# Photoelectric effect The **photoelectric effect** is the emission of [[Electron|electrons]] from a material when [[Electromagnetic_radiation|light]] falls on it. Its importance is not that it happens but that it happens the wrong way round for a wave: the maximum energy of the ejected electrons depends on the light's *frequency* and not at all on its brightness, and below a threshold frequency no electrons appear however intense the beam. [[Albert_Einstein|Einstein]] explained this in 1905 by proposing that light is absorbed in discrete quanta of energy h·f, giving `K_max = h·f − phi`, where φ is the [[Work_function|work function]] of the surface.[^einstein1905] In the microsim below the reader has three controls: the light's frequency, its intensity, and the metal — [[Caesium|caesium]], [[Sodium|sodium]], [[Zinc|zinc]] or [[Copper|copper]], with work functions 2.1, 2.3, 4.3 and 4.7 eV.[^up3-ch6] Below the threshold `f0 = phi/h` the detector reads zero, and turning the intensity to maximum does not change that — the single most important thing on the screen. Above threshold, raising the intensity multiplies the number of electrons while leaving their energy alone, and raising the frequency does the reverse. The measured quantity is the stopping potential, the reverse voltage that just turns the current off, defined by `e·V_s = K_max`; plotting V_s against f gives a straight line of slope h/e = 4.14×10⁻¹⁵ V·s and intercept −φ/e (derived). That line is the experiment Robert Millikan carried out in 1916 in an effort to disprove Einstein, and which instead measured Planck's constant.[^millikan1916] Caesium is the element placed on this page, because its low work function puts its threshold at 590 nm (derived), inside the visible range. On the [[Physics]] flagship this article serves Part I — History, the *20th century* section (row P12). The Michelson–Morley experiment had already shown classical physics failing on space and time; this is where it fails on light itself, and where the quantum ideas that produce the [[Bohr_model|Bohr atom]] three sections later enter with a laboratory measurement behind them. ## Emission mechanism Light delivers energy to an electron bound in a material; if it delivers more than the binding energy, the electron leaves with the remainder as kinetic energy. Everything interesting is in how that energy is delivered. ### Experimental observation of photoelectric emission The classic apparatus is an evacuated tube with an illuminated metal plate and a collecting electrode, with a variable voltage between them and a sensitive current meter. Four results emerge, and three of them are impossible on the wave picture.[^up3-ch6] First, emission begins immediately on illumination, with no measurable delay even at very low intensity — where a wave spreading its energy over the whole surface would need a substantial time to concentrate enough on one electron. Second, the photocurrent is proportional to intensity, which a wave picture does predict. Third, the maximum kinetic energy of the electrons is completely independent of intensity, and is read off as the stopping potential `e·V_s = K_max`: making the light ten times brighter gives ten times the current at exactly the same stopping voltage. Fourth, there is a threshold frequency below which nothing is emitted at all, whatever the intensity or the exposure time. These are the four the microsim isolates. The intensity slider moves the height of the current trace and nothing else; the frequency slider moves the stopping potential and nothing else; and the metal selector moves the threshold. A worked case from the Portal Books fixes the scale: light of frequency 6.66×10¹⁴ s⁻¹ ejecting electrons of kinetic energy 7.74×10⁻²⁰ J implies a threshold frequency of 5.49×10¹⁴ s⁻¹, which is a work function of 2.27 eV and a threshold wavelength of 546 nm (derived).[^blackstock-photo] ### Theoretical explanation Einstein's 1905 proposal was that the energy of light is not spread continuously through the wave but localised in quanta of magnitude h·f, and that photoemission is a one-quantum, one-electron transaction.[^einstein1905] An electron absorbs a whole quantum or none; the energy it needs to escape the surface is the [[Work_function|work function]] φ; and what is left is kinetic energy, so `K_max = h·f − phi`. Every one of the four observations follows in a line. There is no delay because the transaction is instantaneous. Intensity is the number of quanta per second, so it sets the number of electrons. Energy per quantum depends on frequency alone, so K_max does too. And when h·f < φ no single quantum can pay the escape cost, so no amount of light helps. The equation also makes a quantitative prediction that goes beyond explaining the pattern: the slope of K_max against f must be [[Planck_constant|Planck's constant]], the same constant [[Max_Planck|Planck]] had introduced in 1900 to fit the [[Black-body_radiation|black-body]] spectrum, arrived at from a completely unrelated experiment.