Density of Unit Cell
The density of a unit cell is the ratio of the mass of atoms present in the unit cell to its volume. In solid state chemistry, understanding this density is essential to estimate the material’s strength, packing efficiency, and real-world usability.
Formula to Calculate Density
Density (ρ) = (Z × M) / (a³ × NA)
Where:
- ρ = Density of unit cell (g/cm³)
- Z = Number of atoms per unit cell
- M = Molar mass (g/mol)
- a = Edge length of the unit cell (cm)
- NA = Avogadro’s number = 6.022 × 10²³ mol⁻¹
Number of Atoms per Unit Cell (Z)
- Simple Cubic (SC): Z = 1
- Body-Centered Cubic (BCC): Z = 2
- Face-Centered Cubic (FCC): Z = 4
Edge Length Conversion
Convert the edge length a to centimeters:
- 1 pm = 1 × 10⁻¹⁰ cm
- 1 nm = 1 × 10⁻⁷ cm
Example Problem
Calculate the density of a metal having FCC structure with molar mass = 63.5 g/mol and edge length = 361 pm.
Given:
- Z = 4 (FCC)
- M = 63.5 g/mol
- a = 361 pm = 361 × 10⁻¹⁰ cm
- NA = 6.022 × 10²³ mol⁻¹
Density, ρ = (4 × 63.5) / [(361 × 10⁻¹⁰)³ × 6.022 × 10²³]
= 254 / [4.71 × 10⁻²³ × 6.022 × 10²³]
= 254 / 2.837
ρ ≈ 8.95 g/cm³
Significance of Unit Cell Density
- Indicates the mass-to-volume ratio of a solid
- Crucial for materials engineering and design
- Assists in selecting materials for lightness or strength
- Enables comparison between experimental and calculated densities
🌟 Conclusion: The density of a unit cell is a fundamental concept in solid state chemistry. It links atomic-level structure to macroscopic properties, helping in the development of strong, efficient, and lightweight materials.
