# Light That Frees Electrons

Laplace’s Mini World · Plate 58 · Matter, Light & Sound · Matter

> Light falling on a metal can knock electrons out, but only if each packet of light carries enough energy. Brighter light frees more electrons, not faster ones; bluer light frees faster ones.

- Interactive model: https://world.lapla.si/en/photoelectric/
- Embed: https://world.lapla.si/embed/en/photoelectric/
- 中文: https://world.lapla.si/zh/photoelectric/
- Updated: 2026-10-29

## 01 Ultraviolet and a Spark

In 1887, working on electromagnetic waves, Heinrich Hertz noticed that the small spark at his receiver jumped a shorter gap once it was shaded. Testing one cause after another, he traced it to the ultraviolet light of the transmitter’s spark: ultraviolet falling on the gap helped the spark across, and glass and mica blocked the effect.

The next year Wilhelm Hallwachs connected a polished zinc plate to an electroscope and lit it with an arc lamp. Charged negatively, the gold leaves lost 70 % of their spread in 5 seconds and closed in 10; charged positively, they lost only 10 % in 60 seconds. The light drew away negative charge.

In 1899 J. J. Thomson measured the particles that ultraviolet light carried off a metal: the same charge-to-mass ratio as cathode rays, and a mass about a thousandth of a hydrogen atom’s (his estimate). Today they are called electrons.

*1887 Hertz · 1888 Hallwachs · 1899 Thomson*

## 02 Three Things Waves Can’t Explain

In the wave picture, light’s energy spreads out evenly, and brighter light carries more of it; an electron that soaks up enough is shaken free. Then brighter light should give faster electrons, light of any colour should work if it is bright enough, and in dim light the electrons should take a while to gather the energy.

Experiments said otherwise. In 1902 Philipp Lenard made his arc lamp about 70 times brighter, and the voltage needed to stop the electrons changed by less than 1 %: more light brought more electrons, not faster ones. A zinc plate does not respond to visible light, however bright.

Millikan estimated in 1916 that, in the wave picture, a standard candle 3 metres away would have to shine on an atom-sized spot for at least 4 hours before it could free one electron. In fact the electrons leave the moment the light is on.

*Brighter, not faster (Lenard 1902) · the wrong colour never works · no waiting*

## 03 One Quantum, One Electron

In March 1905 Albert Einstein sent off a paper with a “heuristic point of view”: light’s energy is not spread out continuously but made of a finite number of energy quanta, each localised at a point, absorbed or produced only whole. For light of frequency f, one quantum carries h f. Today it is called a photon.

He took the simplest case: one quantum gives all its energy to one electron. Leaving the metal costs the electron some of it, the work function W; the rest becomes kinetic energy, at most h f − W.

So when h f is less than W no electron leaves, however bright the light; brighter light only means more photons and so more electrons, each with the same energy. The wave packets and bright dots in the tube are a drawing: packets for photons, dots for electrons.

*Largest kinetic energy = h f − W · one photon, one electron · h = 6.626 × 10⁻³⁴ J s*

## 04 The Work Function

The work function is the least energy it takes to pull an electron out through a metal’s surface, and every metal has its own. From photoelectric measurements on polycrystalline surfaces, as compiled by H. B. Michaelson in 1977: caesium 2.14 eV, potassium 2.30, sodium 2.75, zinc 4.33, copper 4.65, platinum 5.65.

The work function sets the lowest frequency, W/h, and so the longest wavelength: about 579 nm for caesium, where yellow light just works; 539 nm for potassium, a little bluer than green; 451 nm for sodium, blue; 286 nm for zinc, ultraviolet only. That is why Hallwachs’s zinc plate needed ultraviolet.

It also depends on the surface. Copper’s (110) face has 4.48 eV, its (111) face 4.98; a film of something else on the surface changes it too. Michaelson put the agreement between careful measurements at one or two tenths of an electronvolt.

*Work functions (Michaelson 1977): Cs 2.14 · K 2.30 · Na 2.75 · Zn 4.33 · Cu 4.65 · Pt 5.65 eV*

## 05 The Phototube, Cut Open

The phototube on the bench is an evacuated glass bulb. Its back half is coated inside with a film of metal, the cathode, which the light reaches through the front; a ring of wire hangs in the middle, the anode. Two leads run out through the glass press at the bottom to the base.

