Metallic bonding — electron sea, band theory (intro): Question bank

True or false — justify

Metallic bonding is a subtype of ionic bonding.

False. Ionic bonds localise & transfer electrons to specific anions at fixed sites; metals delocalise & share electrons over the whole lattice — that shared pool is why they conduct and bend. See Ionic bonding.

A metal's electrical conductivity increases as you heat it.

False for metals. Electrons are already all delocalised, so heat frees no new carriers; instead hotter cations vibrate and scatter the moving electrons, so metallic conductivity falls with temperature. See Electrical conductivity.

A completely filled valence band means the solid must be an insulator.

False. Mg has a full 3s band, but the empty 3p band overlaps it — those overlapping empty states let electrons move, so Mg conducts. A full band blocks conduction only if a gap sits above it.

In the band model, more atoms in the crystal make each energy level spacing larger.

False.

N

atomic orbitals spread over a fixed energy window, so the spacing

\approx window / N \to 0

N \to 1 0^{23}

— the levels merge into a near-continuous band, not a wider spread.

A semiconductor conducts better when heated.

True. Heating promotes electrons across the small gap, and the carrier count grows as

n \propto e^{- E_{g} /2 k_{B} T}

— the opposite temperature trend from a metal. See Semiconductors & doping.

Aluminium has a stronger metallic bond than sodium.

True. Al donates 3 valence electrons vs Na's 1, and

Al^{3 +}

is smaller than

Na^{+}

; more electrons in the sea plus a tighter cation both strengthen the lattice–sea glue (m.p. 660 °C vs 98 °C).

Iron's hardness is fully explained by the simple "few s/p electrons" story.

False. Fe's partially-filled 3d orbitals also overlap and delocalise, adding many more electrons (~8 effective) to the sea — that extra 3d bonding, not the s/p picture, is why Fe is so hard and high-melting. See Transition metals & d-orbitals.

Diamond and silicon are both giant covalent, so both are insulators.

False. Both are group-14 giant covalent, but Si's gap (

\approx 1.1

eV) is small enough for thermal promotion while diamond's (

\approx 5.5

eV) is not — Si is a semiconductor, diamond an insulator.

Spot the error

"Na conducts because its 3s electron leaves the atom entirely and becomes a free ion."

The electron is delocalised, not ionised away as a separate particle — it roams the whole crystal while the

Na^{+}

kernels stay put. Conduction is drift of this shared sea, not migration of ions.

"The factor of 2 in

e^{- E_{g} /2 k_{B} T}

comes from splitting the band gap into two halves."

The 2 comes from the Fermi level sitting near mid-gap in an intrinsic semiconductor, so

E_{C} - E_{F} \approx E_{g} /2

in the Boltzmann factor. It is not an ad-hoc halving of the gap.

"Metals are malleable because their metallic bonds are weak."

Wrong cause. Metals bend because the electron sea is non-directional — slide a layer of cations and the sea just re-glues them, no bond points snap. The bonds can be very strong (tungsten m.p. > 3400 °C) yet still malleable.

"Ionic solids are malleable for the same reason metals are."

Sliding an ionic layer lines up like charges, causing repulsion and shattering. Only the metal's directionless sea survives shear; ionic lattices are brittle.

"A conductor is any material with

E_{g} > 0

but small."

A conductor has $E_{g} = 0$ — either bands overlap or the valence band is only half-filled. A small but nonzero gap is a semiconductor.

"Heating a metal frees more electrons from the cations, boosting conduction."

All valence electrons are already delocalised, so none are left to free. Heat only adds cation vibration that scatters carriers, lowering conductivity.

Why questions

Why can't sodium bond ionically with itself?

An ionic bond needs a donor and an acceptor, but Na has a low electronegativity — neither atom wants the extra electron, so no anion forms. The electrons instead pool into a shared sea.

Why do metals shine?

The free electrons absorb and immediately re-emit photons across a wide range of frequencies, reflecting most incident light — that broadband re-emission is the metallic lustre. See Electrical conductivity.

Why does a smaller cation radius strengthen the metallic bond?

Packing the same positive charge into a smaller volume brings the cores closer to the electron sea, so the electrostatic attraction between lattice and sea is stronger. See Ionization energy & atomic radius.

Why do we even need band theory if the electron sea already explains conduction?

The sea can't produce the discrete allowed/forbidden energy bands or predict the size of a band gap, so it can't cleanly separate insulators, semiconductors and conductors. Quantum band theory supplies the gap. See Covalent bonding & MO theory.

Why does Mg conduct despite having a filled 3s subshell?

Its empty 3p band overlaps the filled 3s band, so electrons find empty states right beside occupied ones with no gap to climb.

Edge cases

What is the band gap of a perfect conductor, and what does that mean physically?

E_{g} = 0

: empty states lie immediately above filled ones (overlap or half-filled band), so an applied field accelerates electrons with no energy barrier.

At absolute zero (0 K), does an intrinsic semiconductor conduct?

Essentially no — with

T \to 0

the factor

e^{- E_{g} /2 k_{B} T} \to 0

, so no electrons are thermally promoted across the gap; it behaves like an insulator.

If two atoms bond, how many molecular orbitals form, and how does that scale to a solid?

Two atomic orbitals give two molecular orbitals (bonding + antibonding);

N

atoms give $N$ orbitals packed into a fixed window that merge into a band. See Covalent bonding & MO theory.

What happens to metallic-bond strength for a hypothetical atom donating zero valence electrons?

With no electrons in the sea there is nothing to glue the cations — no metallic bond forms at all, consistent with

strength \propto (electrons donated) / (cation radius) = 0

Where does the Fermi level sit in a metal versus an intrinsic semiconductor?

In a metal

E_{F}

lies inside a partly-filled or overlapping band (occupied states available at

E_{F}

); in an intrinsic semiconductor it sits near mid-gap, in the forbidden region.

Recall Quick self-test

Cover the answers and re-run the "Spot the error" block — those five sentences hide the four most-tested traps: delocalisation-not-ionisation, the mid-gap origin of the 2, non-directional malleability, and the metal-vs-semiconductor temperature trend.

See also: Giant structures / lattices · Metallic bonding (parent)