Calculate the maximum kinetic energy of ejected electrons, the threshold frequency, or the stopping voltage in the photoelectric effect, using Einstein's equation KEmax = hf − φ.
Inputs
Frequency of the incident light, in terahertz (1 THz = 10¹² Hz).
Wavelength of the incident light, in nanometres.
Minimum energy needed to eject an electron from the metal's surface. Sodium ≈ 2.3 eV, zinc ≈ 4.3 eV, copper ≈ 4.7 eV.
Result
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Enter the light's frequency (or wavelength) and the work function above to compute.
⚠️ No electrons are emitted at this frequency — the photon energy is below the work function. Raising the light's intensity will not help; only raising its frequency above the threshold will start emission.
The photoelectric effect — light knocking electrons out of a metal surface — looks simple in the lab but broke classical physics when it was first studied carefully.
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Walk-through
How to Use This Calculator
3 steps▸
1
Describe the incident light
Choose whether to enter the light's Frequency (in terahertz) or Wavelength (in nanometres) from the dropdown, then fill in that value. The two are related by c = fλ, so either one fully describes the photon's energy.
2
Enter the work function
Enter the material's work function φ in electronvolts (eV) — the minimum energy needed to eject an electron from its surface. Common metals: sodium ≈ 2.3 eV, zinc ≈ 4.3 eV, copper ≈ 4.7 eV, platinum ≈ 6.35 eV.
3
Read the result on any of the three tabs
Max KE shows the maximum kinetic energy of ejected electrons (or "No emission" if the photon energy is below the work function). Threshold Frequency shows the minimum frequency that can eject an electron from this material at all. Stopping Voltage shows the retarding voltage that would just stop the fastest electrons.
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Reference
Formula & Methodology
3 formulas▸
Maximum kinetic energy
KEmax = hf − φ
Einstein's photoelectric equation: the maximum kinetic energy of an ejected electron equals the incident photon's energy (hf, where h is Planck's constant and f is the light's frequency) minus the work function φ — the energy the electron must spend escaping the metal's surface. If hf < φ, KEmax would be negative, which is unphysical — no electrons are emitted at all, regardless of how intense the light is.
Threshold frequency
f₀ = φ / h
The threshold frequency is the frequency at which KEmax is exactly zero — the minimum photon energy that can still eject an electron. Light below f₀ (equivalently, wavelength longer than λ₀ = hc/φ) can never produce photoelectrons from this material, no matter how bright the source.
Stopping voltage
V₀ = KEmax / e
The stopping voltage (or stopping potential) is the retarding voltage that just barely stops the fastest photoelectrons before they reach a collecting electrode, eV₀ = KEmax. Because KEmax is naturally expressed in electronvolts and e is the electron's charge, the stopping voltage in volts is numerically equal to KEmax in eV.
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Glossary
Key Terms Explained
7 terms▸
Photoelectric effect ↗The emission of electrons from a material's surface when light of sufficiently high frequency shines on it. Its explanation by Einstein in 1905 — light behaves as discrete photons rather than a continuous wave — earned him the 1921 Nobel Prize in Physics and was pivotal evidence for quantum theory.
Work function (φ) ↗The minimum energy needed to remove an electron from a material's surface into free space, measured in electronvolts (eV). It is a property of the material and its surface condition, not of the incident light.
Threshold frequency (f₀) ↗The minimum light frequency that can eject a photoelectron from a given material, f₀ = φ/h. Below this frequency, no photoelectrons are emitted no matter how intense the light.
Stopping voltage (V₀) ↗The reverse (retarding) voltage applied between the emitting surface and a collector electrode that is just enough to stop the fastest-moving photoelectrons from reaching the collector, satisfying eV₀ = KEmax.
Photon energy ↗The energy carried by a single photon of light, E = hf = hc/λ. It depends only on the light's frequency (or wavelength), not its intensity.
Electronvolt (eV) ↗A unit of energy equal to the energy gained by a single electron accelerated through a potential difference of one volt (1 eV ≈ 1.602 × 10⁻¹⁹ joules). It is the natural unit for atomic and photoelectric energies because it keeps the numbers small and human-readable.
Einstein's photoelectric equation ↗The relationship KEmax = hf − φ, which correctly predicted that photoelectron kinetic energy depends only on light frequency, not intensity — a result the classical wave theory of light could not explain.
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Scenarios
Real-World Examples
3 worked examples▸
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Physics student
Near-UV light on sodium
Input as FrequencyFrequency (f) 750 THzWork function (φ) 2.3 eV
Photon energy hf = 4.1357 × 10⁻¹⁵ eV·s × 750 × 10¹² Hz ≈ 3.10 eV. KEmax = 3.10 − 2.3 ≈ 0.80 eV, so electrons are ejected with up to about 0.80 eV of kinetic energy. Sodium's threshold frequency works out to roughly 556 THz (λ₀ ≈ 539 nm, green light) — this violet-blue light comfortably clears it.
