What is the photoelectric effect?

The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency strikes it. Albert Einstein explained it in 1905 by treating light as discrete packets (photons), each carrying energy E = hf. If that energy exceeds the metal's work function φ, the surplus appears as kinetic energy of the ejected electron: KE = hf − φ. The discovery earned Einstein the 1921 Nobel Prize in Physics and was foundational evidence for quantum mechanics.

What is the work function, and why does it differ between metals?

The work function φ is the minimum energy needed to liberate one electron from the surface of a metal. It varies because different metals bind their conduction electrons with different strengths. Alkali metals like caesium (1.95 eV) have very loosely bound electrons, so even visible red light can eject them. Transition metals like platinum (5.65 eV) need deep-UV photons. The work function is not a fundamental constant — it depends on surface cleanliness, crystal face orientation, and temperature.

How does stopping voltage relate to kinetic energy?

Stopping voltage Vₛ is the reverse potential you apply across the photoelectric cell to just stop the fastest ejected electrons (those with maximum KE). The relationship is simply eVₛ = KE, so Vₛ = KE / e, where e = 1.6022×10⁻¹⁹ C. If you measure Vₛ experimentally and know the photon frequency, you can calculate Planck's constant h from the slope of a Vₛ-vs-f graph — which is exactly how Millikan verified Einstein's equation in 1916.

Why does light below the threshold frequency never eject electrons, no matter how bright?

Because brightness (intensity) increases the number of photons, not the energy of each individual photon. An electron must absorb one whole photon at a time, and if hf < φ the photon simply does not carry enough energy to overcome the work function, regardless of how many photons per second arrive. Only increasing the frequency (shortening the wavelength) increases individual photon energy.

What units does this calculator use?

Work function can be entered in eV (more intuitive for atomic-scale energies) or in joules. Frequencies are displayed in THz (terahertz) to keep numbers manageable; wavelengths are in nanometres. Kinetic energy and photon energy results are shown in eV for easy comparison with work functions, with the joule equivalent shown in the working steps. All internal arithmetic is done in SI base units to avoid rounding errors.

Can I use this for X-ray or gamma-ray photons?

Yes — just enter the wavelength in nm. Hard X-rays have wavelengths of 0.01–10 nm and gamma rays go below 0.01 nm. The calculator uses exact values of h and c, so it handles any photon frequency in the electromagnetic spectrum. At very high photon energies the simple KE = hf − φ still holds, though in practice Compton scattering and pair production become more relevant at MeV energies.

Photoelectric Effect Calculator

Q: What units does this calculator use?

Work function can be entered in eV (more intuitive for atomic-scale energies) or in joules. Frequencies are displayed in THz (terahertz) to keep numbers manageable; wavelengths are in nanometres. Kinetic energy and photon energy results are shown in eV for easy comparison with work functions, with the joule equivalent shown in the working steps. All internal arithmetic is done in SI base units to avoid rounding errors.

Q: Can I use this for X-ray or gamma-ray photons?

Yes — just enter the wavelength in nm. Hard X-rays have wavelengths of 0.01–10 nm and gamma rays go below 0.01 nm. The calculator uses exact values of h and c, so it handles any photon frequency in the electromagnetic spectrum. At very high photon energies the simple KE = hf − φ still holds, though in practice Compton scattering and pair production become more relevant at MeV energies.

The photoelectric effect calculator applies Einstein’s 1905 photoelectric equation to solve for any of the five key quantities: maximum kinetic energy of emitted electrons, stopping voltage, threshold frequency, threshold wavelength, or individual photon energy. Select a preset metal or type any work function directly, enter the photon’s wavelength in nanometres or frequency in terahertz, and the result appears instantly with a full step-by-step working trace you can copy to your clipboard.

Background and theory

When a photon of frequency f strikes a metal surface, it transfers its entire energy E = hf to a single conduction electron. If that energy is at least as large as the metal’s work function φ, the electron escapes. Whatever energy remains above φ becomes the electron’s maximum kinetic energy:

KE = hf − φ

This is Einstein’s photoelectric equation. The constants are:

h = 6.6261 × 10⁻³⁴ J·s (Planck’s constant)
c = 2.9979 × 10⁸ m/s (speed of light)
e = 1.6022 × 10⁻¹⁹ C (elementary charge; also converts J to eV)

From the master equation the calculator derives four further results on demand:

Quantity	Formula	Meaning
Stopping voltage	Vₛ = KE / e	Reverse voltage that halts the fastest electrons
Threshold frequency	f₀ = φ / h	Minimum frequency that triggers emission
Threshold wavelength	λ₀ = hc / φ	Maximum wavelength (longest photon) that triggers emission
Photon energy alone	E = hf = hc / λ	Energy of one photon regardless of the metal

How it works

Choose your calculation target from the dropdown, select or type a work function, then enter the photon’s wavelength (nm) or frequency (THz). The tool converts between the two in real time — useful for checking that a 250 nm UV photon corresponds to roughly 1200 THz. For threshold frequency and threshold wavelength only the work function is needed; no photon input is required.

Every result shows the derived value in eV (easy to compare with work function tables) and the joule equivalent in the expanded working panel. Use “Show working” to trace each arithmetic step, then “Copy working” to paste it into a lab report or homework answer.

Worked example

Problem: A copper plate (φ = 4.5 eV) is illuminated with 200 nm UV light. What is the maximum kinetic energy of the ejected electrons, and what stopping voltage would halt them?

Step 1 — photon energy:

f = c / λ = 2.9979×10⁸ / (200×10⁻⁹) = 1.499×10¹⁵ Hz

E = hf = 6.6261×10⁻³⁴ × 1.499×10¹⁵ = 9.928×10⁻¹⁹ J = 6.20 eV

Step 2 — kinetic energy:

KE = E − φ = 6.20 eV − 4.5 eV = 1.70 eV

Step 3 — stopping voltage:

Vₛ = KE / e = 1.70 eV / e = 1.70 V

So the copper plate emits electrons with up to 1.70 eV of kinetic energy, and a 1.70 V reverse bias would stop the fastest ones entirely.

Now try it with caesium (φ = 1.95 eV) at the same wavelength: the kinetic energy rises to 4.25 eV — much easier to detect and the reason alkali metals were historically favoured in photocells.

Physical significance

The photoelectric effect was the first experimental proof that light energy is quantised. Classical wave theory predicted that any intensity of light would eventually eject electrons if given enough time — but experiments showed a hard threshold: below a certain frequency, no electrons were ever emitted regardless of brightness. Einstein’s photon hypothesis resolved this instantly. Today the effect underpins photodiodes, solar panels, X-ray detectors, image sensors, and photomultiplier tubes used in particle physics experiments.

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