[^planck1901] Millikan spent a decade testing it, believing the quantum hypothesis untenable, and in 1916 reported a value of h from photoelectric data agreeing with Planck's.[^millikan1916] Einstein received the 1921 Nobel Prize in Physics, awarded in 1922, specifically for this law rather than for relativity.[^nobel1921] ### Photoemission from atoms, molecules and solids The same physics appears with three different thresholds. In a free atom or molecule the process is photoionization: the initial states are discrete, the threshold is the [[Ionization_energy|ionization energy]], and the ejected electron's energy spectrum is a set of lines, one per occupied orbital. In a solid the initial states form continuous bands, the threshold is the work function — set by the [[Fermi_level|Fermi level]] together with a surface dipole that depends on crystal face and contamination — and the spectrum is a continuum carrying the shape of the occupied [[Electronic_band_structure|band structure]].[^up3-ch6] Emission from a solid is usually described in three steps: optical excitation of an electron in the bulk, transport to the surface, and escape across the barrier. The middle step is what makes the technique surface-sensitive, because an excited electron loses energy to other electrons within a few nanometres; only those created very near the surface escape with their energy intact. That is a limitation for studying bulk properties and the whole basis of photoelectron spectroscopy as a surface tool. ## History The effect was found by accident, explained a generation later, and confirmed by a physicist who set out to refute the explanation. ### 19th century Heinrich Hertz noticed in 1887, while doing the experiments that confirmed [[Maxwell's_equations|Maxwell's equations]], that ultraviolet light shining on the electrodes of his spark gap made the spark jump more readily.[^hertz1887] Wilhelm Hallwachs showed the following year that an illuminated zinc plate loses negative charge, and Aleksandr Stoletov built the first working photocell. What was being emitted stayed unclear until J. J. Thomson's identification of the electron at the end of the decade allowed the carriers to be identified by their charge-to-mass ratio. ### 20th century Philipp Lenard established the crucial facts in 1902: the energy of the emitted electrons does not grow with the intensity of the light, and does grow with its frequency.[^lenard1902] This was flatly inconsistent with the wave theory, which had otherwise been unbroken for a century. Einstein's quantum explanation followed in 1905 in the first of that year's papers — the one he himself called revolutionary — and was resisted for over a decade, including by Planck, who regarded the light-quantum as going far beyond anything the black-body derivation required.[^einstein1905] Millikan's 1916 measurement removed the empirical objections without converting him: he reported that Einstein's equation "accurately represents the energy of electron emission" while continuing to regard the underlying hypothesis as unreasonable.[^millikan1916] The Nobel committee's 1921 citation, awarded in 1922, named the law and not the hypothesis behind it.[^nobel1921] Photoemission then became a tool rather than a puzzle: photomultipliers from the 1930s, photoelectron spectroscopy from the 1960s, and the detectors described below. ### 21st century Modern work asks not whether the effect is instantaneous but how instantaneous. Attosecond light pulses, generated by high-harmonic techniques and recognised by the 2023 Nobel Prize in Physics, make it possible to time the emission itself, and measurements on metal and gas targets find small but reproducible delays between photoemission from different initial states — a consequence of transport and of the final-state interaction rather than a failure of the one-quantum picture.[^nobel2023] Intense laser fields add regimes Einstein's linear relation does not cover. When many quanta are absorbed together, electrons can be emitted with energies well above h·f − φ, or from below the single-quantum threshold; the transaction is still quantised, but no longer one quantum at a time. Angle-resolved photoemission has meanwhile become the standard way of measuring the electronic structure of [[Semiconductor|semiconductors]], superconductors and topological materials directly. ## Uses and effects Because the emitted electron carries away the photon's energy minus a known offset, photoemission is both a detector of light and a spectrometer of matter. ### Photomultipliers A photomultiplier tube pairs a photocathode with a chain of dynodes at successively higher potentials. One photoelectron strikes the first dynode and liberates several secondary electrons, which strike the next, and after ten or more stages the single initial electron has become a pulse large enough to register — which is what makes counting