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Lab technician
Red light below the threshold
Input as WavelengthWavelength (λ) 650 nmWork function (φ) 2.3 eV
650 nm red light has a photon energy of only about 1.91 eV — below sodium's 2.3 eV work function. KEmax comes out negative, so the Max KE tab reports "No emission." Making the red light brighter adds more photons per second, but each one still carries too little energy — intensity cannot substitute for frequency here.
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Instrumentation engineer
Measuring stopping voltage
Input as FrequencyFrequency (f) 900 THzWork function (φ) 4.3 eV
Photon energy ≈ 3.72 eV is still below zinc's 4.3 eV work function, so this frequency also produces no emission and 0 V stopping voltage. Raising the frequency to roughly 1,040 THz (zinc's threshold) or higher is needed before a measurable stopping voltage — and therefore a measurable KEmax — appears.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
The photoelectric effect — light knocking electrons out of a metal surface — looks simple in the lab but broke classical physics when it was first studied carefully. Einstein's 1905 explanation, that light delivers its energy in discrete photon packets rather than as a continuous wave, became one of the founding results of quantum mechanics.
How the Photoelectric Effect Calculator works
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The calculator applies Einstein's photoelectric equation, KEmax = hf − φ, where h is Planck's constant, f is the incident light's frequency, and φ is the target material's work function. You can enter the light either as a frequency (THz) or a wavelength (nm) — internally the calculator converts wavelength to frequency via c = fλ before applying the formula, since energy depends on frequency, not wavelength directly. From KEmax it also derives the threshold frequency f₀ = φ/h (the point where KEmax hits zero) and the stopping voltage V₀ = KEmax/e (the retarding potential that halts the fastest photoelectrons). All three quantities come from the same two inputs — the tabs simply choose which one is promoted to the headline result.
Inputs and what they mean
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Frequency is entered in terahertz (10¹² Hz) since visible-to-UV light sits in the hundreds-of-THz range; wavelength is entered in nanometres for the same reason. The work function is entered directly in electronvolts, since that is how it is universally tabulated for real materials — typical metals range from about 2 eV (alkali metals like sodium, cesium) up to nearly 6.5 eV for platinum. The threshold frequency and stopping voltage depend only on the work function (and, for stopping voltage, on the light's frequency too) — they are properties of the material and the chosen light source, not adjustable independently.
Limits and edge cases
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When the incident photon energy is below the work function, KEmax is mathematically negative — physically this means zero photoelectrons are emitted, not a beam of negative-energy electrons, so the calculator reports "No emission" rather than a negative kinetic energy on the headline result. This calculator assumes an ideal, clean metal surface and normal-incidence monochromatic light; real photoemission experiments see surface contamination, work-function variation across crystal facets, and a spread of electron energies below KEmax due to electrons escaping from below the very top atomic layer. It also does not model photon flux, quantum efficiency, or the photoelectric current itself — only the energetics of the fastest ejected electron.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for the photoelectric effect?+
Einstein's photoelectric equation is KEmax = hf − φ, where KEmax is the maximum kinetic energy of an ejected electron, h is Planck's constant, f is the incident light's frequency, and φ is the material's work function.
How do you find the threshold frequency?+
The threshold frequency is f₀ = φ/h, the frequency at which KEmax is exactly zero. It depends only on the material's work function, not on the intensity or wavelength of any particular light source shining on it.
What happens if the light is below the threshold frequency?+
No electrons are emitted at all, no matter how intense the light is. Below the threshold, every photon carries less energy than the work function requires, so increasing the number of photons (intensity) cannot compensate — only raising the frequency above the threshold starts emission.
How is stopping voltage calculated?+
Stopping voltage is V₀ = KEmax/e, the retarding voltage that just stops the fastest photoelectrons from reaching a collector electrode. Because KEmax is expressed in electronvolts, the stopping voltage in volts is numerically equal to KEmax in eV.
What units does this calculator use?+
Light frequency is entered in terahertz (THz) or wavelength in nanometres (nm); the work function is entered in electronvolts (eV). Results are reported in eV for kinetic energy and photon energy, in THz/PHz for frequency, in nm for wavelength, and in volts (V) for stopping voltage.
Does increasing light intensity increase the electrons' kinetic energy?+
No. Increasing intensity increases the number of photons per second, which ejects more electrons per second (a larger photoelectric current) — but each electron's maximum kinetic energy is set only by the light's frequency, via KEmax = hf − φ, not by how bright the light is. This was the key experimental result the classical wave theory of light could not explain.
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