The Photoelectric Effect

Photoelectric effectImage via Wikipedia     The photoelectric effect was discovered in 1887 by Gustav Ludwig Hertz while performing experiments directed toward confirming Maxwell’s theory of electromagnetic waves. He observed that charged particles (electrons) were ejected from metal surfaces when the surface was illuminated by light. The electron flux was
strongly dependent upon the wavelength of the light. Although Hertz did not follow up on his discovery, one of his students, Philipp Eduard Anton von Lenard, reported quantitative measurements of the effect in 1902. For this work Lenard received the Nobel Prize in 1905. The citation reads: “for his work on cathode rays.” Subsequently, in 1925, Hertz shared the Nobel Prize for a different body of work, a subject that will be discussed later in this chapter.Experiment for the Photoelectric EffectImage via Wikipedia
    The origin of the photoelectric effect remained a mystery until, in one of his three remarkable papers
published in 1905, Albert Einstein, using Max Planck’s treatment of blackbody spectra, explained the effect. Subsequently, in 1916, Robert Andrews Milliken performed detailed experiments that confirmed Einstein’s explanation. Einstein received the Nobel Prize in 1921 for this work, although many think that his work on relativity also deserves a prize. The citation for Einstein’s prize reads: “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” Milliken was also awarded a Nobel Prize, his in 1923, the citation for which reads: “for his work on the elementary charge of electricity and
on the photoelectric effect.”
    In 1901 Max Karl Ernst Ludwig Planck published his revolutionary hypothesis. In equation form, it is
                                 E = nhν           (1.1)
where E and ν are the energy and frequency of an oscillator in the solid; n is a positive integer. The constant h = 6.626 × 10−34 J·s is Planck’s constant. For this innovation Planck was awarded the Nobel Prize in 1918, the citation for which reads “in recognition of the services he rendered to the advancement of Physics by his
discovery of energy quanta”.
    Equation 1.1, the Planck relation, is often written in terms of the angular frequency ω = 2πν and = h/2π. The symbol is read “h-bar” and
                               E = n ω (1.2)
Einstein’s explanation of the photoelectric effect rested on Planck’s assumption that Equation 1.1 also applied to light emitted by the oscillators. As a consequence, it was inferred that light (electromagnetic radiation) could be considered to be made up of bundles or “quanta” called photons, each having energy E and frequency ν. Thus was born the concept of wave particle duality. That is, light exhibits both particle properties, quanta having energy E, and wave properties as represented by the frequency ν. It is common to speak of light in terms of the wavelength λ rather than the frequency, in which case Equation 1.1 takes the form
                                    E = hc
                                           λ                             (1.3)
where c is the speed of light.
    Now, what are the details of the photoelectric effect? The observations are best understood in terms of the experiments. A schematic diagram of the apparatus used by Lenard, and later Milliken, is shown in Fig. 1.1a.
    Light of a fixed frequency (monochromatic light) illuminates an elemental metal, the photocathode. Electrons are emitted from the photocathode, collected on the

Fig. 1.1 (a) Schematic diagram of the apparatus used in the photoelectric effect.
The photocathode and anode are labeled PC and A,respectively. Monochromatic light of frequency hν illuminates the photocathode. (b) Simulated data

anode, and measured using an ammeter as shown in Fig. 1.1. The photocathode and the anode are encased in a glass envelope fromwhich the air has been evacuated. The potential difference between the photocathode and the anode is variable as shown and may be either positive or negative. Because the ejected electrons acquire kinetic energy, the anode voltage VA, if sufficiently negative, can repel them and prevent them from being collected and detected.
    Several modes of data acquisition are employed, but one of the most striking is a plot of VA versus IA at fixed intensity of the light I . As seen in the hypothetical data in Fig. 1.1b for three different intensities, the anode current saturates at sufficiently high values of VA, but the value of the stopping voltage VA = −VS at which the electrons are turned around is independent of the intensity. This shows unequivocally that the electron kinetic energy is not determined by the intensity of the light. Moreover, experiments performed with different frequencies show that the value of VS changes with both the frequency of the light and the material out of which the photocathode is constructed.
    Einstein explained these data in terms of quanta of light called photons. These photons each carry an amount of energy in accord with Equation 1.1. Thus, the kinetic energy imparted to each electron (having charge of magnitude e) depends upon the energy per photon, not I , the number of photons per second falling upon the photocathode. Einstein wrote a simple relation between the photon energy hν, the electron kinetic energy KE, and the stopping voltage VS
                                           KE = hν − eVS                     (1.4)
Equation 1.4 tells us that the kinetic energy of the ejected electron is equal the photon energy hν minus the energy required to liberate the electron from the photocathode. This amount of energy, called the work function W = eVS, differs for each different photocathode material. Equation 1.4 is usually written in the form
                                            KE = hν − W                        (1.5)
and is known as the Einstein relation.
    It is not our goal here to study the photoelectric effect in detail. We wish to note that Einstein’s explanation clearly showed that light exhibited particle characteristics. While the wave properties of light had been known for centuries before the photoelectric effect, its explanation in terms of particles was revolutionary.

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reference : C.E. Burkhardt, J.J. Leventhal, Foundations of Quantum Physics, 1
DOI: 10.1007/978-0-387-77652-1 1, C Springer Science+Business Media, LLC 2008
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