The vacuum lets the electrons fly all the way to the anode without hitting gas molecules. With the anode on the supply’s positive side, the freed electrons make a current, read by the microammeter in the circuit.

Ordinary glass stops ultraviolet shorter than about 300 nm, so a tube meant for it has a quartz bulb or window. The model shows the principle, not any maker’s tube; the bulb is drawn larger than life and cut open on the side facing the camera.

*Evacuated bulb · cathode: a metal film inside · anode: a wire ring · leads through the glass press*

## 06 A Voltage That Stops Them

Turn the supply round so that the anode sits U volts below the cathode. The electrons slow down on their way and arrive with e U less kinetic energy; those with too little are pushed back to the cathode.

The larger U, the fewer electrons reach the anode and the smaller the current. At one voltage even the fastest fall short and the current drops to zero: the stopping voltage, Us. The fastest electrons’ kinetic energy is e × Us; a stopping voltage of 1 volt means 1 electronvolt.

So a voltage tells the largest kinetic energy without timing a single electron. Potassium under blue 436 nm light has a stopping voltage of about 0.54 V; its fastest electrons leave at about 438 km/s.

*Largest kinetic energy = e × Us · potassium, 436 nm: Us ≈ 0.54 V · fastest electrons about 438 km/s*

## 07 Brighter: More Electrons

With the iris open wider, more photons reach the cathode each second, more electrons leave and the current rises. Twice the intensity, twice the current.

The stopping voltage does not move: each photon’s energy is unchanged, and the fastest electrons are as fast as before. Einstein wrote exactly this in 1905: the electrons’ distribution of speeds does not depend on the intensity, and their number is in proportion to it.

*Intensity 50 % and 100 % · twice the current · the same stopping voltage, 0.54 V*

## 08 Bluer: Faster Electrons

The monochromator turns from green to ultraviolet. Potassium’s work function is 2.30 eV: a photon of green 546 nm light carries 2.27 eV, just short, and frees no electron at all; blue 436 nm light carries 2.84 eV, leaving at most 0.54 for the electron; ultraviolet at 365 nm carries 3.40 eV and leaves 1.10.

The higher the frequency, the higher the stopping voltage and the faster the fastest electrons: from about 438 km/s to about 621 km/s. The longer an electron’s tail in the tube, the faster it is (a drawing).

*Potassium: 546 nm none · 436 nm 0.54 V · 405 nm 0.76 V · 365 nm 1.10 V*

## 09 Millikan’s Straight Line

Einstein’s equation predicts that the stopping voltage plotted against frequency is a straight line with slope h/e, the same for every metal; where it meets the frequency axis is that metal’s lowest frequency.

Robert Millikan did not believe in light quanta and spent ten years testing the equation. He sealed sodium, potassium and lithium in a vacuum tube, shaved fresh metal surfaces inside it with a knife driven by electromagnets outside (“a machine shop in vacuo”), and lit them with lines of a mercury lamp. In 1916 he reported that his sodium points lay on a straight line, none off by more than 0.01 V, and that its slope gave h = 6.57 × 10⁻³⁴ J s, to about 0.5 %.

Yet he wrote that the “semi-corpuscular theory” behind the equation “seems at present to be wholly untenable.” Einstein received the Nobel Prize in Physics for 1921 (awarded in 1922) “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect”; Millikan received the 1923 prize “for his work on the elementary charge of electricity and on the photoelectric effect”.

*Slope = h/e, the same for every metal · Millikan 1916: h = 6.57 × 10⁻³⁴ J s · exact today: 6.626 × 10⁻³⁴*

## 10 No Waiting

In the wave picture, electrons under dim light must first gather enough energy; by Millikan’s estimate it would take hours. In fact they leave as soon as the light arrives.

In 1928 Ernest Lawrence and Jesse Beams, using a Kerr cell as a shutter, found that a potassium hydride surface gave off electrons less than 3 nanoseconds after the light began. That was as fine as their instruments could tell.

Attosecond light pulses later showed finer differences: in 2007, electrons from different levels of a tungsten crystal left about 100 attoseconds apart; in 2010, two kinds of electrons from neon atoms about 21 attoseconds apart, a figure revised since. These are delays between electrons, not time spent gathering energy.

