Illustrated Physics
physics, drawn
Concept

Nuclear recoil — where it appears

The motion a nucleus takes up when it absorbs or emits a particle, by momentum conservation. Its energy goes as the momentum squared over twice the mass, so a heavy nucleus can absorb almost any momentum for very little energy.

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

A mass that goes missing as light. For six captures of a slow neutron — ¹H to ²H, ¹²C to ¹³C, ⁵⁶Fe to ⁵⁷Fe, ²⁸Si to ²⁹Si, ³⁵Cl to ³⁶Cl and ³²S to ³³S — the mass that disappears, the atom plus the neutron less the atom formed, in thousandths of an atomic mass unit, against the energy released as gamma rays, in MeV, both computed from the tabulated atomic masses. All six lie on the line Δm = E/c², whose slope is one atomic mass unit per 931.494 MeV: ¹H → ²H loses 2.388 mu and releases 2.225 MeV; ¹²C → ¹³C loses 5.310 mu and releases 4.946 MeV; ⁵⁶Fe → ⁵⁷Fe loses 8.208 mu and releases 7.646 MeV; ²⁸Si → ²⁹Si loses 9.097 mu and releases 8.474 MeV; ³⁵Cl → ³⁶Cl loses 9.211 mu and releases 8.580 MeV; ³²S → ³³S loses 9.277 mu and releases 8.642 MeV. Drawn this way the line is a definition — the energies were computed from the masses. The experiment of 2005 measured the two quantities for silicon and sulphur independently, the masses as frequencies and the energies as angles, and asked whether they still fell on it.

The test of mass and energy that needs a ruler

The most direct test of E = mc² weighed two silicon atoms and measured a gamma ray. A silicon-28 nucleus that captures a slow neutron becomes silicon-29 and loses three ten-thousandths of its mass as gamma rays; weigh both atoms in a trap where they circle a magnetic field, measure the gamma rays by the angle at which a silicon crystal diffracts them, and the two sides agree to four parts in ten million. What the comparison needed is the interesting part: the recoil of the atom, a correction four hundred times larger than the precision, computed from the momentum relativity gives to light; angles of a few hundred picoradians; and a chain of constants tying a frequency and a ruler to the same number.

relativity · Mass-energy The price of a pair depends on who pays it. The lowest energy of a photon that can make an electron–positron pair when struck on a stationary partner, against the partner's mass: 2mc²(1 + m/M), from requiring that the total four-momentum have the invariant mass of what is left at rest in the centre of momentum. For a lead nucleus it is 2mc² to better than one part in a hundred thousand, the figure every textbook quotes. For a proton it is 0.054 per cent above. For a free electron it is exactly twice, 4mc², or 2.04 MeV, even though the partner is the very same mass as the pair's members. The rest energy created is unchanged; what rises is what has to be carried off by the partner and the pair together.

The partner that sets the price of a pair

Every textbook says it takes 1.02 MeV to make an electron and a positron from light, twice the electron's rest energy. Done in empty space, it cannot be done at any energy at all. Next to a lead nucleus it costs 1.02 MeV. Next to a lone electron, a particle exactly as heavy as the ones being made, it costs 2.04. Nothing about the pair has changed. What changes the price is who has to carry the momentum away.

relativity · Mass-energy

Named alongside it

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

AntiprotonAtomic mass unitBethe heitler formulaBinding energyBragg diffractionFour-momentumInvariant massE = mc²Neutron capturePair productionPenning trapPlanck constant

All concepts