The h in E = hf
The energy of a photon is its frequency times this number.
Science · Physics
The Planck constant
Introduced 1900
Physics — quantum mechanics
The Planck constant, symbol h, is the constant of proportionality between the energy of a photon and its frequency: E = hf. Max Planck introduced it in 1900 as what he later called an act of desperation, to make the theory of black-body radiation match experiment, and in doing so accidentally founded quantum mechanics. Energy, it turned out, comes in discrete packets. The constant has the dimensions of action — energy multiplied by time, the same as angular momentum — and its tininess is the reason quantum effects are invisible at everyday scales. The reduced constant ħ = h/2π appears throughout quantum mechanics, including in Heisenberg's uncertainty principle. Since 20 May 2019 h has had an exact defined value, 6.62607015 × 10⁻³⁴ joule seconds, and it is what now fixes the kilogram.
How to spot them
- ▸Its symbol is h, and its 'reduced' version wears a bar and equals h/2π
- ▸Introduced in 1900 by its author's own description as an act of desperation
- ▸Since 2019 it is exact by definition, and it is what defines the kilogram
- ▸Multiply it by a photon's frequency to get that photon's energy
- ▸It has the dimensions of action: energy times time
Key facts
Introduced in 1900 to cure the ultraviolet catastrophe of black-body radiation (1900)
Its author called the step an act of desperation and spent years trying to avoid it.
Since 20 May 2019 it has an exact value, and defining it fixes the kilogram (2019)
6.62607015 × 10⁻³⁴ joule seconds, exactly, by international agreement.
Divided by 2π it acquires a bar and turns up in Heisenberg's uncertainty principle
Δx Δp ≥ ħ/2; the reduced form is sometimes called the Dirac constant.
Combined with c and G it yields a length of about 1.6 × 10⁻³⁵ metres
The natural units its author proposed in 1899, independent of any human convention.
Its discovery won the 1918 Nobel Prize in Physics (1918)
Awarded for the discovery of energy quanta; the prize was presented in 1920.
Key ideas
- Classical physics predicted a black body would radiate infinite energy at short wavelengths — the 'ultraviolet catastrophe'. Assuming energy came only in multiples of hf cut off the high frequencies and matched the observed curve exactly.
- Because h is about 10⁻³⁴ in SI units, the quantum steps are absurdly small for anything the size of a cricket ball, which is why the world looks continuous.
- The constant sets the scale of the uncertainty principle: position and momentum cannot both be sharp, and the product of their uncertainties cannot fall below ħ/2.
Quick-fire facts
- •Named after Max Planck, who introduced it in a paper presented to the German Physical Society on 14 December 1900 — often taken as the birthday of quantum theory
- •Exact value since 2019: h = 6.62607015 × 10⁻³⁴ J s
- •The reduced Planck constant ħ = h/2π ≈ 1.054571817 × 10⁻³⁴ J s is also called the Dirac constant
- •Its dimensions are those of action, identical to angular momentum
- •Einstein used it in 1905 to explain the photoelectric effect, the work for which he won the 1921 Nobel Prize
- •Planck received the 1918 Nobel Prize in Physics for the discovery of energy quanta
- •Planck units — Planck length ≈ 1.6 × 10⁻³⁵ m, Planck time ≈ 5.4 × 10⁻⁴⁴ s, Planck mass ≈ 2.2 × 10⁻⁸ kg — are built from h, c and G
- •The Planck mass is oddly macroscopic: about the mass of a flea's egg, unlike the other Planck units
- •Robert Millikan measured h accurately in 1916 while trying, and failing, to disprove Einstein's photoelectric equation
- •The Kibble balance turns a fixed h into a measured mass, which is how the kilogram is realised today
Drill it — 9 cards
1 / 9new card
Sources
- NIST Reference on Constants, Units and Uncertainty — CODATA Value: Planck constant
- The Nobel Foundation — The Nobel Prize in Physics 1918