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Using Quantum Theory of Light, Photoelectric Effect by Einstein Planck -What is the main idea of the Author's argument? What is the main essence of

Using "Quantum Theory of Light, Photoelectric Effect" by Einstein Planck

-What is the main idea of the Author's argument? What is the main essence of the piece?

-What ways does the author use to propose and support their argument? What is the underlying structure and evidence used?

-What are the strengths and limitations of the authors argument?

-How can the findings and documented work be simplified?

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Chapter IX: Einstein 101 Concerning a Heuristic Point of View about the Creation and Transformation of Light Albert Einstein There is a profound formal difference between the theoretical representations of gases and other ponderable bodies which physicists have constructed and Maxwell's theory of electromagnetic processes in so-called empty space. Whereas we may consider the state of a body as being completely determined by the positions and velocities of, to be sure, a very large but finite number of atoms and electrons, we must use continuous spatial functions to specify the electromagnetic state of a region, so that a finite number of parameters cannot be considered as sufficient to describe completely the electromagnetic state of a region of space. According to Maxwell's theory, in all cases of pure electromagnetic phenomena, hence in the case of light, the energy must be considered as a continuous spatial function; whereas the energy of a ponderable body, according to the current concepts of physicists, can be represented by a sum taken over the atoms and electrons. The energy of a ponderable body can break up into arbitrarily many, arbitrarily small parts; whereas the energy of a ray of light emitted by a point source of light distributes itself continuously throughout an ever-increasing volume of space according to Maxwell's theory (or, more generally, according to any wave theory). The wave theory, operating with continuous spatial functions, has proved to be correct in representing purely optical phenomena and will probably not be replaced by any other theory. One must, however, keep in mind that the optical observations are concerned with temporal mean values and not with instantaneous values; and it is possible, in spite of the complete experimental verification of the theory of diffraction, reflection, refraction, dispersion, and so on, that the theory of light that operates with continuous spatial functions may lead to contradictions with observations if we apply it to the phenomena of the generation and transformation of light. It appears to me, in fact, that the observations of "black-body radiation," photoluminescence, the generating of cathode rays [by] or light ongsed ultraviolet radiation, and other groups of phenomena related to the thus problem.. . generation and transformation of light can be understood better on the assumption that the energy in light is distributed discontinuously in space. According to the presently proposed assumption, the energy in a beam of light emanating from a point source is not distributed continuously over larger and larger volumes of space but consists of a 2 Annalen der Physik, 17 (1905), 132-148. Translated by the Editors of Annalen der Physik.102 Chapter IX: Einstein finite number of energy quanta, localized at points of space, which move without subdividing and which are absorbed and emitted only as units. In what follows, I want to present the thinking and indicate the facts that have led me along the present path in the hope that the point of view associated with these ideas may prove useful to some researchers in their investigations. VIII. ON THE PRODUCTION OF CATHODE RAYS BY IRRADIATING SOLID BODIES The traditional view that the energy of light is distributed continuously through the region illuminated runs into great difficulty in trying to explain photoelectric phenomena, as was outlined in a trail- blazing paper by Lenard. According to the concept that the exciting radiation consists of energy quanta with energy content hu, the production of cathode rays by light can be understood as follows:" Quanta of energy penetrate into the surface layer of the body; and their energy. at least in part, is transformed into kinetic energy of electrons. The simplest explanation is that a quantum transfers all its energy to a single electron; we shall assume that this occurs.... An interior electron with kinetic energy will have lost some of this kinetic energy by the time it reaches the surface. Besides this we must assume that each electron will have to do some work (an amount characteristic of the body) when it leaves the body." The electrons lying right at the surface of the body will leave the body with the greatest velocity normal to the surface. The kinetic energy of such electrons is hv- P . [What follows is section 8 of Einstein's paper, sections 1-7 and 9 are omitted. The omitted sections treat, among other topics, black-body radiation, Planck's derivation of elementary energy quanta, and the entropy of radiation.] [Annalen der Physik, 8 (1902), 169-170. We gave a brief summary of Lenard's findings above.] [That the light which stimulates the photoelectric effect "consists of energy quanta with energy content /v" is the "heuristic" point of view proposed in this