individual photons possible. Photomultipliers read out scintillation detectors in nuclear medicine and particle physics, and large arrays of them line neutrino observatories. ### Image sensors Solid-state sensors use the *internal* photoelectric effect: the absorbed quantum promotes an electron across the [[Band_gap|band gap]] of a [[Semiconductor|semiconductor]] rather than ejecting it into vacuum, and the freed charge is collected in a pixel well. The threshold condition is the same in form, with the band gap in place of the work function, which is why silicon sensors stop responding in the near infrared. The same physics in a different geometry is a [[Solar_cell|solar cell]]. ### Photoelectron spectroscopy Illuminating a sample with photons of known energy and measuring the kinetic-energy spectrum of the emitted electrons gives the binding energies of the occupied states directly, through `E_B = h·f − K − phi`. X-ray photons reach core levels, whose energies are element-specific and shift slightly with chemical environment, making X-ray photoelectron spectroscopy a standard tool for surface composition and oxidation state. Ultraviolet photons reach the valence band; adding an angle measurement converts the electron's momentum into a crystal momentum, mapping the band structure point by point. ### Night vision devices An image intensifier is a photomultiplier with position preserved. Light forms an image on a photocathode, the liberated electrons are accelerated through a microchannel plate that multiplies them locally, and they strike a phosphor screen to reform a much brighter image. The useful sensitivity extends into the near infrared, which requires a photocathode of low work function; this is the same requirement that puts [[Caesium|caesium]] compounds in almost every such device. ### Spacecraft A spacecraft in sunlight loses electrons continuously from its illuminated surfaces and charges positive as a result, settling at the potential where the returning current of ambient [[Plasma_(physics)|plasma]] electrons balances the photoemission. Surfaces in shadow charge negative instead, from the plasma alone, and can reach far larger magnitudes. The resulting differential charging between adjacent surfaces is a real hazard, capable of producing arcs that damage electronics, and spacecraft are designed with conductive coatings and grounding straps to prevent it. ### Moon dust The Moon has no atmosphere and no global magnetic field, so solar ultraviolet strikes the [[Regolith|regolith]] directly and the sunlit surface charges positive by photoemission. Individual dust grains charge too, and the finest of them can be lifted electrostatically against the weak lunar gravity. Apollo-era observations of a glow above the horizon at lunar sunrise are usually attributed to sunlight scattered by such levitated grains, and adhesion of charged dust to suits, seals and optics was among the most persistent operational problems of the surface missions. ## Cross section and competing processes Photoelectric absorption is one of several ways a photon can interact with matter, and which one dominates depends almost entirely on energy. At low photon energies the photoelectric effect is overwhelmingly the most probable, and its cross section rises steeply with atomic number — the reason lead shields X-rays and bone is visible on a radiograph while soft tissue is not. As the photon energy rises past the binding energies of the inner shells, the photoelectric cross section falls away sharply and Compton scattering takes over: the photon is not absorbed but scattered off a weakly bound electron, transferring part of its energy and continuing with a longer wavelength.[^up3-ch6] Above 1.022 MeV — twice the rest energy of the electron — a third channel opens, in which the photon converts in the field of a nucleus into an electron–positron pair, and this dominates at high energy.[^up3-ch11] The practical consequence is that the same material behaves completely differently across the spectrum. The cross-section curve for a given element has a series of sharp steps, the absorption edges, at exactly the binding energies of its shells, and those edges are the fingerprint used in X-ray absorption spectroscopy. Below each edge the photon cannot eject an electron from that shell at all — the same threshold condition the microsim shows at visible frequencies, repeated at every shell of every element. ## See also - [[Work_function]] - [[Planck_constant]] - [[Photon]] - [[Albert_Einstein]] - [[Max_Planck]] - [[Bohr_model]] - [[Solar_cell]] - [[Electronvolt]] ## References [^up3-ch6]: Sanny, Jeff; Ling, Samuel, et al. (2016). *University Physics Volume 3*. OpenStax, CC BY. Chapter 6, "Photons and Matter Waves", pp. 241–294 (page to pin) — the photoelectric apparatus and its four observations, the stopping potential, the work-function table (caesium 2.1 eV, sodium 2.3 eV, zinc 4.3 eV, copper 4.7 eV — values to pin against the