Answer
Hall Coefficient Calculation – Sodium and Copper
🔷 Concept Overview
The Hall coefficient (RH) is a measure of the type and density of charge carriers in a conductor or semiconductor.
RH = 1 / (n × e)
- n: number density of charge carriers (electrons/m³)
- e: elementary charge = 1.6 × 10⁻¹⁹ C
To find n for a metal, use:
n = (NA × ρ) / M
- NA: Avogadro’s number = 6.022 × 10²³ mol⁻¹
- ρ: density (kg/m³)
- M: molar mass (kg/mol)
🔹 (a) For Sodium (Na)
- Molar mass: 0.023 kg/mol
- Density: 970 kg/m³
n = (6.022 × 10²³ × 970) / 0.023 ≈ 2.54 × 10²⁸ electrons/m³
RH = 1 / (2.54 × 10²⁸ × 1.6 × 10⁻¹⁹) ≈ 2.45 × 10⁻¹⁰ m³/C
🔹 (b) For Copper (Cu)
- Molar mass: 0.0635 kg/mol
- Density: 8960 kg/m³
n = (6.022 × 10²³ × 8960) / 0.0635 ≈ 8.5 × 10²⁸ electrons/m³
RH = 1 / (8.5 × 10²⁸ × 1.6 × 10⁻¹⁹) ≈ 7.35 × 10⁻¹¹ m³/C
✅ Final Results
- Sodium (Na): 2.45 × 10⁻¹⁰ m³/C
- Copper (Cu): 7.35 × 10⁻¹¹ m³/C