electron to be a negative charge of unknown nature during his analysis of the photoelectric effect. Einstein presented his hypothesis that light may behave as a particle to find a plausible explanation of the photoelectric effect. He found the measured cutoff frequency of light below which light might not eject electrons from metal-surfaces in photocells regardless of how much light is shone on the surface as a proof of truth of his hypothesis. Such frequency may be explained also, according to the previously introduced definitions, as the minimum energy quanta that may gain a quantized potential in photocells. This explanation may find plausible explanations of the found measurements of the photoelectric effects for different metal surfaces, stopping voltages into photocells and the photoelectric effect of X-rays. Einstein’s hypothesis of the photoelectric effect failed to find plausible explanations of such measurement results. According to the principles of conservation of momentum, there is a minimum quantity of photons that may lead to bouncing an atomic electron out of its orbit. So, considering Einstein’s theory as a perfect hypothesis that explains the photoelectric effect may be a misconception.
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Einstein explained the experimental characteristics of the photo-electric effect by the concept that the photon is a localized packet of electromagnetic radiation with the mechanism: photon + atom → emitted electron. A classical plane wave theory of light concluding that the photoelectric effect can be explained without localized photons is reexamined and found to have been flawed in predicting no time delay for photoelectron emission; this accords with Millikan's conclusion (based upon energy conservation) that a classical plane wave would entail a delay prior to emission of the order of hours. The quantification of Einstein's localized packet concept as a solitary wave one wavelength in length (one period long in time) predicts a delay of one period of the photon's oscillating field, which accords with the experimentally measured response time being a few femtoseconds.
In this paper, we explain the photoelectric effect in a variant of the standard model of non relativistic quantum electrodynamics, which is in some aspects more closely related to the physical picture, than the one studied in [5]. Now, we can apply our results to an electron with more than one bound state and to a larger class of electron-photon interactions. We will specify a situation, where the second order of ionization probability is a weighted sum of single photon terms. Furthermore, we will see that Einstein's equality [Formula: see text] for the maximal kinetic energy E kin of the electron, energy hν of the photon and ionization gap △E is the crucial condition, for these single photon terms to be nonzero.
The critical and correct scientific analysis of the generally accepted theory of the external photoelectric effect is proposed. The methodological basis for the analysis is the unity of formal logic and of rational dialectics. It is shown that Einstein’s formulation of the law of the photoelectric effect is not free from the following objection. The terms of Einstein’s formula characterize the quantitative determinacy (i.e., energy) which belongs and is related to the different material objects: “photon”, “electron in metal”, and “electron not in metal”. This signifies that Einstein’s formula represents violation of the formal-logical laws of identity and absence (lack) of contradiction. The correct mathematical formulation of the law of the external photoelectric effect within the framework of the system approach is proposed. The correct formulation represents the proportion by relative increments of the energy of the incident photon and the energy of the emitted electron. The proportion describes the linear relationship between the energy of the incident photon and the energy of the emitted electron.