Photoelectric Effect Formula
The photoelectric effect formula E = hf - φ calculates the kinetic energy of electrons emitted when light strikes a metal surface.
The Formula
When light with sufficient energy strikes a metal surface, it ejects electrons. This is the photoelectric effect, first explained by Albert Einstein in 1905.
The kinetic energy of the ejected electron equals the photon's energy minus the work function of the metal. If the photon energy is less than the work function, no electrons are emitted regardless of light intensity.
Variables
| Symbol | Meaning |
|---|---|
| KE | Maximum kinetic energy of the emitted electron (in joules, J, or electron volts, eV) |
| h | Planck's constant (6.626 × 10⁻³⁴ J·s, or 4.136 × 10⁻¹⁵ eV·s) |
| f | Frequency of the incident light (in hertz, Hz) |
| φ | Work function of the metal (minimum energy to free an electron, in J or eV) |
Common Work Functions
| Metal | Work Function (eV) |
|---|---|
| Cesium | 2.1 |
| Sodium | 2.3 |
| Aluminum | 4.1 |
| Copper | 4.7 |
| Gold | 5.1 |
Example 1
Ultraviolet light with frequency 1.2 × 10¹⁵ Hz strikes a sodium surface (φ = 2.3 eV). What is the maximum kinetic energy of emitted electrons?
Calculate photon energy: E = hf = (4.136 × 10⁻¹⁵)(1.2 × 10¹⁵)
E = 4.96 eV
KE = hf − φ = 4.96 − 2.3
KE = 2.66 eV
Example 2
Light with wavelength 400 nm strikes a copper surface (φ = 4.7 eV). Are electrons emitted?
Convert wavelength to frequency: f = c / λ = (3 × 10⁸) / (400 × 10⁻⁹)
f = 7.5 × 10¹⁴ Hz
Photon energy: E = hf = (4.136 × 10⁻¹⁵)(7.5 × 10¹⁴) = 3.10 eV
Compare: 3.10 eV < 4.7 eV (work function)
No electrons are emitted — photon energy is below the work function.
When to Use It
Use the photoelectric effect formula when dealing with light-matter interactions at the quantum level.
- Determining if a given light frequency can eject electrons from a specific metal
- Calculating the kinetic energy of photoelectrons
- Finding the threshold frequency or wavelength for electron emission
- Understanding solar cell and photovoltaic device physics
- Spectroscopy and surface analysis experiments