Photoelectric Effect Calculator
Enter the wavelength or frequency of incident light and choose a metal (or enter a custom work function) to instantly calculate the photon energy, maximum kinetic energy of the emitted electron, stopping potential, and threshold frequency and wavelength. Switch between wavelength and frequency input, and between eV and Joules for the work function. All results update as you type.
Formula
Worked example
Ultraviolet light of wavelength 300 nm hits a sodium surface (work function 2.36 eV). Photon energy: E = hc/lambda = (6.626e-34 × 2.998e8) / (300e-9) = 4.136 eV. Since 4.136 eV > 2.36 eV, electrons are ejected. Kmax = 4.136 - 2.36 = 1.776 eV. Stopping potential Vs = 1.776 V. Threshold wavelength = hc/phi = 526 nm, so any UV below 526 nm will work.
What is the photoelectric effect?
The photoelectric effect is the emission of electrons from a metal surface when light shines on it. It was first observed by Heinrich Hertz in 1887, but classical wave theory could not explain its key features: the existence of a threshold frequency below which no electrons are emitted no matter how bright the light, and the fact that brighter light produces more electrons but does not increase their kinetic energy. In 1905, Albert Einstein resolved the puzzle by proposing that light comes in discrete packets of energy called photons, each carrying an energy E = hf, where h is Planck's constant and f is the frequency of the light. This insight earned Einstein the 1921 Nobel Prize in Physics and gave quantum mechanics one of its most important experimental foundations.
How to use this calculator
Select whether you want to enter the incident light as a wavelength (in nanometres) or a frequency (in terahertz). Then choose a metal from the preset list - cesium, potassium, sodium, and other common materials have their work functions pre-filled from NIST data. Alternatively, select 'Custom work function' and enter your own value in eV. All results update instantly: you get the photon energy in both eV and Joules, the maximum kinetic energy of the ejected electron (Kmax), the stopping potential needed to halt the fastest electrons, the threshold frequency and wavelength for the chosen material, and the non-relativistic speed of the fastest emitted electron. The energy bar chart shows photon energy, work function, and Kmax side by side, and the curve below plots how Kmax changes across a range of wavelengths for the same material.
Einstein's photoelectric equation explained
Einstein's equation is Kmax = hf - phi, where Kmax is the maximum kinetic energy of the emitted electron, h is Planck's constant (6.626 x 10^-34 J·s), f is the photon frequency, and phi is the work function of the metal - the minimum energy required to free an electron from the surface. If hf < phi, the photon does not have enough energy to free any electrons, regardless of intensity. If hf = phi, electrons are just barely freed with zero kinetic energy - this defines the threshold frequency f0 = phi / h and the threshold wavelength lambda0 = hc / phi. If hf > phi, the surplus energy goes into kinetic energy of the electron. The stopping potential Vs is the minimum reverse voltage needed to bring the fastest electrons to rest: Vs = Kmax / e, where e is the elementary charge. These relationships are all independent of light intensity; only the frequency matters for whether and how energetically electrons are emitted.
Practical applications of the photoelectric effect
The photoelectric effect underpins a wide range of modern technology. Photomultiplier tubes, used in medical imaging (PET scanners) and particle physics detectors, amplify tiny flashes of light by successive photoelectric emission and electron multiplication. Photodiodes and CCD image sensors in cameras convert photons to electrons using semiconductor versions of the same principle. Solar cells exploit a related effect in semiconductor p-n junctions to convert sunlight directly into electrical current. Photoelectric smoke detectors use an ionization chamber where light interruption signals the presence of smoke particles. X-ray photoelectron spectroscopy (XPS), a key analytical technique in materials science, measures the kinetic energies of photoelectrons to identify elements and chemical bonding states at surfaces.
