Planck constant

• 1. The Desperate Act Of 1900

  ›

  Max Planck stood before the problem of black-body radiation in the final years of the nineteenth century. He needed a mathematical expression to predict the observed spectral distribution of light emitted by physical bodies. Existing theories failed to match reality across all wavelengths. Wien's law worked for short wavelengths and high temperatures but broke down elsewhere. Lord Rayleigh had derived a formula that predicted long wavelengths reasonably well yet failed dramatically at short wavelengths. This failure became known later as the ultraviolet catastrophe.

  Planck hypothesized that equations of motion for light described harmonic oscillators for each possible frequency. He examined how entropy varied with temperature while trying to match existing laws. His initial result gave an approximate function for the spectrum. The expression included a constant he called h, which was thought to be an auxiliary quantity. He soon realized his solution was not unique because different solutions yielded different entropies. To save his theory, Planck used statistical mechanics, describing it as "an act of desperation".

  He imposed a new boundary condition requiring energy quantization. Planck stated this was "a purely formal assumption" and admitted he did not think much about it at the time. Applying this approach to Wien's displacement law showed the energy element must be proportional to oscillator frequency. He calculated the value from experimental data on black-body radiation. His result fell within 1.2% of the currently defined value.

• 2. Light As Packets Of Energy

  ›

  Albert Einstein published a paper in 1905 discussing the photoelectric effect using light quanta. Heinrich Hertz had published the first thorough investigation of electron emission from metal surfaces in 1887. Philipp Lenard conducted another particularly thorough study in 1902. Before Einstein's work, electromagnetic radiation like visible light behaved as waves according to classical physics. Scientists measured intensity as energy transferred per unit time and space.

  The kinetic energy of emitted photoelectrons remained independent of light intensity but depended linearly on frequency. If frequency dropped below a threshold corresponding to the material's work function, no electrons were emitted regardless of brightness. Rising intensity caused more photoelectrons to emit with identical kinetic energy rather than higher energy for fewer particles. Einstein explained these observations by proposing light itself is quantized into small packets called photons.

  The size of these energy packets matched Planck's earlier "energy element". The constant of proportionality between incident light frequency and photoelectron kinetic energy proved equal to the Planck constant h. Robert Andrews Millikan later confirmed Einstein's predictions through experimental work. This discovery earned Einstein the Nobel Prize in Physics in 1921.

• 3. Electrons In Discrete Orbits

  ›

  John William Nicholson developed an atomic model in 1912 where electron angular momentum related by h divided by two. Niels Bohr quoted Nicholson in his own 1913 paper about the hydrogen atom. An electron within this Bohr atom could only possess certain defined energies determined by specific equations involving the speed of light and the Rydberg constant. This approach allowed Bohr to account for the Rydberg formula describing hydrogen spectra.

  Bohr introduced the quantity known as the reduced Planck constant as the quantum of angular momentum. He used this value alongside other constants to define discrete angular momentum values within early atomic theory. The transition from one energy level to another produced visible light at wavelengths like 656 nanometres appearing red. These transitions demonstrated how electrons moved between fixed orbits rather than continuous paths. The model explained why atoms emit light at specific frequencies instead of a broad spectrum.

• 4. The Tradeoff Of Measurement

  ›

  Werner Heisenberg formulated fundamental limits on measurement precision using the Planck constant to relate position and momentum uncertainties. Given numerous particles prepared in identical states, uncertainty in their position and uncertainty in their momentum obeyed a specific inequality. The inverse relationship forced a tradeoff in quantum experiments where measuring one quantity precisely made the other imprecise. One example involved time versus energy pairs following similar rules.

  A cornerstone of the entire theory lay in the commutator relationship between position operator and momentum operator. This mathematical structure ensured that physical action could not have arbitrary values but was restricted to integer multiples of a very small quantity. Classical physics failed to explain quantization of energy while modern quantum theory replaced fixed trajectories with wavefunctions spread through space and time. The uncertainty principle became a defining feature distinguishing microscopic behavior from macroscopic expectations.

• 5. Matter As Waves In Space

  ›

  Louis de Broglie generalized the Planck-Einstein relation in 1923 by postulating that the constant represented proportionality between momentum and quantum wavelength for any particle. This hypothesis extended beyond photons to include all elementary particles like electrons or neutrons. Experiments confirmed this idea soon after its proposal. The de Broglie wavelength of a particle equals Planck's constant divided by linear momentum.

  These relations formed temporal and spatial parts of special relativistic expressions using four-vectors. The energy of a photon with angular frequency related directly to the constant while linear momentum connected to angular wavenumber. Electrodynamics incorporated these relationships throughout quantum theory. The concept demonstrated that matter possessed an associated wavelength inversely proportional to its momentum, challenging classical notions of solid objects moving along predictable paths.

• 6. The Kilogram Fixed By Light

  ›

  Metrologists fixed the exact value of the Planck constant in 2018 to redefine the SI unit of mass. Technologies such as the Kibble balance measured the kilogram by fixing this numerical value when expressed in joule-seconds. The metre and second were already defined through the speed of light and hyperfine transition of caesium-133 atoms. This change eliminated reliance on physical artifacts kept in vaults near Paris.

  The new definition stated the kilogram is determined by taking the fixed numerical value of h to be exactly 6.62607015 times ten to the minus thirty-four joule-seconds. Since the reduced Planck constant has an exact defined value, calculations involving it achieve arbitrary precision without limiting uncertainty. This redefinition anchored mass measurement to fundamental constants rather than human-made standards. The decision took place during voting at the General Conference on Weights and Measures in Versailles, France, in November 2018.