*Wave estimate: about 4 hours · 1928: under 3 ns · 2007: a relative delay of about 100 as*

## 11 Where It Works Today

Photomultiplier tubes use the effect directly: light frees electrons from a photocathode, and a chain of dynodes knocks out more at every stage, multiplying the current up to 10⁸ times. The “ultra bialkali” cathode made in 2007 frees 43 electrons for every 100 photons at 350 nm. Third-generation night-vision tubes work alike: a gallium arsenide photocathode frees electrons, each channel of a microchannel plate multiplies them a few hundred times, and a phosphor screen turns them back into light.

The image sensors in cameras (CCD and CMOS) also free electrons with light, but the electrons stay in the silicon: they move from bound states into the conduction band, where they can flow. This is the internal photoelectric effect. Silicon’s band gap is 1.12 eV, so it hardly absorbs light longer than about 1.1 µm. The CCD’s inventors shared the 2009 Nobel Prize in Physics.

Solar cells use the internal effect too. In 1961 William Shockley and Hans Queisser found that a single-junction cell with a 1.1 eV gap could reach at most about 30 %; by the 2026 efficiency tables, the record for a large (140 cm²) silicon cell is 28.1 %.

*External effect: photomultipliers, image intensifiers · internal effect: image sensors, solar cells*

## 12 Five Parts

The phototube comes apart into five pieces: the glass bulb, the cathode film, the anode ring, the press with its leads, and the base.

The part under the pointer lifts out alone and is named; left alone, all five carry their names.

*Bulb · cathode · anode · press and leads · base*

## 13 Measure h

The bench offers four cathode metals, seven lines of the mercury lamp, the intensity and a retarding voltage. The reading is the current; “Find the stopping voltage” raises the voltage from zero until the current stops and marks the point on the lower chart.

Several lines on one metal put the points on a straight line whose slope is h/e, and the readout gives h from it. Another metal shifts the line without changing its slope; zinc frees electrons only with the 254 nm line.

This is an ideal phototube: no contact potential, no electrons from the anode, kinetic energies spread evenly from zero to the largest, intensity counted in photons per second, and 80 µA at full intensity (a set value).

*Computed here: e × Us = h f − W · work functions from Michaelson 1977 · wavelengths from NIST*

**Try this**: With a potassium cathode, switch the mercury line from 436 nm to 365 nm: how far does the stopping voltage rise? At half the intensity, what happens to the current and to the stopping voltage?

## What the Model Leaves Out

The bench is a model of the principle: the mercury lamp, monochromator, iris, phototube, supply and microammeter are drawn, not copied from any maker, and the bulb is larger than life. The beam and the photons and electrons in the tube are a drawing, not to scale in size, number or speed; real light cannot be seen from the side. The lab uses an ideal tube. In a real one, a contact potential between cathode and anode shifts the measured stopping voltage as a whole, and Millikan measured it separately; stray light on the anode frees electrons there too, giving a small reverse current; the electrons’ energies are not spread evenly, so the current runs smoothly down to zero near the stopping voltage instead of meeting it at a corner; and the chance that a photon frees an electron (the quantum efficiency) changes with the metal, its surface and the frequency.

## Easily Misread

Intensity sets how many electrons leave, not how fast; frequency sets how fast the fastest are. “Photon” is not a word of 1905: Einstein wrote of energy quanta, and his equation has no h but Rβν/N, which is today’s h. A work function is not a fixed number: crystal faces and clean or dirty surfaces change it by tenths of an electronvolt; the sodium Millikan measured in 1916 stopped responding near 6,800 Å, about 1.8 eV, far below the handbook value. In camera sensors and solar cells the electrons never leave the silicon: that is the internal photoelectric effect, not the external one of the phototube, where they fly out of the metal. Einstein’s Nobel Prize was not for relativity. Millikan confirmed the equation yet for years did not accept light quanta.

## Common questions

### How did Einstein explain the photoelectric effect?

He took the simplest case: one quantum gives all its energy to one electron.

