Foundations — Metallic bonding — electron sea, band theory (intro)

This page assumes nothing. Before you read the parent note Metallic bonding you must be fluent with each item below. Each one gets: plain words → the picture → why the topic needs it. They are ordered so each new idea rests on the previous.

1. Atom, nucleus, electron

Plain words. An atom is the smallest neutral unit of an element. Inside it sits a tiny, heavy, positively-charged nucleus (protons + neutrons), and around it whir the light, negatively-charged electrons.

The picture. A dot in the middle (nucleus) with faint clouds of electrons around it. The whole atom is neutral: the number of positive charges in the nucleus equals the number of electrons outside.

Why the topic needs it. Metallic bonding is a story about which electrons stay and which leave. If you can't tell the nucleus from its electrons, "the electron leaves the atom" is meaningless.

2. Valence electrons vs core electrons

Plain words. Electrons live in layers (shells) at different distances. The valence electrons are the ones in the outermost occupied shell — the loosely-held ones. Everything underneath is the core (nucleus + inner electrons), which stays put.

The picture. Onion rings. The outermost ring holds the valence electrons (drawn loosely, ready to leave). The inner rings + nucleus form a tight bundle we call the ion-core or kernel.

Why the topic needs it. The parent's whole model is "positive kernels in a sea of valence electrons." Kernel = atom minus valence electrons. You must split every atom into these two parts in your head.

3. Ion, cation, anion

Plain words. An ion is an atom that has lost or gained electrons, so it is no longer neutral. Lost electrons → net positive → a cation. Gained electrons → net negative → an anion.

The picture. Take a neutral atom. Pluck one electron away: the leftover has one more proton than electron → it carries charge $+1$, written ${\text{Na}}^{+}$. The little superscript $+$ means "one unit of positive charge."

Why the topic needs it. In a metal, atoms become cations (${\text{Na}}^{+}$, ${\text{Mg}}^{2+}$, ${\text{Al}}^{3+}$). Bond strength depends on how much positive charge each kernel carries — so the superscript number is doing real work, not decoration. This also lets you contrast metals with Ionic bonding, where a cation hands its electron to a specific anion instead of a shared pool.

4. Electrostatic attraction

Plain words. Opposite charges pull together; like charges push apart. The pull between a positive and a negative charge is electrostatic attraction.

The picture. A $+$ and a $-$ with an arrow pulling them toward each other. Closer together or bigger charges → stronger pull.

Why the topic needs it. The metallic bond itself is nothing but electrostatic attraction between the positive kernels and the negative electron sea. No new force — just $+$ pulling on $-$, spread over the whole crystal.

5. Ionization energy & atomic radius

Plain words. Ionization energy is the energy needed to pull one electron off an atom — small ionization energy means the atom gives up an electron easily. Atomic (or ionic) radius is how big the atom/ion is — the distance from nucleus to outer edge.

The picture. A staircase: cheap first step (easy to remove the loosest valence electron), then a huge jump to remove a core electron. For radius: a balloon whose size shrinks when you increase the nuclear pull.

Why the topic needs it.

• Low ionization energy is why metals bond metallically at all — their valence electrons come off cheaply, feeding the sea.
• Radius controls the distance in Coulomb's rule: a smaller cation packs its charge closer, giving stronger attraction. This is the second lever behind Na < Mg < Al bond strength.

See Ionization energy & atomic radius for the full trend.

6. "Delocalised" vs "localised"

Plain words. A localised electron is stuck at one spot — belonging to a single atom or a single bond. A delocalised electron belongs to no single atom; it can roam over the whole structure.

The picture. Localised = a dog on a short leash tied to one post. Delocalised = a dog let loose in a huge fenced field — free anywhere inside, but it can't escape the metal.

Why the topic needs it. This one word separates the three bonding types you'll meet:

• Ionic bonding: electron localised on an anion.
• Covalent bonding & MO theory: electron localised in a bond between two atoms.
• Metallic bonding: electron delocalised over the whole lattice.

Delocalisation is why metals conduct: a free-roaming electron can drift when you apply a push.

7. Lattice / giant structure

Plain words. A lattice is a regular, repeating 3-D arrangement of particles — the same pattern stretching across the whole crystal. "Giant" means it repeats indefinitely, not a small molecule.

The picture. Ball-bearings stacked in neat rows and layers, extending in every direction. In a metal the balls are the kernels; the spaces between them hold the electron sea.

Why the topic needs it. Metals are giant lattices of kernels. Properties like malleability come from sliding whole layers of this lattice — you can't picture that without the lattice image first.

8. Electric field, current, conductivity

Plain words. An electric field is a push on charges (what a battery sets up in a wire). Current is the resulting flow of charge. Conductivity measures how easily a material carries current.

The picture. Tilt the field like tilting a table; the loose electrons (marbles) roll downhill → a steady drift = current.

Why the topic needs it. "Metals conduct" means: apply a field → delocalised electrons drift → current. Every conductivity claim in the parent, and the whole conductor/semiconductor/insulator table, is measured against this idea. See Electrical conductivity.

9. Energy level, orbital, and the jump to "bands"

Plain words. An electron in an atom can only sit at certain fixed energy levels — never in between, like rungs on a ladder. An orbital is one such allowed home for (up to two) electrons.

The picture. A ladder. Each rung is an allowed energy. Electrons fill from the bottom rung up.

Why the topic needs it — the band idea. When atoms come together, their identical ladder-rungs cannot stay identical (two electrons can't share the exact same state). So each shared rung splits into many slightly-different rungs — one per atom. With $N\approx 10^{23}$ atoms, the split rungs are so densely packed they look like a solid smear: a band.

10. The symbols in the parent's equations

Before you read the parent, decode these once:

Why the topic needs it. The parent's headline formula $n\propto e^{-E_g/(2k_{B}T)}$ just says: the number of free carriers falls off exponentially as the gap $E_g$ grows, and rises as temperature $T$ grows. Once you know each symbol, this sentence and the equation are the same thing.

Prerequisite map

Equipment checklist

Test yourself — cover the right side. If any answer is shaky, reread its section above before the parent note.

Ready? Now open the parent note.