Illustrated Physics
physics, drawn
Concept

Stimulated emission — where it appears

The emission of a photon by an excited atom when triggered by another photon of the same frequency, the new photon matching the first in direction and phase. It is the amplifying process in lasers and masers, and Einstein deduced it in 1917 from the balance of thermal radiation.

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

Why a flip of the spin takes eleven million years. Spontaneous emission rates against frequency on logarithmic axes. The two lines are the rates an electric dipole of e a₀ and a magnetic dipole of one Bohr magneton would give, both rising as the cube of the frequency; they differ by α²/4, 1.3 × 10⁻⁵, the square of the ratio of the two moments. Measured lines sit near them: Lyman α at 6.3 × 10⁸ s⁻¹, Hα and sodium's D line near 10⁸, and hydrogen's 21 cm line at 2.87 × 10⁻¹⁵ s⁻¹ — a lifetime of 11.0 million years. Its slowness is two factors multiplied: a magnetic moment rather than an electric one, and a frequency nearly a million times lower, cubed.

The line that takes eleven million years

A hydrogen atom in its ground state can flip its electron's spin relative to the proton's and emit a photon of 21 centimetres. Left alone, one atom takes eleven million years to do it. The Galaxy is nonetheless bright at that wavelength, because there is so much hydrogen, and because the flip is so slow that the line's brightness counts atoms without caring how hot they are.

quantum · Atomic spectra The circle of electrons a wave can talk to. Electron velocities along and across the magnetic field, in units of c. Shaded: a horseshoe of 10 keV electrons (speed 0.195c), the shape a beam takes when it is driven down into a strengthening field, with the electrons moving up along the field missing. Curves: the electrons a wave travelling across the field can exchange energy with, for wave frequencies of 0.995, 0.980, 0.960 times the cyclotron frequency. Because a faster electron is heavier and circles more slowly, at Ω/γ, each resonance is a semicircle of radius c√(1 − ω²/Ω²): 0.100, 0.199, 0.280c. A wave at 0.981Ω resonates with the horseshoe's middle.

The radio that only heavier electrons can make

Above every aurora the Earth broadcasts a gigawatt of radio that no one on the ground can hear. It comes out just below the frequency at which electrons circle the field there, and it is a maser — amplified by the electrons themselves. The surprise is what makes the amplifier work. Without relativity it could not: summed over every electron, a wave at the circling frequency is always absorbed. The few per cent by which a fast electron is heavier, and circles more slowly, is not a correction to the mechanism. It is the mechanism.

astrophysics · Radiating charge

Named alongside it

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

Column densityCyclotron frequencyCyclotron motionDipole fieldFine structure constantHyperfine structureLandau dampingMagnetic dipole transitionMagnetospherePopulation inversionRelativistic massSpin temperature

All concepts