Chemca Formula Sheet - Solid State

CHEMCA

EXAM MASTER FORMULA SHEET

The Solid State

High-Yield Revision for JEE Main, Advanced & NEET

1. Cubic Unit Cell Analysis

Property	Simple (SCC)	Body Centered (BCC)	Face Centered (FCC)
Rank (\(Z\))	1	2	4
Relation (\(a\) & \(r\))	\(a = 2r\)	\(a = \frac{4r}{\sqrt{3}}\)	\(a = 2\sqrt{2}r\)
Coord. No.	6	8	12
Packing Eff.	52.4%	68%	74%

2. Density Calculation

The Master Equation:

\[ \rho = \frac{Z \times M}{a^3 \times N_A} \]

\(Z\) = Effective no. of atoms per unit cell

\(M\) = Molar mass (g/mol) | \(a\) = Edge length (cm)

\(N_A\) = \(6.022 \times 10^{23} \text{ mol}^{-1}\)

3. Voids & Radius Ratio Rule

Void Count:

In a packing of \(N\) atoms:

• Octahedral Voids (OV) = \(N\)
• Tetrahedral Voids (TV) = \(2N\)

Bragg's Law:

\[ n\lambda = 2d \sin \theta \]

Radius Ratio (\(r_+ / r_-\)):

Ratio Range	Coord. No.	Geometry	Example
0.155 – 0.225	3	Trigonal Planar	\(B_2O_3\)
0.225 – 0.414	4	Tetrahedral	\(ZnS\)
0.414 – 0.732	6	Octahedral	\(NaCl\)
0.732 – 1.000	8	Cubic	\(CsCl\)

4. Point Defects

Schottky Defect

Equal number of cations and anions are missing from their sites.
Effect: Density Decreases.
Shown by: Ionic solids with high coordination no. (\(NaCl, KCl, AgBr\)).

Frenkel Defect

An ion (usually cation) is dislocated to an interstitial site.
Effect: Density Stays Same.
Shown by: Ionic solids with low coordination no. (\(ZnS, AgCl, AgBr\)).

AgBr shows BOTH Schottky and Frenkel defects

5. Metal Excess & F-Centers

F-Center (Farbe Center): Anionic vacancy occupied by an electron. Responsbile for color in ionic crystals (e.g., Yellow \(NaCl\), Pink \(LiCl\)).

Paramagnetic: Weakly attracted to magnetic field (Unpaired \(e^-\)).

Diamagnetic: Weakly repelled by magnetic field (All paired \(e^-\)).

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