This photoelectric effect calculator applies Einstein’s equation Kmax = hf − φ: given light wavelength and a metal’s work function, it finds the fastest ejected electrons’ energy, the stopping potential, and the threshold where emission just begins.
| Photon energy | – |
| Kmax of ejected electrons | – |
| Stopping potential | – |
| Threshold wavelength λ₀ | – |
Einstein’s Equation: The Photon Pays φ, the Electron Keeps the Change
The photon side is our Photon Energy Calculator. Part of our Physics Calculators collection.
Worked Example (Verified)
- 300 nm UV on sodium-type surface, φ = 2.3 eV (defaults): photon E = 1240/300 = 4.13 eV → Kmax = 4.13 − 2.3 = 1.83 eV, stopping potential 1.83 V, threshold λ₀ = 1240/2.3 = 539 nm (green — anything redder fails on this metal)
- Metal work functions (eV, standard tables): Cs 2.14, K 2.29, Na 2.36, Ca 2.87, Zn 4.3, Cu 4.7, Pt 5.65 — the alkali metals emit under visible light; the noble ones demand UV
- Intensity changes the COUNT of electrons, never their max energy — Millikan spent a decade verifying Einstein’s linear K-vs-f plot and measured h from its slope, hating the conclusion the whole way
Effect Discipline
- Kmax is for the LEAST-bound electrons (surface, escaping cleanly); most electrons lose energy on the way out and emerge slower — the spectrum runs 0 → Kmax.
- Stopping potential in volts numerically equals Kmax in eV — by the definition of the electron-volt.
- Threshold frequency f₀ = φ/h and λ₀ = hc/φ are the same boundary said twice; below f₀, no emission at any intensity or exposure time.
- Real surfaces dirty: oxide layers and contamination shift effective φ — handbook values assume clean metal in vacuum.
Related Tools
- Photon Energy Calculator — E = hf in J and eV
- De Broglie Wavelength Calculator — the electrons’ own waves
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate photoelectric Kmax?
Kmax = hf − φ = (1240/λ in nm) − φ, all in eV. For 300 nm light on a 2.3 eV work function: 4.13 − 2.3 = 1.83 eV. If hf < φ, Kmax is negative — meaning no electrons are emitted at all. This calculator also gives stopping potential and threshold wavelength.
What is stopping potential?
The reverse voltage that halts even the fastest photoelectrons: e·Vs = Kmax, so Vs in volts equals Kmax in eV numerically (1.83 V for the worked example). It’s how Kmax is actually measured in the lab — turn the dial until the photocurrent dies.
Why doesn’t brighter light make faster electrons?
Because energy arrives in photon-sized packets: one electron absorbs one photon. Brighter light = more photons = more electrons at the SAME max energy. This single observation killed the classical wave prediction and earned Einstein the Nobel (for this, not relativity).
What is the threshold wavelength?
λ₀ = hc/φ ≈ 1240/φ(eV) nm — the longest wavelength that can still eject: 539 nm for φ = 2.3 eV (sodium family). Redder light fails regardless of intensity; each metal’s λ₀ is its photoelectric fingerprint, exploited in photomultipliers and night-vision photocathodes.
Which metals respond to visible light?
Those with φ below ~3.1 eV (λ₀ > 400 nm): the alkalis and calcium — Cs (2.14), K (2.29), Na (2.36), Ca (2.87). Zinc (4.3) and copper (4.7) need UV; platinum (5.65) needs deep UV. That’s why practical photocathodes are alkali compounds.
Is this photoelectric effect calculator free?
Yes — free, instant, no sign-up.