Planck's Constant

Determination of Planck's constant using LEDs

Planck's constant (h) is a fundamental physical constant, first introduced by the German physicist Max Planck in 1900. Its significance lies in showing that a quantum — a discrete packet of energy — can be calculated from the frequency of radiation using Planck's constant. It describes the behaviour of particles and waves at the atomic scale, as well as the particle-like nature of light.

An LED (light emitting diode) is a two-terminal semiconductor device that emits light. In its unbiased state, a potential barrier exists across the p–n junction of the LED. When a forward voltage is applied externally, this barrier height decreases. At a certain voltage the barrier becomes low enough that the LED begins to emit light: electrons crossing the junction are excited, and as they fall back to a lower energy state they release energy in the form of light. This specific voltage is known as the knee voltage, or threshold voltage. Beyond this point the current through the LED continues to rise while the voltage across it stays nearly constant.

Theory

When an LED emits light, the energy of the emitted photon is given by:

E = hc / λ

where

• c = speed of light
• h = Planck's constant
• λ = wavelength of the emitted light

At the knee voltage V, the energy supplied to each electron crossing the junction is:

E = eV

Since this energy is converted into the emitted photon's energy, equations (1) and (2) can be equated:

eV = hc / λ

By measuring the knee voltage V for LEDs of known, different wavelengths λ, this equation can be rearranged to solve directly for Planck's constant:

h = (e / c) λV

This calculation is repeated for each LED using its respective knee voltage and wavelength, and the average of the individual h values gives the final experimental estimate of Planck's constant.