paper. Here v is the light frequency and h is Planck's constant. Einstein actually writes here not / but rather a quotient of three other constants, introduced in the omitted sections of this paper. But inasmuch as he elsewhere shows his own expression to be equal to Planck's we take the liberty of substituting the simpler formula hv throughout.] [The necessity for an electron to do work specifically to leave the surface of a body can be compared to the phenomenon of surface tension in a fluid. The work required is called the "work function"; Einstein denotes it by P in the expression that follows.]Chapter IX: Einstein 103 If the body is charged to the positive potential /7 ... and if /7 is large enough to prevent a discharge of the body,' then we must have Me = hv - P. where e is the electric charge of the electron, or nQ = Nhv - P* where Q is the charge of a gram equivalent of a single charged ion and P* is the potential of this amount of negative charge relative to the body. If we place ( = 9.6 x 10 , then /7x 10 is the potential in volts that the body acquires on being irradiated in a vacuum." In order to see at first if the derived relationship is of the right order of magnitude as obtained empirically we place p* = 0, v = 1.03 x 10" (corresponding to the ultraviolet limit of the solar spectrum ) and [Nh = 4.01x10 ]. We obtain [/7= 4.3x10 abvolts or 4.3] volts, which agrees in order of magnitude with the results of Lenard." If the derived formula is correct, then [/7) must be a linear function of the frequency whose slope [is independent of] the nature of the material being studied."3 [Electrons can leave the body only against the attractive influence of the positive potential /7: if the latter is sufficiently great, none will be able to escape. We have used @ to denote charge, in place of Einstein's E in the original paper, to avoid confusion with the electric field vector.] "[The equation /Q = Nhy - P* is simply the previous equation, multiplied through by Avogadro's number N. Thus @ is equal to Ne, the faraday (see Chapters I and III). ] "[ The faraday equals 96,500 cou or about 9.6 x 10' abcou. With @ expressed in abcoulombs and h in erg-seconds, /7 will be given in erg/abcou or abvolts. Hence /7x 10" will express the potential in volts.] "[Sunlight comprises wavelengths as small as 2902 x 10" cm, corresponding to frequencies as great as 1.03 x 10" cycles/sec. It is not obvious why there should be any upper limit to the frequencies of solar radiation; but a similar limitation is found in light emitted by hydrogen and by excited gases generally. Bohr will study the case of hydrogen in the next chapter. ] " [ Although Einstein actually expresses the relation in terms of other constants, they are equivalent to the values h = 6.55 x 10" erg-sec, as had been estimated by Planck, and Avogadro's number N = 6.17 x 10" molecules/mole, estimated by Einstein in an earlier section of this paper. Note that Einstein's (1905) evaluation of A predates Millikan's oil-drop experiments, which began in 1909. It happens to be only two or three percent higher than the presently accepted figure based on determination of the electron charge; but as Einstein readily admits (in his paper on the Brownian motion), it was doubtful by as much as-594. Therefore Einstein regards the calculation in this paragraph as capable of testing the theory only-as he states in the next sentence-"in order of magnitude."] "[In the experiments mentioned above, Lenard had found that when the cathode is illuminated by direct sunlight, electrons are emitted until the cathode acquires a potential on the order of a few volts.] "[That is, the energy acquired by the electrons will be proportional to the change in the frequency of the exciting light.]104 Chapter IX: Einstein Our point of view, as far as I can see, does not contradict Lenard's observed properties of the photoelectric phenomena. If each quantum of energy of the exciting light gives up its energy to an electron independently of all the other quanta. then the velocity distribution of the electrons, that is, the characteristic of the produced cathode ray, is independent of the intensity of the exciting radiation; on the other hand the number of electrons leaving the body, all other conditions being the same, will depend on the intensity of the exciting radiation. In the above we assumed that the energy of at least a part of the quantum of the exciting light is given completely to one electron. If we do not make this reasonable assumption, we obtain in place of the above equation the following: nQ + P* S Nhv. For cathode luminescence, which is the inverse of the process discussed above, we obtain by analogous reasoning nQ + P* 2 Nhv. For the substances investigated by Lenard /70 is significantly larger than hy since the potential through which the cathode rays had to move, just to emit visible light, equaled hundreds of volts in some cases, and thousands of volts in other cases. We may thus assume that the kinetic energy of an electron is used to produce numerous light quanta. EXPERIMENT: THE PHOTOELECTRIC EFFECT As Einstein explains, the most energetic electrons among those released from the illuminated cathode will have energy per unit charge of amount [Kv) = hve - P/e [That is, the number of electrons emitted (per second) from the cathode will be directly proportional to the intensity of the exciting light.]

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