Questions: Solid State Chemistry Fundamentals

Question 1

In the rock salt (NaCl) structure, what is the coordination number of each ion?

• A. Na⁺ has coordination number 4, Cl⁻ has coordination number 4
• B. Na⁺ has coordination number 6, Cl⁻ has coordination number 6
• C. Na⁺ has coordination number 8, Cl⁻ has coordination number 8
• D. Na⁺ has coordination number 6, Cl⁻ has coordination number 4

Answer: (B)

In the rock salt structure, each Na⁺ is surrounded by six Cl⁻ ions in an octahedral arrangement, and each Cl⁻ is surrounded by six Na⁺ ions in an octahedral arrangement. Both ions have coordination number 6. This structure is adopted when the radius ratio r⁺/r⁻ falls in the range that stabilizes octahedral coordination (~0.414-0.732). The rock salt structure can be described as two interpenetrating face-centered cubic lattices, one of Na⁺ and one of Cl⁻, offset by half a unit cell edge.

Question 2

Band theory explains metallic conductivity by showing that partially filled bands allow electrons to move freely through the solid under an applied electric field.

• T. True
• F. False

Answer: True

When N atoms come together in a solid, each atomic orbital splits into N molecular orbitals forming a near-continuous band. If the band is partially filled (as in metals like sodium, where the 3s band is half-full), there are empty states immediately above the occupied states — electrons can be promoted to these states by an infinitesimally small electric field, enabling conduction. In an insulator, the highest occupied band (valence band) is completely full and separated from the empty band (conduction band) by a large energy gap; electrons cannot be promoted, so no conduction occurs. Semiconductors have a small gap that thermal energy can bridge.

Question 3

A perfect crystal with no defects would be a better catalyst than one with vacancies and surface steps.

• T. True
• F. False

Answer: False

Defects are often the catalytically active sites. Surface vacancies, steps, edges, and kinks provide under-coordinated atoms with unsatisfied valences that can bind and activate substrate molecules. A perfect, flat crystal surface has fewer such sites and is generally less reactive. This is why nanoparticles (with high surface-to-volume ratios and many edge/corner atoms) are more catalytically active per atom than bulk materials. In ionic solids, oxygen vacancies create sites for oxide ion migration (important in solid oxide fuel cells) and can trap electrons, creating localized color centers.

Question 4

Explain why the band gap determines whether a solid is a metal, semiconductor, or insulator, and describe how doping a semiconductor changes its conductivity.

Model answer: The band gap is the energy difference between the top of the valence band (highest occupied states) and the bottom of the conduction band (lowest empty states). Metals have no band gap — their valence and conduction bands overlap or the valence band is partially filled. Insulators have a large band gap (>3 eV) that thermal energy cannot bridge. Semiconductors have a small band gap (0.1-3 eV) where some thermal excitation of electrons into the conduction band occurs. Doping introduces impurity atoms: n-type doping (e.g., phosphorus in silicon) adds extra electrons near the conduction band edge, dramatically increasing conductivity; p-type doping (e.g., boron in silicon) creates holes in the valence band that act as positive charge carriers.

The semiconductor industry is built on the ability to tune conductivity over many orders of magnitude through controlled doping. This is why silicon — with a conveniently sized band gap of 1.1 eV and an easily grown oxide layer — became the foundation of modern electronics.