See: [03 One Quantum, One Electron](https://world.lapla.si/en/photoelectric/#quanta)

### Why doesn’t brighter light give faster electrons?

The stopping voltage does not move: each photon’s energy is unchanged, and the fastest electrons are as fast as before.

See: [07 Brighter: More Electrons](https://world.lapla.si/en/photoelectric/#brighter)

### Why does zinc need ultraviolet light?

The work function sets the lowest frequency, W/h, and so the longest wavelength: about 579 nm for caesium, where yellow light just works; 539 nm for potassium, a little bluer than green; 451 nm for sodium, blue; 286 nm for zinc, ultraviolet only.

See: [04 The Work Function](https://world.lapla.si/en/photoelectric/#work)

### How did Millikan measure Planck’s constant?

In 1916 he reported that his sodium points lay on a straight line, none off by more than 0.01 V, and that its slope gave h = 6.57 × 10⁻³⁴ J s, to about 0.5 %.

See: [09 Millikan’s Straight Line](https://world.lapla.si/en/photoelectric/#millikan)

### Do camera sensors use the photoelectric effect?

The image sensors in cameras (CCD and CMOS) also free electrons with light, but the electrons stay in the silicon: they move from bound states into the conduction band, where they can flow.

See: [11 Where It Works Today](https://world.lapla.si/en/photoelectric/#today)

## Sources

1. [H. Hertz (1887): Ueber einen Einfluss des ultravioletten Lichtes auf die electrische Entladung, Annalen der Physik 267, 983 (ultraviolet light helps the spark across; glass and mica block it)](https://doi.org/10.1002/andp.18872670827)
2. [W. Hallwachs (1888): Ueber den Einfluss des Lichtes auf electrostatisch geladene Körper, Annalen der Physik 269, 301 (a negatively charged zinc plate loses 70 % of its spread in 5 s, a positive one 10 % in 60 s)](https://doi.org/10.1002/andp.18882690206)
3. [J. J. Thomson (1899): On the Masses of the Ions in Gases at Low Pressures, Phil. Mag. 48, 547 (the carriers freed by ultraviolet light are those of cathode rays, about a thousandth of a hydrogen atom’s mass)](https://doi.org/10.1080/14786449908621447)
4. [P. Lenard (1902): Ueber die lichtelektrische Wirkung, Annalen der Physik 313, 149 (the initial speeds do not depend on the intensity: about 70 times the light changed them by under 1 %)](https://doi.org/10.1002/andp.19023130510)
5. [A. Einstein (1905): Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Annalen der Physik 17, 132 (energy quanta of light, one to one electron, a straight line whose slope does not depend on the substance, the number of electrons in proportion to the intensity)](https://doi.org/10.1002/andp.19053220607)
6. [A. B. Arons, M. B. Peppard (1965): English translation of Einstein’s 1905 paper, Am. J. Phys. 33, 367](https://doi.org/10.1119/1.1971542)
7. [R. A. Millikan (1916): A Direct Photoelectric Determination of Planck’s “h”, Phys. Rev. 7, 355 (sodium shaved in vacuum, the mercury lines, the straight line, h = 6.57 × 10⁻²⁷ erg s to about 0.5 %, his doubts about light quanta, the four-hour estimate)](https://doi.org/10.1103/PhysRev.7.355)
8. [R. A. Millikan (1949): Albert Einstein on His Seventieth Birthday, Rev. Mod. Phys. 21, 343 (“I spent ten years of my life testing that 1905 equation”)](https://doi.org/10.1103/RevModPhys.21.343)
9. [R. A. Millikan (1924): The electron and the light-quant from the experimental point of view, Nobel lecture](https://www.nobelprize.org/uploads/2018/06/millikan-lecture.pdf)
10. [nobelprize.org: the Nobel Prize in Physics 1921 (awarded in 1922) and its citation](https://www.nobelprize.org/prizes/physics/1921/summary/)
11. [nobelprize.org: the Nobel Prize in Physics 1923 and its citation](https://www.nobelprize.org/prizes/physics/1923/summary/)
12. [nobelprize.org: the Nobel Prize in Physics 2009, press release (the CCD)](https://www.nobelprize.org/prizes/physics/2009/press-release/)
13. [NIST: CODATA 2022 fundamental physical constants (h and e exact)](https://physics.nist.gov/cuu/Constants/Table/allascii.txt)
14. [H. B. Michaelson (1977): The work function of the elements and its periodicity, J. Appl. Phys. 48, 4729 (preferred work functions, crystal faces, agreement within 0.1⁠–⁠0.2 eV)](https://doi.org/10.1063/1.323539)
15. [NIST Atomic Spectra Database: lines of mercury (Hg I)](https://physics.nist.gov/PhysRefData/ASD/lines_form.html)
16. [E. O. Lawrence, J. W. Beams (1928): The Element of Time in the Photoelectric Effect, Phys. Rev. 32, 478 (less than 3 × 10⁻⁹ s)](https://doi.org/10.1103/PhysRev.32.478)
17. [A. L. Cavalieri et al. (2007): Attosecond spectroscopy in condensed matter, Nature 449, 1029 (a delay of about 100 as in tungsten)](https://doi.org/10.1038/nature06229)
18. [M. Schultze et al. (2010): Delay in photoemission, Science 328, 1658 (21 as in neon; revised by M. Isinger et al., Science 358, 893, 2017)](https://doi.org/10.1126/science.1189401)
19. [Hamamatsu Photonics: Photomultiplier Tubes: Basics and Applications, 4th ed. (external and internal photoelectric effect, gain up to 10⁸, the ultra bialkali cathode’s 43 % at 350 nm)](https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/etd/PMT_handbook_v4E.pdf)
20. [Ioffe Institute NSM database: silicon’s band structure (gap 1.12 eV at 300 K)](http://www.ioffe.ru/SVA/NSM/Semicond/Si/bandstr.html)
21. [W. Shockley, H. J. Queisser (1961): Detailed Balance Limit of Efficiency of p-n Junction Solar Cells, J. Appl. Phys. 32, 510 (at most 30 % at a 1.1 eV gap)](https://doi.org/10.1063/1.1736034)
22. [M. A. Green et al. (2026): Solar cell efficiency tables (Version 68), Joule 10, 102494; as reported by pv magazine (Longi’s 140 cm² silicon cell at 28.1 %)](https://pv-magazine-usa.com/2026/06/08/all-solar-cell-efficiencies-at-a-glance-updated-7/)
23. [RCA (1963): Phototubes and Photocells, technical manual PT-⁠60 (cathode, anode, envelope and base; the caesium–antimony cathode; ordinary glass cutting off ultraviolet below about 300 nm; energy spread, dark current)](https://bitsavers.mirrorservice.org/components/rca/1963_PT-60_RCA_Phototubes_and_Photocells.pdf)
24. [US patent 6,597,112 B1 (2003): Photocathode for night vision image intensifier (the third generation’s gallium arsenide cathode, the microchannel plate)](https://patents.google.com/patent/US6597112B1/en)

