Photoelectric Effect Work Function Calculator

Calculation mode

Choose the known measurements. The calculator derives the rest automatically.

Frequency

Wavelength

Maximum kinetic energy (Kmax)

Often measured from electron energy analysis.

Stopping potential (Vs)

Kmax = eVs. Use a nonnegative value.

Threshold frequency (f0)

At threshold, electrons just escape with Kmax ≈ 0.

Threshold wavelength (λ0)

Cutoff wavelength above which emission stops.

Formula used

Einstein photoelectric equation links photon energy to electron emission:

E = h f = h c / λ
K_max = E − φ
K_max = e V_s
Threshold: φ = h f₀ = h c / λ₀

Here, h is Planck’s constant, c is light speed, e is elementary charge, φ is the work function, and V_s is the stopping potential.

How to use this calculator

Select the measurement set you have in Calculation mode.
Enter frequency or wavelength and choose the correct unit.
Provide either K_max or V_s, or use threshold inputs.
Press Calculate to show results above the form.
Use CSV or PDF buttons to export your computed values.

Example data table

Material	Frequency	Stopping potential	Computed work function
Sodium (example)	6.2 × 10¹⁴ Hz	0.75 V	≈ 1.81 eV
Zinc (example)	9.0 × 10¹⁴ Hz	0.50 V	≈ 3.22 eV
Copper (example)	1.1 × 10¹⁵ Hz	0.90 V	≈ 3.65 eV

These values are illustrative for practice and validation.

Built for clean classroom, lab, and engineering workflows.

Photoelectric Effect Work Function Guide

1) What the work function represents

The work function (Φ) is the minimum energy needed to eject an electron from a material surface. It is usually reported in electronvolts (eV). Typical values are about 2–5 eV for many metals, while alkali metals can be lower. A smaller Φ means electrons are emitted using lower-frequency light.

2) Energy balance behind emission

Einstein’s photoelectric equation links the incoming photon energy to electron emission. Photon energy is E = h f, where h is Planck’s constant and f is frequency. When emission occurs, the excess energy appears as the electron’s maximum kinetic energy: K_max = h f − Φ.

3) Threshold frequency and cutoff wavelength

The threshold frequency is f₀ = Φ / h. Light below this frequency cannot eject electrons, regardless of intensity. A related parameter is the cutoff wavelength λ₀ = c / f₀. For example, Φ = 2.0 eV corresponds to a cutoff wavelength near 620 nm (visible red).

4) Stopping potential connects to electron energy

In experiments, a reverse voltage can stop the most energetic electrons. The stopping potential V_s satisfies e V_s = K_max. This calculator can compute Φ from measured V_s and frequency (or wavelength), helping you infer material properties from laboratory data.

5) Using wavelength or frequency inputs

You can enter light as frequency (Hz) or as wavelength (m, nm, or Å). Internally, wavelength is converted using f = c / λ. This lets you work with spectroscopy-style data (wavelength) or electronics-style data (frequency) without manual conversions.

6) Common units and practical ranges

Photon energies for ultraviolet light often fall in the 4–10 eV range, while visible photons are roughly 1.6–3.1 eV. If your computed K_max becomes negative, the chosen Φ is too large for the given light, indicating no emission under the idealized model.

7) Intensity versus frequency (key interpretation)

Increasing intensity raises the number of emitted electrons (current), but it does not increase K_max. Only frequency changes photon energy. This distinction is a classic result that helped establish the quantum nature of light.

8) Measurement tips and uncertainty

Real surfaces may oxidize or be contaminated, shifting the effective work function. Temperature and surface roughness can also matter. For best results, measure V_s at several frequencies and fit a straight line of V_s versus f; the intercept estimates Φ / e.

FAQs

1) What is the work function measured in?

Work function is commonly measured in electronvolts (eV). One eV equals the energy gained by an electron across a 1‑volt potential difference, making it convenient for surface and photon-energy calculations.

2) What happens if photon energy is less than the work function?

No photoelectrons are emitted in the ideal model. The photon energy is insufficient to overcome the binding energy at the surface, so the emission threshold is not reached.

3) How do I get frequency from wavelength?

Use f = c / λ, where c is the speed of light. If λ is in nanometers, convert to meters first by multiplying by 10⁻⁹.

4) Why does stopping potential relate to maximum kinetic energy?

The reverse voltage removes kinetic energy from electrons. The smallest voltage that halts the most energetic electrons satisfies eV_s = K_max, linking electrical measurements to electron energy.

5) Does higher intensity increase electron kinetic energy?

No. Higher intensity mainly increases the number of photons arriving per second, so more electrons may be emitted, but each photon still carries the same energy set by frequency.

6) Can this calculator estimate threshold wavelength?

Yes. If you know Φ, it can compute the threshold frequency f₀ = Φ/h and the cutoff wavelength λ₀ = c/f₀, which marks the emission boundary.

7) Why might my experimental work function differ from tables?

Surface contamination, oxidation, roughness, and temperature can shift the effective work function. Instrument calibration and contact potentials may also introduce offsets in measured stopping potentials.