Einstein Photoelectric Equation

Book 07

1. INTRODUCTION

In 1922 Albert Einstein was awarded the Nobel Prize in physics 1921 for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect. The photoelectric effect refers to change of electrical conduction properties in matter induced by light and other forms of electromagnetic radiation. In order to induce this effect, the absorption of incident light by matter should cause a generation of charged carriers, such as conduction electrons and positive holes in the case of a semiconductor, or free electrons (photoelectrons) emitted from a metal surface with immobile positive ions left behind. These two phenomena are called the internal photoelectric effect and external photoelectric effect, respectively, the mathematical concept was refered as Einstein Photoelectric Equation.

In 19th-20th century, the study of the external photoelectric effect was of major importance in the development of physics. Several experimental results had been accumulated, but some of them could not be accounted for on the basis of electromagnetic wave theory of James C. Maxwell. Einstein published a paper on March 17, 1905, in Bern, Switzerland and submitted to “Annalen der Physik” (Annuals of Physics) . In this paper proposed the concept of “light quanta” and beautifully explained the law of the photoelectric effect.

 Of course, the idea of a granular structure of radiation implied the particle nature of light and inherently challenged the prevailing well-established electromagnetic theory of light. Consequently, it took more than ten years before his theory finally came to be admitted and honored by a majority of physics community. However, there exist evidence that Einstein’s photon hypothesis or corpuscular theory of light, along with de Broglie’s material wave theory of particles, eventually urged the progress of quantum mechanics. From the viewpoint of application of physics to human life, Einstein’s photoelectric theory seems to be far more important than any other physics theory discovered by him. Today, it still gives us the basis for photo-detection devices such as photomultipliers, photodiodes, and CCD image sensors, as well as photovoltaic energy converters.

2. PHOTON HYPOTHESIS AND EXPLANATION OF PHOTOELECTRIC EFFECT

First of all, let us study the original paper by Einstein published in 1905. At the end of introductory part on the second page of his paper, Einstein wrote: “Indeed, it seems to me that the observation regarding black-body radiation, photoluminescence, production of cathode rays by ultraviolet light, and other groups of phenomena associated with the generation or conversion of light can be understood better if one assumes that the energy of light is discontinuously distributed in space. According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of quanta of energy that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.

He overcame this difficulty by introducing the famous Einstein Photoelectric Equation with

eq1

 Where Emax the maximum kinetic energy of photoelectrons, h is isis the energy of light quantum of incident radiation, and W is the work done by each photoelectron to required the metal surface (later named as “the work function”). Here it was assumed that a single light quantum is absorbed in the metal and the total or part of the energy of light quantum is transferred to a single electron to be emitted.

3. EVOLUTION OF THE PHOTON HYPOTHESIS

In the beginning of 20th century, it was difficult to verify the validity of Einstein’s photoelectric above equation by precise measurements. In 1916, Robert Millikan, after his endeavour over 10 years, finally provided an incontrovertible proof of the direct proportionality between the kinetic energy of photoelectrons and the frequency of absorbed light . He showed that the proportionality constant h is independent of the material and nature of the surface, and that its value is about 6.57×10-27 erg sec, which is in close agreement with the value obtained by Max Planck in 1900 (6.55×10-27 erg sec). Planck was awarded the Nobel Prize in physics 1918 in recognition of the services he rendered to the advancement of physics by his discovery of energy quanta, whereas Millikan in 1923 for his work on the elementary charge and on the photoelectric effect.

 Meanwhile, Einstein published a paper on the quantum theory of radiation. He described the emission and absorption process of single light quantum in two-level transitions in molecules, and discussed the probability coefficients for the spontaneous emission, induced emission and absorption. This theory with so-called Einstein’s A and B coefficients became of great importance to help develop the theoretical background for the invention of lasers in the latter half of the 20th century. Moreover, in this paper he showed that the momentum (recoil) p of a light quantum with energy E is equal to E/c, that is

eq2

The Compton Effect is the increase of wavelength of an X-ray that has been scattered by electron. This change in wavelength is greater when the scattering angle of X-ray is larger. In 1923, Compton published a full discussion of the effect. He assumed that each quantum of incident X-ray energy is concentrated in a single particle and acts as a unit onto a single electron. Then the electron recoils and a new energy quantum is generated for the scattered X-ray. On the basis of this quantum-corpuscular assumption and the conservation principles of energy and momentum with the aid of Eq. (3) and the theory of relativity, he was able to obtain the famous formulae, which splendidly explained all the experimental results. Compton’s contribution to the proof of Einstein’s hypothesis of radiation is enormous, and he was awarded the Nobel Prize in physics 1927 for his discovery of wavelength change in diffused X-rays. Einstein’s idea of corpuscular view of light quantum also stimulated Louis de Broglie towards his idea of material wave associated with electron and other particles proposed in 1924 in his doctoral thesis.

Theoretical Background

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this quation was refered as Einstein Photoelectric Equation

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