Density of Unit Cell
In solid state chemistry, the density of a unit cell refers to the mass of all atoms contained within the unit cell divided by the volume of the unit cell. Understanding this property allows scientists and engineers to predict the material’s compactness, strength, and practical usability.
Formula to Calculate Density
Density (ρ) = (Z × M) / (a³ × NA)
Where:
- ρ = Density (g/cm³)
- Z = Number of atoms per unit cell
- M = Molar mass (g/mol)
- a = Edge length (in 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
- 1 pm = 1 × 10⁻¹⁰ cm
- 1 nm = 1 × 10⁻⁷ cm
Example Problem
Calculate the density of a metal with FCC structure. Molar mass = 63.5 g/mol. Edge length = 361 pm.
- Z = 4 (FCC)
- M = 63.5 g/mol
- a = 361 pm = 361 × 10⁻¹⁰ cm
- NA = 6.022 × 10²³ mol⁻¹
ρ = (4 × 63.5) / [(361 × 10⁻¹⁰)³ × 6.022 × 10²³] ≈ 8.95 g/cm³
Significance of Unit Cell Density
- Indicates mass-to-volume ratio of materials
- Important for metallurgy and materials selection
- Crucial for designing strong and lightweight materials
- Confirms experimental data with theoretical models
Conclusion: The density of a unit cell connects atomic structure with macroscopic properties, making it vital for science, technology, and engineering applications.
Related topics: Crystal Lattices & Unit Cell |
Quiz Time!
MCQ 1: What is the value of Z for a BCC unit cell?
- A. 1
- B. 2 ✅
- C. 3
- D. 4
MCQ 2: In the density formula, what does ‘a’ represent?
- A. Atomic number
- B. Atomic radius
- C. Edge length of unit cell ✅
- D. Avogadro’s number
True/False: “FCC unit cells have a coordination number of 8.”
Answer: ❌ False. FCC has a coordination number of 12.
True/False: “Density increases with more atoms per unit cell if all other factors remain constant.”
Answer: ✅ True.
