Illustrated Physics
physics, drawn
Concept

Ionisation energy — where it appears

The least energy needed to remove an electron from an atom, molecule or ion: 13.6 electronvolts for hydrogen's ground state. Light whose photons each carry less can still ionise if it is intense enough, by absorbing several photons at once or by tunnelling through the barrier its field creates.

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

What correlation is worth, to a helium atom and to H⁻. The energy needed to remove the second electron, by three descriptions, as a fraction of the measured value, for the negative hydrogen ion and for helium. Helium: one shared orbital 23.07 eV, one electron in and one out 23.83 eV, measured 24.59 eV — the simple picture is 94 per cent right. H⁻: −0.74, 0.362 and 0.755 eV — the simple picture is not merely inaccurate but has the wrong sign. The energy the simple picture misses — the electrons avoiding each other — is about 1.5 eV in both; in helium it is a small correction to 24.6 eV, and in H⁻ it is everything.

The ion that exists because its electrons keep apart

Add a second electron to a hydrogen atom and it holds on, by three-quarters of an electronvolt. The simplest respectable calculation says it should not — that the two electrons, sharing one orbital, repel each other more than the proton can hold them, and the ion falls apart. The same calculation gets helium's energy right to two per cent. The difference is not a failure of the method but a measure of what it leaves out: the two electrons avoiding each other. In helium that is a small correction. In the negative hydrogen ion it is the whole of the binding, and that ion is what makes the Sun opaque.

quantum · Atomic structure A hydrogen atom tilted by a laser field. The potential energy of hydrogen's electron along the direction of a laser's electric field at the field's peak, in atomic units (one unit of energy is 27.2 eV, one of length 0.053 nm), for peak intensities of 3 × 10¹³ and 10¹⁴ W/cm² and at the barrier-suppression intensity, 1.37 × 10¹⁴; the dashed line is the bound level, 13.6 eV below the ionisation limit. The field tips the Coulomb well into a barrier on one side. At 3 × 10¹³ W/cm² the barrier is 15 atomic units thick at the level — 0.8 nm — at 10¹⁴, 6; at the suppression intensity its top has fallen to the level and the electron can leave without tunnelling at all. The barrier is real only for the fraction of the laser's period that the field stays near its peak.

The atom a light wave opens like a wall

Red light cannot free an electron from hydrogen: each photon carries 1.55 electronvolts and the electron is bound by 13.6. Make the light intense enough, though, and the atom ionises anyway — by absorbing nine photons at once, or, at higher intensity, by having its potential tipped over by the light's electric field until the electron tunnels out through the side. Which of the two happens is decided by a single ratio, found by Leonid Keldysh in 1964: how long the electron needs to get through the barrier, against how long the field holds still. The tunnelling side of that ratio is where attosecond physics begins.

quantum · Tunnelling

Named alongside it

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

Atomic structureAttosecond pulseEffective nuclear chargeElectron correlationHelium atomHigh harmonic generationKeldysh parameterLaserMultiphoton ionisationNegative ionPonderomotive energyScreening

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