--- title: "Photoelectric evidence: the voltage is not yet the energy" description: "How did a family of current–voltage curves become a test of Einstein’s law?" canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/photoelectric-stopping-potential-contact/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/photoelectric-stopping-potential-contact/" last_modified: "2026-10-18" --- [Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/) Nobel A · Evidence and control # Photoelectric evidence: the voltage is not yet the energy Sandbox Physics · 2026-10-15 How did a family of current–voltage curves become a test of Einstein’s law? ## The current is measured; the endpoint is inferred No instrument shows the kinetic energy of each emitted electron; the stopping potential is inferred from where the current dies out. Light falls on an emitting surface, and an electrode facing it collects the electrons. Raising a retarding voltage steadily reduces the photocurrent. Repeating the scan at several light frequencies gives a family of curves. That endpoint can be blurred by dark current, by emission from the collector itself, by the finite spectral width of the light and by the spread of initial electron energies. The maximum emission energy is a different quantity from the average energy and from the number of electrons collected. A useful test has to say which of these each plotted point stands for. Read the evidence: R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan ## What the straight line actually tests The equation below is the ideal energy balance for one photon freeing one electron from a surface. The stopping potential is the size of the retarding voltage, taken as positive, once contact fields are accounted for. The elementary charge is positive, the frequency is that of the incoming light, and the work function is the least energy an electron needs to leave that particular surface. The relation holds only above the threshold frequency. A frequency scan tests two things: that the points lie on a straight line, and that its slope equals Planck’s constant divided by the elementary charge. A different but stable surface shifts the intercept and leaves this universal slope unchanged. A single nonzero photocurrent, or a straight line over too narrow a frequency range, shows much less. $$ eV_{\mathrm{stop}}=K_{\max}=h\nu-\Phi $$ Read the evidence: R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan ## Why two metals introduce a hidden voltage The voltmeter reading cannot go straight into the ideal energy equation. The emitter and collector usually have different surfaces, and the contact potential between them changes the retarding energy an electron actually meets. The sign of the correction also depends on how the circuit voltage is defined. Millikan spent much of his effort preparing alkali-metal surfaces and measuring or stabilizing the contact electromotive force. His paper reports that the contact potential changed as a surface aged and absorbed gas. A constant offset mainly shifts the intercept. A drift that follows the order in which the frequencies were measured can bias the slope too. Read the evidence: R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan CaltechAUTHORS, Millikan’s 1916 photoelectric paper — institutional record ## Intensity and frequency change different things With weak light, where photons act one at a time, and with frequency and surface held fixed, more intensity mainly means more electrons emitted per second. A higher frequency changes their maximum energy instead. A measured current is proportional to intensity only once collection efficiency and saturation are under control. This rule does not hold for every light source or material. Heating, space charge, changes in the surface and multiphoton emission can all alter the comparison. They do not undo a test made under the conditions it states, but they keep the textbook intensity rule from becoming a law without limits. Read the evidence: R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan ## Millikan accepted the law but not the picture behind it In his introduction Millikan separates the success of Einstein’s energy relation from his own doubts about localized particles of light. That is what makes the paper valuable: its author accepted the quantitative result and still disputed the physical picture offered for it. The evidence did not arrive with everyone agreeing on what it meant. Einstein’s 1921 prize emphasizes the photoelectric law; Millikan’s 1923 prize covers both the elementary charge and his photoelectric work. The slope of the stopping potential gives only a ratio of two constants. Getting Planck’s constant out of it needs an independently established charge scale, which is where the oil-drop measurement comes in. Read the evidence: R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan Nobel Prize in Physics 1921 — official award record Robert A. Millikan — official 1923 award facts ## Using the Lab to compare energies The photoemission Lab has two separate instruments: a hemispherical analyzer and a guarded radial retarding collector. The collector keeps simulated counts with the shutter open and closed at several frequencies and intensities, then fits the central edges and their slope against frequency. Without an independent reference, the contact potential and the work function cannot be told apart. The data are simulated for teaching; they are not Millikan’s measurements or his historical contact correction. A good exercise is to ask which parts of a graph survive an unknown constant voltage offset. The slope may; the inferred threshold need not. Then ask what happens if the offset drifts between frequency settings. Questions like these tie the prediction to the measurement that would test it. Read the evidence: R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan ## Continue with the models These teaching Labs produce simulated data, which are separate from the historical observations discussed above. - [Measure retarding currents and find the stopping potential at each light frequency](https://sandboxphysics.com/labs/photoemission-analyzer/) ## Sources and reading notes Millikan’s 1916 paper is readable in the APS scan, and Caltech’s library entry confirms the citation. This article keeps his distinction between the measured photopotential, the contact potential and the emission energy inferred from them. It does not digitize or refit any historical curve. 1. [R. A. Millikan (1916), A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355–388 — original scan](https://journals.aps.org/pr/pdf/10.1103/PhysRev.7.355) 2. [CaltechAUTHORS, Millikan’s 1916 photoelectric paper — institutional record](https://authors.library.caltech.edu/records/45t7b-bvc23) 3. 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