Solid State — MHT-CET Chemistry

Formulas (1)

• Seven Crystal Systems, Fourteen Bravais Lattices · Bravais count
  $$3 + 2 + 4 + 2 + 1 + 1 + 1 = 14 \text{ lattices in } 7 \text{ systems}$$

Reference tables (2)

Watch out for (3)

• Reading 'NOT true' as 'true'
  → Crystalline Versus Amorphous Solids
• Ice as an ionic or covalent solid
  → Ionic, Covalent Network, Molecular and Metallic Solids
• Swapping 7 and 14
  → Seven Crystal Systems, Fourteen Bravais Lattices

Formulas (3)

• Particles Per Unit Cell and Coordination Number · Sharing fractions
  $$n = \tfrac{1}{8}\,n_{\text{corner}} + \tfrac{1}{2}\,n_{\text{face}} + \tfrac{1}{4}\,n_{\text{edge}} + n_{\text{body}}$$
• Edge Length From Radius: Where the Atoms Touch · Edge–radius relations
  $$a_{\text{sc}} = 2r,\qquad a_{\text{bcc}} = \frac{4r}{\sqrt{3}},\qquad a_{\text{fcc}} = 2\sqrt{2}\,r$$
• Unit Cell Volume and the Volume of Its Atoms · Cell volume and atom volume
  $$V_{\text{cell}} = a^3,\qquad V_{\text{atoms}} = n \cdot \tfrac{4}{3}\pi r^3$$

Watch out for (3)

• Counting the eight corners as eight particles
  → Particles Per Unit Cell and Coordination Number
• Inverting the bcc relation
  → Edge Length From Radius: Where the Atoms Touch
• Cubing the picometres
  → Unit Cell Volume and the Volume of Its Atoms

Formulas (4)

• Packing Efficiency: 52.4%, 68%, 74% · Packing efficiency
  $$\text{PE} = \frac{n \cdot \tfrac{4}{3}\pi r^3}{a^3} \times 100:\quad \tfrac{\pi}{6},\ \tfrac{\sqrt{3}\pi}{8},\ \tfrac{\pi}{3\sqrt{2}}$$
• Occupied Volume, Void Volume and the Volume Per Particle · Occupied and void volume
  $$V_{\text{occ}} = \text{PE}\cdot V,\qquad V_{\text{void}} = (1-\text{PE})\,V,\qquad V_{\text{particle}} = \frac{\text{PE}\cdot V}{n}$$
• Tetrahedral and Octahedral Voids: 2N and N · Void counts
  $$N_{\text{tet}} = 2N,\qquad N_{\text{oct}} = N,\qquad N = n_{\text{mol}} \times 6.022 \times 10^{23}$$
• Formula of a Compound From the Voids the Cations Fill · Cations from void fraction
  $$n_{\text{A}} = f_{\text{tet}} \cdot 2N + f_{\text{oct}} \cdot N,\qquad \text{formula} = \text{A}_{n_{\text{A}}}\text{B}_{N}$$

Watch out for (4)

• Giving 74% for bcc
  → Packing Efficiency: 52.4%, 68%, 74%
• Reporting the occupied volume when ONE particle is asked
  → Occupied Volume, Void Volume and the Volume Per Particle
• Swapping the two counts
  → Tetrahedral and Octahedral Voids: 2N and N
• Forgetting the factor 2 on tetrahedral voids
  → Formula of a Compound From the Voids the Cations Fill

Formulas (5)

• The Density Formula and the Lumped Constants · Density of a cubic crystal
  $$\rho = \frac{n\,M}{a^3\,N_A}$$
• Molar Mass From Density · Molar mass
  $$M = \frac{\rho\,a^3 N_A}{n}$$
• Unit Cell Volume From Density and Molar Mass · Cell volume
  $$a^3 = \frac{n\,M}{\rho\,N_A}$$
• Which Structure? Solve for n · Particles per cell
  $$n = \frac{\rho\,a^3 N_A}{M} = \frac{\rho\,a^3}{m_{\text{atom}}}$$
• Counting Unit Cells and Atoms in a Mass or a Volume · Counting cells
  $$N_{\text{cells}} = \frac{w}{\rho\,a^3} = \frac{V}{a^3} = \frac{w}{M}\cdot\frac{N_A}{n},\qquad N_{\text{atoms}} = n\,N_{\text{cells}}$$

Watch out for (5)

• Using n = 4 for bcc
  → The Density Formula and the Lumped Constants
• Dividing by N_A when the lump already contains it
  → Molar Mass From Density
• Trusting a printed exponent over the order of magnitude
  → Unit Cell Volume From Density and Molar Mass
• Stopping at n and not naming the cell
  → Which Structure? Solve for n
• Counting cells when atoms are asked
  → Counting Unit Cells and Atoms in a Mass or a Volume

Formulas (1)

• Band Gap, n-Type and p-Type Doping · Dopant rule
  $$\text{Group 15 (P, As, Sb)} \to n\text{-type};\qquad \text{Group 13 (B, Al, Ga, In)} \to p\text{-type}$$

Reference tables (2)

Watch out for (3)

• Calling every missing-ion picture Frenkel
  → Point Defects: Schottky, Frenkel, Impurity and Non-Stoichiometric
• Confusing 'n' with 'negative charge on the dopant'
  → Band Gap, n-Type and p-Type Doping
• Picking O₂ because it is magnetic
  → Diamagnetic, Paramagnetic, Ferromagnetic