## Data

The lab computes Einstein’s equation, e Us = h f − W, with the exact SI values of h and e (NIST, CODATA 2022), the photoelectric work functions compiled by H. B. Michaelson (J. Appl. Phys. 48, 4729, 1977) and the mercury wavelengths of the NIST Atomic Spectra Database. The history is from the original papers: H. Hertz (1887), W. Hallwachs (1888), J. J. Thomson (1899), P. Lenard (1902), A. Einstein (Annalen der Physik 17, 132, 1905; English translation by A. B. Arons and M. B. Peppard, 1965), R. A. Millikan (Phys. Rev. 7, 355, 1916; Rev. Mod. Phys. 21, 343, 1949), E. O. Lawrence and J. W. Beams (1928), and nobelprize.org; today’s devices from Hamamatsu Photonics’ photomultiplier handbook, the Ioffe Institute’s silicon data, W. Shockley and H. J. Queisser (1961), M. A. Green et al.’s efficiency tables (version 68, 2026) and US patent 6,597,112. The bench is a model of the principle, not any maker’s instruments. Material presets, parts and the softbox studio of the site’s model kit are ported from AirsupHQ/machine-skill (MIT, © 2026 Air Supply Technologies Inc.).

## Licence CC BY-NC 4.0

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## Cite this plate

Laplace’s Mini World, Plate 58, “Light That Frees Electrons”, https://world.lapla.si/en/photoelectric/, CC BY-NC 4.0, updated 2026-10-29.