Before we can rank stability, shift hydrides, or argue about singlets and triplets on the parent page the parent topic, we must earn every symbol it throws at you. Nothing below assumes you have seen chemistry notation before line one.
Picture a carbon atom as a tiny nucleus (a heavy positive lump) with electrons — light, negatively charged specks — living in "rooms" around it called orbitals. An orbital is just a region of space where an electron is likely to be found.
What figure s01 shows: the coral blob in the middle is the nucleus (positive); the green specks are electrons; the dashed lavender ovals are orbitals — the rooms electrons live in. Notice the electrons are outside the nucleus: all of chemistry happens out here, in the orbitals.
Why does chemistry care so much about pairs? Because electrons are most comfortable (lowest energy) when paired up, spinning in opposite directions inside the same room. A lone, unpaired electron is restless — and that restlessness is exactly what makes free radicals reactive (we meet them by name in §1).
Before any table, two counting words and the five characters of the whole story.
Now meet the five reactive intermediates — the cast the parent page keeps referring to. Each is defined by its electron count and charge.
Now the picture that makes the whole parent table click — the intermediates lined up by outer-electron count.
What figure s02 shows: left to right, electron count grows. The coral atom (6 e⁻, a + sign) is the carbocation — most starving. The butter atom (7 e⁻, one dot = one unpaired electron) is the free radical. The mint atom (8 e⁻, two dots = a lone pair, a − sign) is the carbanion — electron-rich. The lavender "C:" and its nitrogen partner on the right are the carbene and nitrene, also stuck at 6. The big arrow underneath is the moral: moving right = from grabbing to giving.
Read the same story as a table:
Outer electrons
Name(s)
What it feels
6 (a sextet, 2 short)
carbocation, carbene, nitrene
electron-starving → wants to grab
7 (one short, one unpaired)
free radical
mildly starving, restless
8 (a full octet) with a spare pair carrying the charge
This single reading unlocks the parent's unifying rule: + species are stabilised by pushing electrons toward them; − species are stabilised by pulling electrons away. Same rule, opposite directions.
The parent note says carbocations are "sp², planar" and carbanions are "sp³, pyramidal." Those labels describe shape, and shape decides how well an atom can spread out charge. They are built directly on the orbital "rooms" from §0 — carbon just mixes those rooms into new shapes.
What figure s03 shows: three carbons with the same central dot but different numbers of sticks. The mint one (left) has 4 sticks poking into 3-D — a pyramid (sp³). The coral one (middle) has 3 sticks all in a flat plane, with a pale lavender dumbbell (the empty p-orbital) standing straight up and down — that dumbbell is the carbocation's landing pad. The butter one (right) has just 2 sticks in a straight line (sp). Fewer things around carbon → flatter/straighter shape.
Why does the topic need this? Because a flat sp² carbocation has a clean, empty p-orbital pointing up and down — a perfect landing pad for neighbouring electrons to spill into. That geometry is why stabilisation (hyperconjugation, resonance) can even happen. Full details live in Hybridisation and s-character.
Carbenes and nitrenes each have two non-bonding electrons. Nature has two ways to place them, and the parent page hinges on this choice.
What figure s04 shows: on the left (singlet) both spare electrons crowd into ONE box, pointing opposite ways (↑↓) — paired, no lonely electron. On the right (triplet) the two electrons live in SEPARATE boxes, both pointing the same way (↑ ↑) — two lonely electrons, a diradical.
You do not need quantum spin maths here — just the picture of "both in one room" versus "one in each room." The words singlet/triplet are historical labels for these two arrangements.
The parent note leans on three "ways to move electron density." Each is a separate vault topic; here is the one-picture meaning so the parent's stability arguments make sense.
A single stick "—" between two atoms represents how many electrons?
Two — one shared pair.
Which geometry does sp² give, and what special orbital does it leave?
Flat/planar (120°), leaving one empty p-orbital perpendicular to the plane.
What is the difference between "↔" and "→"?
"↔" links resonance pictures of the same species; "→" means one thing becomes another.
Which curly arrow means one electron, and where is it used?
The single-barbed fish-hook arrow; used in radical (one-electron) mechanisms.
Draw the electron picture of a free radical vs a carbanion.
Radical = one dot (7 e⁻, unpaired); carbanion = a lone pair ":" carrying a − charge (8 e⁻).
Why does a triplet scramble geometry but a singlet preserve it?
Singlet forms both bonds at once (concerted, no time to twist); triplet is a diradical that forms one bond, pauses, and can rotate freely before the second — that rotation scrambles it.
Rank the three stabilising effects by strength.
Resonance (M) > hyperconjugation > inductive (I).
In a 1,2-shift, does the hydrogen carry its electrons?
Yes — it migrates as hydride H−, dragging its bonding pair.
Why does higher s-character hold a carbanion's lone pair better?
s-orbitals sit closer to the nucleus, so electrons are held tighter and lower in energy (sp > sp² > sp³).
