Photoelectric effect calculator
Light on a metal: photon energy, electron energy, stopping potential and cut-off.
How do you calculate the photoelectric effect?
Each photon carries E = hf = hc/λ and gives all of it to one electron. The electron spends the work function φ to leave the metal, and what is left is its maximum kinetic energy: K_max = hf − φ (OpenStax University Physics, Volume 3, equation 6.14). With hc = 1239.84 eV·nm (OpenStax rounds it to 1240), a 430 nm photon has 2.88 eV; on calcium (φ = 2.71 eV) that leaves K_max = 0.17 eV, so a stopping potential of 0.17 V is just enough to stop the electrons (OpenStax Example 6.7). If the photon energy is below φ, no electrons come out at all, however bright the light.
What are the cut-off frequency and wavelength?
The photon energy exactly equals the work function at f_c = φ/h, or λ_c = hc/φ; bluer light ejects electrons, redder light does not (OpenStax equations 6.15 and 6.16). OpenStax Example 6.5: silver has φ = 4.73 eV, so λ_c = 262 nm and 300 nm light ejects nothing from it, while sodium (2.46 eV) has a cut-off of 504 nm and would respond. Visible light spans about 400 to 750 nm (OpenStax problem 62), so of the eight metals in Table 6.1 only sodium can be set off by visible light, and only by the shorter wavelengths, below 504 nm; the other seven have cut-offs between 195 and 304 nm, in the ultraviolet. The Which metals? tab shows this for any wavelength.
How do I find the work function from the stopping potential?
Measure the voltage V₀ that just stops the photocurrent; the fastest electrons then have K_max = eV₀, and φ = hf − eV₀. OpenStax Example 6.6: 180 nm light and a stopping potential of 0.80 V give φ = 1240/180 − 0.80 = 6.09 eV and a cut-off frequency of 1.47 × 10¹⁵ Hz. Use the Stopping potential tab; with the exact hc the work function is 6.088 eV.
Does brighter light give the electrons more energy?
No. Brighter light means more photons per second, so more electrons and a bigger current, but each electron still absorbs one photon and gets hf − φ at most. That is why the stopping potential does not change with intensity, and why classical wave theory could not explain the effect (OpenStax University Physics, Volume 3, section 6.2). Only a higher frequency (a shorter wavelength) raises K_max.
Where do the work functions come from?
The metals are the eight in OpenStax Table 6.1, “Typical Values of the Work Function for Some Common Metals”: sodium 2.46 eV, aluminum 4.08, lead 4.14, zinc 4.31, iron 4.50, copper 4.70, silver 4.73 and platinum 6.35. Real values depend on the surface, its cleanliness and the crystal face, so treat them as typical; choose “Other” to type your own. h, c and e are the exact SI values, so answers can differ from textbook ones, which use hc = 1240 eV·nm, in the third digit. For the photon energy alone use the wavelength calculator.
Sources: OpenStax University Physics, Volume 3, section 6.2 (equations 6.12 to 6.16, Table 6.1, Examples 6.5 to 6.7); NIST, SI exact constants h, c and e. Related: wavelength calculator (photon energy), de Broglie wavelength calculator, blackbody radiation calculator and Rydberg equation calculator.