Light that knocks out electrons
In 1887 Heinrich Hertz noticed that ultraviolet light made sparks jump more easily, and soon after, Wilhelm Hallwachs showed that UV light drains the charge of a negatively charged zinc plate. Light was freeing electrons from the metal. The puzzle was that the energy of those electrons did not depend on how bright the light was, only on its color.
In 1905 Albert Einstein explained why: light comes in packets, photons, each carrying an energy E = h × f. An electron absorbs one photon and escapes only if that photon brings more energy than the work function φ, the energy that binds electrons to the surface. Whatever is left becomes the electron’s kinetic energy:
K_max = h × f − φ
How the calculator works
You enter the wavelength of the light and pick a metal (or type your own work function). The calculator gives:
- the photon energy, E = 1,239.84 ÷ λ (in eV, with λ in nm)
- the maximum kinetic energy of the electrons, E − φ
- the stopping voltage, which equals K_max in volts
- the threshold wavelength λ₀ = 1,239.84 ÷ φ and threshold frequency
- the maximum speed of the electrons
Worked example
Violet light at 400 nm falling on sodium (φ ≈ 2.36 eV):
| Result | Value |
|---|---|
| Photon energy | 3.100 eV |
| Maximum electron energy | 0.740 eV |
| Stopping voltage | 0.740 V |
| Threshold wavelength | 525.4 nm |
| Threshold frequency | 570.6 THz |
| Maximum electron speed | about 510 km/s |
Any light with a wavelength longer than 525 nm, such as yellow or red light, cannot free electrons from sodium, however bright it is.
Other metals at 400 nm
| Metal | Work function | Threshold | Electrons at 400 nm? |
|---|---|---|---|
| Cesium | 2.14 eV | 579 nm | Yes, up to 0.96 eV |
| Potassium | 2.29 eV | 541 nm | Yes, up to 0.81 eV |
| Calcium | 2.87 eV | 432 nm | Yes, up to 0.23 eV |
| Zinc | 4.33 eV | 286 nm | No: needs ultraviolet |
| Copper | about 4.7 eV | 264 nm | No: needs ultraviolet |
That is why Hallwachs needed UV light for zinc: at 254 nm, a mercury lamp’s main line, the photons carry 4.88 eV, enough to free electrons with up to 0.55 eV.
Where it is used
Photomultiplier tubes and night-vision devices use cesium-based surfaces with low work functions to detect single photons. Photoelectron spectroscopy measures electron energies to identify elements and chemical bonds. Solar cells rely on a related process, the internal photoelectric effect, where photons free electrons inside a semiconductor rather than out of it.
Work functions depend on the crystal face, surface cleanliness and oxidation, so measured values vary by a few tenths of an electronvolt between sources.