Illustrated Physics
physics, drawn
Concept

Nuclear spin — where it appears

The intrinsic angular momentum of an atomic nucleus, which gives it a small magnetic moment. A nucleus with spin precesses in a magnetic field at a frequency that identifies the element and its chemical surroundings, the basis of NMR and MRI.

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

The entropy each degree of freedom has not yet given up. The entropy carried by each kind of degree of freedom, drawn against the temperature at which it orders and hands that entropy over. Lattice vibrations freeze out around room temperature; electron spins in a paramagnetic salt order in the millikelvin range, which is what makes adiabatic demagnetisation work; and nuclear spins hold R ln(2I+1) — 11.5 joules per kelvin per mole for copper — down to some tens of nanokelvin, where their own dipolar interactions finally sort them out. A copper sample at a microkelvin therefore has a large entropy and violates nothing: its nuclear spin system has not reached its ground state, and the third law is a statement about ground states rather than about thermometers.

A law about spectra, not about heat

The third law is usually met as a statement about cooling. Its statistical form is a statement about a spectrum: the entropy of a system in its ground state is k ln g, and it vanishes only when the ground state is unique. Every apparent exception is a degeneracy or a system that never reached its ground state — and copper nuclei carry eleven joules per kelvin per mole down to a hundred nanokelvin without violating anything.

thermodynamics · Third law Position written as frequency. Four tubes of water side by side in a 1.5 T magnet, their protons all precessing at 63.87 MHz, until a gradient of 10 mT/m is switched on along the row. Then the field, and so the precession frequency, rises steadily across the row, by 425.8 Hz for every millimetre. The signal the receiving coil picks up is a sum of waves at different frequencies, and its spectrum is a picture: the amount of signal at each frequency is the number of protons at the corresponding position. The axis below is position and the axis above it frequency, and they are the same axis. Nothing has been focused. The radio wave at 64 MHz has a wavelength of 4.7 m in air, and the tubes are centimetres apart.

The image made of frequencies

A hydrogen nucleus in a magnetic field precesses at a frequency proportional to the field — 63.87 megahertz in a 1.5 tesla scanner. Make the field rise steadily across the body and every position precesses at its own frequency, so the radio signal the body gives off is a chord whose spectrum is a map of where the protons are. A magnetic resonance image is never focused. It is computed, as a Fourier transform of a signal recorded one number at a time, and its resolution, a millimetre, is set by how strong the gradient is and how long the signal is listened to — not by the wavelength of the radio waves, which is several metres.

quantum · Spin

Named alongside it

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

Chemical shiftDegeneracyEnergy levelsEntropyEquilibriumFourier transformGround stateLarmor precessionMagnetic field gradientMagnetic resonanceMagnetisationMicrostates

All concepts