UNIT 1: SOLID STATE (Crystal Lattice & Unit Cell) CBSE XIITH CHEMISTRY KEY NOTES PART III

 

1.Edge Length (a) and Atomic Radius (r) Relation

Type

SC	$\mathrm{<span\; style="color:\; red;"><b> \; </b></span>\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; }$

$a=\mathrm{<span\; class="base"><span\; class="strut"></span><span\; class="mord">2</span><span\; class="mord\; mathnormal">r</span></span><div><span\; class="mord\; mathnormal"><br></span></div>}$
 BCC 

$\sqrt{3}a=4\mathrm{r\; ------> }$$r=\frac{\sqrt{\mathrm{3/4a}}}{}$

FCC

​

$\sqrt{2}a = 4r$$r = \frac{\sqrt{2}}{4}a$

2. Packing Efficiency

Type	Packing Efficiency	Void Space

SC

52.4%

47.6%

BCC

68.0%

32.0%

FCC

74.0% (maximum for cubic)

26.0%

3. Coordination Number

• SC → 6

• BCC → 8

• FCC → 12

(Coordination number = number of nearest neighboring atoms

 

4. Examples

Structure	Examples

SC

Polonium

BCC	Iron (α-Fe), Sodium, Potassium

FCC	Aluminium, Copper, Gold, Silver, Lead

5.Additional Points

Lattice vs Basis:

• Lattice = periodic array of points.

• Basis = atom(s) associated with each lattice point.

• Crystal structure = Lattice + Basis.

• Number of atoms per unit cell is crucial for calculating density:

  $$\text{Density} = \frac{Z \times M}{N_A \times a^3}$$

  • Where:

    • $Z$= number of atoms per unit cell

    • $M$ = molar mass

    • $N_A$= Avogadro’s number

    • $a$ = edge length