Work functions of common metals
| Metal | Symbol | Work function (eV) | Threshold wavelength (nm) | Notes |
|---|---|---|---|---|
| Cesium | Cs | 2.1 | 591 | Lowest of common metals; used in photomultipliers |
| Potassium | K | 2.29 | 542 | Visible light can eject electrons |
| Sodium | Na | 2.36 | 526 | Classic photoelectric experiment metal |
| Barium | Ba | 2.52 | 492 | Used in vacuum tubes |
| Calcium | Ca | 2.87 | 432 | Near-UV needed |
| Lithium | Li | 2.93 | 423 | Alkali metal; UV or violet light |
| Aluminum | Al | 4.08 | 304 | UV required |
| Silver | Ag | 4.26 | 291 | Common in photodetectors |
| Zinc | Zn | 4.33 | 286 | Historically used in early experiments |
| Copper | Cu | 4.65 | 267 | Far UV required |
| Iron | Fe | 4.7 | 264 | Far UV required |
| Nickel | Ni | 5.15 | 241 | Deep UV required |
| Gold | Au | 5.1 | 243 | Chemically stable; used in research |
| Platinum | Pt | 5.65 | 220 | Highest common work function; deep UV |
Approximate work functions from NIST and CRC Handbook of Chemistry and Physics. Values vary slightly by surface preparation and purity.
Frequently asked questions
Why does the photoelectric effect require a minimum frequency?
Each photon carries a fixed energy E = hf. To free an electron, the photon must deliver at least as much energy as the work function of the metal (the binding energy of the most loosely held surface electrons). Below the threshold frequency f0 = phi/h, each photon is simply too weak to dislodge an electron, regardless of how many photons arrive. Increasing intensity just means more low-energy photons arriving - but none of them can free an electron. Only increasing frequency (energy per photon) can cross the threshold.
What is stopping potential and how is it measured?
When a metal surface emits photoelectrons, a reverse voltage can be applied to decelerate them. The stopping potential Vs is the exact voltage at which even the fastest electrons (those with kinetic energy Kmax) are brought to rest and the photocurrent drops to zero. Measuring Vs lets you determine Kmax = eVs without knowing the electron's speed directly. Millikan used this technique in his 1916 experiments to precisely measure Planck's constant and confirm Einstein's equation.
Can I use visible light to trigger the photoelectric effect?
Yes - for metals with low work functions. Cesium (2.10 eV) and potassium (2.29 eV) have threshold wavelengths around 540-590 nm, which falls in the visible green-yellow range. Sodium's threshold is about 526 nm (green light). Most other metals have work functions above 4 eV, requiring ultraviolet light (wavelength below about 310 nm). This is why the original experiments with zinc required UV and sparked debate about why visible light had no effect.
Does the intensity of light affect the kinetic energy of emitted electrons?
No. Intensity determines how many photons hit the surface per second, so it controls the number of electrons emitted (the photocurrent). But each photon still carries the same energy E = hf, so the maximum kinetic energy of each ejected electron Kmax = hf - phi is unchanged. This was the central puzzle before Einstein: classical wave theory predicted brighter light should push electrons harder, but experiment showed it only produced more electrons, not faster ones.
Why is the electron speed result described as non-relativistic?
The formula v = sqrt(2*Kmax/m_e) comes from classical kinetic energy (KE = 0.5*m*v^2). It is accurate when the electron speed is well below the speed of light (~3x10^8 m/s). For photon energies achievable in a standard lab photoelectric experiment (a few eV), the electron speeds are typically in the range of 10^5 to 10^6 m/s, which is less than 1% of the speed of light, so the non-relativistic approximation is excellent. Relativistic corrections only matter when photon energies reach tens of keV or more (hard X-rays and gamma rays).
What is the work function and how does it vary between metals?
The work function is the minimum energy needed to remove a single electron from the surface of a material. It reflects how strongly the metal's positive ion cores bind the outermost (conduction) electrons. Alkali metals like cesium and potassium have large atomic radii, loosely held valence electrons, and work functions around 2 eV. Transition and noble metals like platinum and gold have tighter electron binding and work functions above 5 eV. The work function also depends on the crystal face of the metal and surface contamination, so published values are averages for polycrystalline surfaces under typical conditions.