Choose your light inputs and metal parameters easily. Get threshold values, electron speed, and stopping voltage. Download results as CSV or PDF for reports.
| Material (φ, eV) | Light (nm) | Photon energy (eV) | KEmax (eV) | Stopping potential (V) | Emission? |
|---|---|---|---|---|---|
| Sodium (2.28) | 450 | ≈ 2.76 | ≈ 0.48 | ≈ 0.48 | Yes |
| Zinc (4.30) | 250 | ≈ 4.96 | ≈ 0.66 | ≈ 0.66 | Yes |
| Copper (4.70) | 300 | ≈ 4.13 | 0.00 | 0.00 | No |
| Cesium (2.14) | 600 | ≈ 2.07 | 0.00 | 0.00 | No |
| Potassium (2.30) | 400 | ≈ 3.10 | ≈ 0.80 | ≈ 0.80 | Yes |
E = h f and f = c / λφ = h f₀ and λ₀ = c / f₀KEmax = E − φe Vs = KEmax (so Vs = KEmax in eV)v = √(2 KE / me)p = √(2 me KE), λdB = h / pΦ = (Intensity × Area) / E; electron rate R = Φ × QE; current I ≈ e RThe photoelectric effect is a benchmark experiment for quantum physics because it links light to discrete energy packets. In real labs it underpins phototubes, vacuum photodiodes, UV sensors, and electron spectroscopy. A key observation is that increasing light intensity mainly increases the number of emitted electrons, while increasing frequency controls the maximum electron kinetic energy.
The work function (φ) is the minimum energy needed to release an electron from a surface. Clean alkali metals commonly sit near 2–3 eV, while many transition metals are closer to 4–5 eV. Surface oxidation, contamination, and roughness can shift φ by tenths of an eV, which is enough to change emission predictions near threshold.
The threshold condition is hf0 = φ. Converting to wavelength gives λ0 = c / f0. As a scale check, φ = 2.5 eV corresponds to f0 ≈ 6.0×1014 Hz and λ0 ≈ 500 nm (visible). φ = 4.5 eV pushes λ0 near 275 nm (ultraviolet).
For a given photon energy E, the maximum kinetic energy is KEmax = E − φ. The calculator reports KE in both eV and joules. When E is only slightly above φ, KE can be small, making measurements sensitive to contact potentials, stray fields, and instrument resolution.
In a stopping-potential setup, the retarding voltage Vs cancels the maximum kinetic energy: eVs = KEmax. Numerically, 1 eV corresponds to 1 V for a single electron. So KEmax = 0.80 eV implies Vs ≈ 0.80 V, a convenient cross-check for your results.
With nonrelativistic electrons (typical here), v ≈ √(2KE/me). Even KE = 2 eV gives v around 8.4×105 m/s, still well below c. Momentum p = √(2meKE) leads to a de Broglie wavelength often on the order of 1 nm, connecting photoemission to wave behavior.
If intensity and illuminated area are known, photon flux is Φ ≈ (Power)/E. For example, 100 W/m² over 2 cm² gives 0.02 W incident. At E ≈ 3 eV (≈4.8×10−19 J), Φ is about 4×1016 photons/s. With 10% quantum efficiency, the ideal current estimate is roughly 0.64 mA.
Differences between prediction and experiment usually come from non-ideal surfaces, energy losses inside the material, space-charge effects at high currents, and spectral bandwidth (not perfectly monochromatic light). When you work near threshold, use consistent units, record uncertainties, and repeat with multiple wavelengths for a reliable slope-intercept analysis.
1) What is the minimum information needed to calculate emission?
Provide one light value (energy, frequency, or wavelength) and one material value (work function, threshold frequency, or threshold wavelength). The calculator derives the rest and reports whether emission is expected.
2) Why does increasing intensity not increase KEmax?
KEmax depends on photon energy (frequency), not on how many photons arrive. Higher intensity means more photons per second, so the electron count can rise, but each electron’s maximum energy is unchanged.
3) Why does the calculator set KE to zero below threshold?
When E < φ, electrons cannot overcome the surface barrier, so emission is not expected. Reporting KE = 0 helps keep derived quantities like stopping potential and speed physically consistent in that case.
4) Is the electron speed formula always valid?
It uses the nonrelativistic approximation v = √(2KE/me). This is accurate for photoelectric energies of a few eV to a few tens of eV, where v remains far below the speed of light.
5) What does “threshold wavelength” mean physically?
It is the longest wavelength (lowest frequency) that can still eject electrons for a given surface. Light with wavelength longer than λ0 has photons that carry too little energy to overcome φ.
6) How should I choose quantum efficiency for the photocurrent estimate?
Use a measured or datasheet value when possible. If unknown, treat it as a scenario parameter (e.g., 1–50%). The estimate assumes ideal collection, so real currents can be lower due to geometry and losses.
7) What is a good way to validate results?
Try two independent light inputs that represent the same radiation (e.g., wavelength and frequency). Also check that Vs numerically matches KEmax in eV and that λ0 decreases as φ increases.
Measure light, predict electrons, and learn quantum behavior today.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.