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Planck constant

portrait of Planck

The constant factor which relates the energy of a photon to its frequency, = (by definition) 6.626 070 15 × 10⁻³⁴ joule seconds. The value was fixed by Resolution 1 of 26ᵗʰ meeting of the CGPM in 2018, and became effective 20 May 2019. Symbol, h.

For comparison with a previous value determined experimentally: according to the 2014 CODATA recommended values, it was 6.626 070 040 × 10⁻³⁴ joule-seconds, with a standard uncertainty of 0.000 000 081 × 10⁻³⁴.

It is named for the German physicist Max Planck (1858 – 1947).

It is often encountered as the reduced Planck constant, symbol ħ (pronounced “h bar”), which is h divided by 2 pi, or 1.054 571 800 x 10⁻³⁴ J s.

Why fix the value of the Planck constant?

At its 24ᵗʰ meeting (Paris, October 2011), the CGPM decided to declare in advance its intention to make the value of the Planck constant a matter of definition, rather than something to be determined experimentally. The new value was to be exactly 6.626 06X × 10⁻³⁴ joule seconds, where X stands for one or more yet to be determined digits. The new definition was not to be adopted before 2014.

This move was part of a grand strategy to base SI upon infinitely rediscoverable natural constants, eliminating any dependence on physical prototypes like the International Prototype of the Kilogram, or two scratches on a metal bar. Earlier, that way of defining the meter had been eliminated by fixing the value of the speed of light in meters per second. Since 1967 the second is the time it takes a cesium-133 atom to emit a certain number of wavelengths of light under specific conditions. The second can now be realized to more decimal places than any other unit. If you know the speed of light exactly, and the second, you have defined the length of the meter.

The Planck constant is given in joule seconds.* The joule, a unit of energy, is

$a fraction, meter squared times kilogram over seconds squared$ .

Setting a fixed numerical value for h makes h exactly equal to that number times this fraction. Meters and seconds we know, so we can solve for the kilogram. The algebra is easy, but the realization with apparatus is extremely challenging.

Planck's was one of two constants which could have been used to define the kilogram, the other being Avogadro's. In the end, after intensive investigation of the value of both constants, the Planck constant was chosen, and is now the constant from which the kilogram is realized.

*A note: Instead of seconds, metrologists use reciprocal hertz (Hz⁻¹, i.e. 1/Hz). We have avoided this complication.