Before you can read the parent note, you need to be fluent in a handful of pictures and symbols. This page builds every single one from nothing, in an order where each rung stands on the one below it.
Everything starts here. If this picture is fuzzy, nothing else lands.
Picture: concentric rings around a bright centre. Inner rings are close and tightly held; outer rings are loose and far.
Why the topic needs it: electron gain enthalpy is the story of one new electron approaching this picture from outside and trying to settle into a ring. No atom picture → no story.
See Atomic Radius for how "how far out is the last shell" is measured, and Periodic Trends Overview for how these pictures line up in the periodic table.
Why "gaseous" matters: if the atom were in a liquid or solid, neighbours would tug on the electron too, muddying the measurement. We insist on (g) so we measure only the atom-versus-electron interaction — nothing else.
Picture: the same atom, but now the outer ring has one (or two) more electron dots than protons in the centre — so the whole thing is out of balance, tilted negative.
Why the topic needs it: worked example 3 adds a second electron (O−→O2−). To see why that costs energy you must first read O− as "already negative" — a picture that will repel the next electron.
Related energy quantities you'll meet next door: Ionization Enthalpy (energy to remove an electron — the reverse spirit) and Electronegativity (an in-a-bond version of "loves electrons").
Picture: the far electron "sees" a nucleus partly hidden behind a cloud of inner electrons — so it feels a weakened central pull.
Why the topic needs it: a bigger Zeff pulls the new electron in harder → energy dropped is larger → ΔegH more negative. This is the attraction half of the tug-of-war.
Picture: a tiny ring packed with dots; the incoming dot has nowhere comfortable to sit and gets shoved.
Why the topic needs it: this crowding is the entire reason for the star anomaly Cl > F. Fluorine's shell is small and crowded, so repulsion cancels a lot of the attraction; chlorine's is roomier, so the electron settles easily and more energy is released.
Picture: boxes for the room; five filled, one empty slot inviting the new electron.
Why the topic needs it: whether the incoming electron finds a gap in the current shell (energy released) or must start a whole new far-out shell (energy costly, like neon) decides the sign. And a half-filled (p3) or full (p6, s2) arrangement is unusually stable and resists newcomers — the exceptions in the "across a period" trend.