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Photoelectric effect
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===Theoretical explanation=== [[File:Photoelectric effect - stopping voltage diagram for zinc - English.svg|thumb|Diagram of the maximum kinetic energy as a function of the frequency of light on zinc|alt=]] In 1905, [[Albert Einstein|Einstein]] proposed a theory of the photoelectric effect using a concept that light consists of tiny packets of energy known as [[photons]] or light quanta. Each packet carries energy <math>h\nu</math> that is proportional to the frequency <math>\nu</math> of the corresponding electromagnetic wave. The proportionality constant <math>h</math> has become known as the [[Planck constant]]. In the range of kinetic energies of the electrons that are removed from their varying atomic bindings by the absorption of a photon of energy <math>h\nu</math>, the highest kinetic energy <math>K_\max</math> is <math display="block">K_\max = h\,\nu - W.</math> Here, <math>W</math> is the minimum energy required to remove an electron from the surface of the material. It is called the [[work function]] of the surface and is sometimes denoted <math>\Phi</math> or <math>\varphi</math>.<ref>{{cite book |last1=Mee |first1=C. |last2=Crundell |first2=M. |last3=Arnold |first3=B. |last4=Brown |first4=W. |year=2011 |title=International A/AS Level Physics |page=241 |publisher=[[Hodder Education]] |isbn=978-0-340-94564-3 }}</ref> If the work function is written as <math display="block">W = h\,\nu_o,</math> the formula for the maximum kinetic energy of the ejected electrons becomes <math display="block">K_\max = h \left(\nu - \nu_o\right).</math> Kinetic energy is positive, and <math>\nu > \nu_o</math> is required for the photoelectric effect to occur.<ref name="Fromhold1991">{{cite book |last=Fromhold |first=A. T. |year=1991 |title=Quantum Mechanics for Applied Physics and Engineering |pages=5β6 |publisher=[[Courier Dover Publications]] |isbn=978-0-486-66741-6 }}</ref> The frequency <math>\nu_o</math> is the threshold frequency for the given material. Above that frequency, the maximum kinetic energy of the photoelectrons as well as the stopping voltage in the experiment <math display="inline">V_o = \frac{h}{e} \left(\nu - \nu_o\right)</math> rise linearly with the frequency, and have no dependence on the number of photons and the intensity of the impinging monochromatic light. Einstein's formula, however simple, explained all the phenomenology of the photoelectric effect, and had far-reaching consequences in the [[History of quantum mechanics|development of quantum mechanics]].
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