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Photoelectric Effect Calculator

The experiment that proved light comes in packets (photons) and earned Einstein his Nobel Prize.

Photon frequency (Hz)

Work function φ (eV)

Kinetic energy (eV)

1.836

KE = hf − φ

Photon energy (eV): 4.136

What you entered

Photon frequency (Hz): 1000000000000000Work function φ (eV): 2.3

1
Photon energy E = hf
6.626e-34 × 1.000e+15= 4.1357 eV
2
KE = hf − φ
4.1357 − 2.3= 1.8357 eV
3
Electron emitted?
E > φ?= Yes

Result

Kinetic energy (eV): 1.836

A photon at 1.00e+15 Hz (4.136 eV) ejects an electron with 1.836 eV of kinetic energy (work function = 2.3 eV).

Photoelectric effect: photon energy against work function

Photon energy is Planck's constant times frequency. Electrons are emitted only if that exceeds the material's work function.

Frequency (Hz)	Work function (eV)	Photon energy (eV)	Kinetic energy (eV)	Emitted?
5e14	2.3	2.0678	0.0000	No
1e15	2.3	4.1357	1.8357	Yes
2e15	2.3	8.2713	5.9713	Yes
1e15	4.5	4.1357	0.0000	No
1.5e15	4.5	6.2035	1.7035	Yes

Rows one and two are the same material at two frequencies, and the threshold is absolute: below it no electrons are emitted at all, no matter how bright the light. That is the observation classical wave theory could not explain and which forced the photon concept - brightness increases the number of electrons but never their energy, while frequency does the opposite. Rows two and four use the same frequency on different materials, showing the work function alone deciding the outcome. Einstein received the Nobel Prize for this explanation rather than for relativity.

Why this disproved classical wave theory

Classical physics predicted that brighter light (any frequency) should eventually eject electrons. Instead, experiments showed that only light above a threshold frequency works, no matter how bright — Einstein explained this by proposing that light energy comes in discrete packets (photons), each carrying E = hf.

The work function is the escape cost

Each metal has a characteristic work function (φ) — the minimum energy needed to free an electron from the surface. If the photon's energy (hf) exceeds φ, the leftover energy becomes the electron's kinetic energy; if not, no electron escapes regardless of light intensity.

Frequently asked questions

UV light at 300 nm hits a sodium surface (work function φ = 2.28 eV). What KE do the ejected electrons have?

Photon energy: E = hc/λ = (6.626×10⁻³⁴ × 3×10⁸)/(300×10⁻⁹) = 6.63×10⁻¹⁹ J = 4.14 eV. KE = E − φ = 4.14 − 2.28 = 1.86 eV. Below 544 nm (threshold wavelength for sodium), no electrons are ejected regardless of light intensity.

Why did the photoelectric effect prove light is quantized?

Classical wave theory predicted that brighter light of any color should eventually eject electrons. Experiments showed: (1) below a threshold frequency, no electrons are ejected no matter how bright; (2) above it, electrons are ejected instantly even in dim light. Only photon theory (E = hf) explains both observations.

How is the photoelectric effect used in technology?

Solar cells are based on the photoelectric effect — photons knock electrons free in semiconductor junctions, creating current. Photomultiplier tubes, night vision, light meters, and automatic doors all detect photons ejecting electrons from a surface. It's also the basis of photoelectron spectroscopy in chemistry.