Physical ChemistryHigh Yield (1-2 Qs in JEE)

Solid State Chemistry Formulas

Unit cell geometry, density formula, packing efficiency of SC/BCC/FCC, radius ratios, and crystal defects.

7 Formulas•430+ Questions in Bank•

Concept Diagram

Cubic Crystal Lattices (SC, BCC, FCC)

Packing geometry and relation between edge length a and atomic radius r for simple cubic, BCC (√3a = 4r), and FCC (√2a = 4r).

\rho = \frac{Z \cdot M}{N_A \cdot a^3} \quad (\rho \text{ in g/cm}^3, \; a \text{ in cm})

Core formula linking atomic mass M, number of atoms per unit cell Z, and edge length a.

Examiner Tip: Remember N_A ≈ 6.022 × 10²³.

\text{SC: } a = 2r \; (52.4\%), \quad \text{BCC: } r = \frac{\sqrt{3}a}{4} \; (68\%), \quad \text{FCC: } r = \frac{a}{2\sqrt{2}} \; (74\%)

Geometric packing efficiency and nearest neighbor distance.

Examiner Tip: FCC / CCP has the maximum possible packing efficiency of 74%.

\frac{r_+}{r_-} < 0.225 \; (\text{Trigonal}), \quad 0.225 - 0.414 \; (\text{Tetrahedral}), \quad 0.414 - 0.732 \; (\text{Octahedral}), \quad 0.732 - 1.0 \; (\text{Cubic})

Predicts coordination number and void geometry in ionic crystals.

Examiner Tip: For N close-packed atoms: Octahedral voids = N, Tetrahedral voids = 2N.

2d_{hkl} \sin\theta = n\lambda, \quad d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}} \quad (\text{Cubic System})

Constructive interference condition for X-rays reflected from crystal planes with Miller indices (h, k, l).

Examiner Tip: For cubic crystals: ratio of spacing d₁₀₀ : d₁₁₀ : d₁₁₁ = 1 : 1/√2 : 1/√3 = 1 : 0.707 : 0.577.

Z = 6, \quad c = 4r\sqrt{\frac{2}{3}} = a\sqrt{\frac{8}{3}}, \quad V_{\text{cell}} = 24\sqrt{2}r^3 = \frac{3\sqrt{3}}{2}a^2c, \quad \text{P.E.} = 74\%

Parameters of hexagonal closest packed unit cell. Coordination number is 12 (same as FCC/CCP).

Examiner Tip: Number of tetrahedral voids = 12, octahedral voids = 6 per HCP unit cell. c/a ratio = √(8/3) ≈ 1.633.

\text{NaCl (6:6): } r_+ + r_- = \frac{a}{2}, \quad \text{CsCl (8:8): } r_+ + r_- = \frac{\sqrt{3}a}{2}, \quad \text{ZnS (4:4): } r_+ + r_- = \frac{\sqrt{3}a}{4}

Distance between nearest cation-anion centers in rock-salt, cesium chloride, and zinc blende crystal lattices.

Examiner Tip: CaF₂ (fluorite) has 8:4 coordination; Na₂O (anti-fluorite) has 4:8 coordination.

\text{Schottky: } \rho_{\text{actual}} < \rho_{\text{theoretical}} \quad | \quad \text{Frenkel: } \rho_{\text{actual}} = \rho_{\text{theoretical}}

Stoichiometric point defects in ionic solids. Schottky forms paired cation-anion vacancies; Frenkel dislocates smaller ion to interstitial site.

Examiner Tip: AgBr shows BOTH Schottky and Frenkel defects (frequent JEE question). Density decreases in Schottky, remains unchanged in Frenkel.

Frequently tested misconceptions in Solid State Chemistry

•Density calculation units: cell edge length a must be in cm (1 Å = 10^(-8) cm) to match density in g/cm³.
•FCC has Z = 4 atoms, BCC has Z = 2 atoms, Simple Cubic has Z = 1 atom.