Planck's constant
/ PLAHNK /
Planck's constant is the tiny number that sets the scale of the quantum world, the way the speed of light sets the scale of relativity. Everyday image: it is the 'grain size' of nature. Just as sand looks smooth from far away but is really made of grains, energy in the atomic world comes in grains rather than a smooth flow, and Planck's constant tells you how big a grain is. Because that grain is fantastically small, we never notice the graininess in everyday life.
Precisely, the energy carried by one photon of light equals Planck's constant times the light's frequency: E = h f. Here f is the frequency (in Hz) and h is Planck's constant, about 6.63 x 10^-34 joule-seconds (J s). A closely related version, the reduced Planck constant, written h-bar (h-bar = h / (2 pi), about 1.05 x 10^-34 J s), shows up whenever angles or rotations are involved. Planck's constant also fixes the smallest possible spread in the uncertainty principle and the size of the lump of angular momentum in the Bohr model.
Why it matters: h is one of the true fundamental constants of nature, and its extreme smallness is exactly why the quantum grain is invisible to us but decisive for atoms. Since 2019 it even defines the kilogram: the SI system now fixes h at an exact value and builds the unit of mass from it. Honest note: h is not zero and not adjustable; it is a fixed feature of the universe, and if it were larger, quantum effects would spill into everyday life.
A single photon of green light (frequency about 5.6 x 10^14 Hz) carries an energy of E = h f, which is roughly 3.7 x 10^-19 J, about 2.3 electron-volts. That is a whisper of energy, which is why one photon does nothing you can feel, yet a stream of them lights a room.
Photon energy is Planck's constant times frequency.
Planck's constant has units of joule-seconds, which is energy times time (or equivalently momentum times length); this combination is called action, so h is nicknamed the quantum of action.