Planck constant

Lore & Background

The Planck constant was formulated as part of Max Planck's successful effort to produce a mathematical expression that accurately predicted the observed spectral distribution of black-body radiation, known as Planck's law. In the last years of the 19th century, Planck was investigating the problem of black-body radiation posed by Kirchhoff some 40 years earlier. At the time, Wien's law fit the data for short wavelengths and high temperatures, but failed for long wavelengths, while the Rayleigh–Jeans law could reasonably predict long wavelengths but failed dramatically at short wavelengths. Approaching this problem, Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency, and derived an approximate mathematical function for the black-body spectrum. He tried to find a mathematical expression that could reproduce Wien's law and the empirical formula for long wavelengths, which included a constant, h, thought to be for Hilfsgröße (auxiliary quantity), and subsequently became known as the Planck constant. Planck soon realized his solution was not unique and resorted to the then-controversial theory of statistical mechanics, which he described as 'an act of desperation'. One of his new boundary conditions was to interpret the vibrational energy of N oscillators not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts, imposing the quantization of energy. Applying this to Wien's displacement law showed that the energy element must be proportional to the frequency of the oscillator, leading to the relation E = hf. Planck was able to calculate the value of h from experimental data on black-body radiation, obtaining 6.55×10⁻³⁴ J⋅s, within 1.2% of the currently defined value.

Reader's Guide

The Planck constant is of foundational importance in quantum mechanics, as it establishes the proportionality between a photon's energy and its frequency, and between a particle's momentum and the wavenumber of its associated matter wave. The closely-related reduced Planck constant, ℏ = h/(2π), is commonly used in quantum physics equations, relating energy to angular frequency and momentum to angular wavenumber. The constant's introduction marked a departure from classical physics, and its implications were further solidified by the work of Rayleigh, Jeans, and Einstein, who independently proved that classical electromagnetism could not account for the observed black-body spectrum, leading to the concept of the 'ultraviolet catastrophe'.

Did You Know?

• Planck later referred to the constant as the 'quantum of action'.
• The reduced Planck constant, ℏ, equals the Planck constant divided by 2π and is commonly used in quantum physics equations.
• Planck's initial calculation of h from experimental data gave 6.55×10⁻³⁴ J⋅s, within 1.2% of the currently defined value.