Illustrated Physics
physics, drawn
Concept

Blackbody radiation — where it appears

The thermal radiation of a body that absorbs everything falling on it, whose spectrum depends only on its temperature. Its shape is Planck's law, peaking at a wavelength inversely proportional to the temperature, and real surfaces are compared with it through their emissivity.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

An atom made of powers of n. Five properties of a hydrogen atom in a level of principal quantum number n, each divided by its value in the ground state, against n from 1 to 300 on logarithmic axes. The radius of a circular orbit rises as n², to 0.53 µm at n = 100; the orbital period as n³, to 1.5 × 10⁻¹⁰ s; the radiative lifetime of the circular state, from the Larmor loss on its orbit, as n⁵ — slope 5.000 — to 0.9 s. The binding energy falls as n⁻², to 1.36 meV, and the electric field that pulls the electron away falls as n⁻⁴, to 3.2 V/cm. Across n = 1 to 300 the lifetime changes by 2 × 10¹² and the ionising field by 8 × 10⁹.

The atom the size of a bacterium

Excite hydrogen's electron to the hundredth level and the atom is a micrometre across, bound by a thousandth of an electronvolt, pulled apart by the field of a torch battery, and — in its most circular state — able to live for nearly a second. Every one of those numbers is a power of n, and together they make the most exaggerated atom there is into one of the most useful.

quantum · Atomic spectra Each wavelength sees from a different height. The weighting functions of 7 infrared channels in a carbon-dioxide band — how much each height contributes to the radiance a satellite measures in that channel — for absorption strengths chosen so that the peaks sit at 3, 8, 14, 20, 27, 35, 43 km. Each is scaled to its own maximum. A channel's peak is where the carbon dioxide above that height amounts to one optical depth: deeper, its emission is absorbed on the way out; higher, there is too little gas to emit. Each function is about 17 km wide at half its peak, the same for every channel, because the absorber's density falls with one scale height, 7 km. The dotted curve is the temperature profile of the standard atmosphere, on its own scale from 180 to 300 K, whose cold tropopause and warm stratosphere the channels between them straddle.

The spectrum that is a thermometer at every height

A satellite looking down at the Earth in the infrared sees, at each wavelength, the glow of whatever layer of air that wavelength escapes from. In the wings of carbon dioxide's great absorption band the air is transparent and the satellite sees the ground; towards the band's centre the gas grows opaque and each wavelength escapes from higher up. A single spectrum is therefore a stack of thermometers at different heights, and weather forecasts are built on reading it. What cannot be read from it is anything much thinner than the ten to twenty kilometres of air each of those thermometers averages over.

quantum · Blackbody

Named alongside it

The objects these essays reach for when they reach for this one.

Bohr modelBrightness temperatureCorrespondence principleField ionisationInverse problemLapse rateLarmor formulaOptical depthPlanck lawRemote sensingRydberg atomScaling law

All concepts