printed table), Einstein's equation, and the Compton effect. Portal Book 079, https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3. The text extraction of Portal Book 079 lost nearly every displayed equation and most worked numbers; `K_max = h·f − phi` and the other forms quoted here are the standard, unambiguous ones and must be verified against the PDF pages, as must the four work-function values, before the page numbers are frozen. [^up3-ch11]: *University Physics Volume 3* (2016), Chapter 11, "Particle Physics and Cosmology", pp. 493–540 (page to pin), for electron–positron pair production and its 1.022 MeV threshold at twice the electron rest energy. Portal Book 079. Same extraction caveat. [^blackstock-photo]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. P. 180, for the photoelectric worked case — light of frequency 6.66×10¹⁴ s⁻¹ giving electrons of kinetic energy 7.74×10⁻²⁰ J, from which the threshold frequency is 5.49×10¹⁴ s⁻¹ — and pp. 176–181 for h = 6.6262×10⁻³⁴ J·s, c = 2.998×10⁸ m/s and 1 eV = 1.602×10⁻¹⁹ J. Portal Book 054, https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry. Sub-manual 05 §A records that the photoelectric equation itself is not written out on p. 180 and that the standard form `KE = h·(nu − nu0)` was supplied, reproducing the book's ν₀ from its stated inputs. Derived here and printed in no book: the work function 2.27 eV and threshold wavelength 546 nm implied by that case; the slope h/e = 4.14×10⁻¹⁵ V·s; and the threshold wavelengths of the four tabulated metals, 590 nm for caesium, 539 nm for sodium, 288 nm for zinc and 264 nm for copper, from λ₀ = h·c/φ with h·c = 1,240 eV·nm. [^einstein1905]: Einstein, Albert (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." *Annalen der Physik* 322 (6): 132–148. The light-quantum hypothesis and its application to photoemission, photoluminescence and photoionization. [^planck1901]: Planck, Max (1901). "Ueber das Gesetz der Energieverteilung im Normalspectrum." *Annalen der Physik* 309: 553–563. The black-body distribution and the first appearance of the constant h, from an experiment unrelated to photoemission. [^millikan1916]: Millikan, Robert A. (1916). "A Direct Photoelectric Determination of Planck's 'h'." *Physical Review* 7 (3): 355–388. The decade-long test of Einstein's linear relation, reporting a value of h in agreement with Planck's while the author continued to reject the light-quantum hypothesis. [^hertz1887]: Hertz, Heinrich (1887). "Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung." *Annalen der Physik* (volume and page range to pin). The incidental observation, made during the experiments confirming Maxwell's theory, that ultraviolet light on the electrodes eases a spark discharge. [^lenard1902]: Lenard, Philipp (1902). "Ueber die lichtelektrische Wirkung." *Annalen der Physik* (volume and page range to pin). The measurements establishing that the energy of the emitted electrons is independent of the light's intensity and increases with its frequency. [^nobel1921]: "The Nobel Prize in Physics 1921." The Nobel Foundation. https://www.nobelprize.org/prizes/physics/1921/summary/ — awarded in 1922 to Albert Einstein, with the citation naming his discovery of the law of the photoelectric effect. [^nobel2023]: "The Nobel Prize in Physics 2023." The Nobel Foundation. https://www.nobelprize.org/prizes/physics/2023/summary/ — awarded to Pierre Agostini, Ferenc Krausz and Anne L'Huillier for experimental methods generating attosecond pulses of light, the technique underlying time-resolved photoemission. ## External links - [*University Physics Volume 3*](https://openstax.org/books/university-physics-volume-3) — OpenStax, CC BY; Chapter 6 is the photons chapter this page follows (Portal Book 079) - [*Chemical Bonding and Organic Chemistry*](https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry), Blackstock, Brewer and Cinel — the worked photoelectric case on p. 180 (Portal Book 054) - [The Nobel Prize in Physics 1921](https://www.nobelprize.org/prizes/physics/1921/summary/) — the award for the law of the photoelectric effect, with the presentation speech - Archival scans of the Hertz, Lenard, Einstein and Millikan papers are listed in the Wikipedia pair's *External links*; none is reproduced here until its URL has been checked. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Photoelectric_effect.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Photoelectric effect* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Photoelectric_effect.html" data-title="Photoelectric effect"></div> *Built from `MICROSIM_GUIDE/specs/sims/Photoelectric_effect.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Photoelectric_effect) : [Wikitube](https://en.wikitube.io/wiki/Photoelectric_effect) · pinned revision [1373790328](https://en.wikipedia.org/w/index.php?oldid=1373790328) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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