Number Density Calculator
Calculate charge carrier number density for materials and conductors
Calculation Configuration
Number Density Calculation: Calculate charge carrier number density from material properties
Formula: n = (N_A × Z × ρ) / M
Material Selection
Input Parameters
Physical Constants
Calculation Results
Conductivity: Excellent Conductor
Very high carrier density - excellent electrical conductivity
Material Properties
Name: Copper (Cu)
Description: Excellent electrical conductor, widely used in wiring
Density: 8,960 kg/m³
Molar Mass: 63.546 g/mol
Free Electrons/Atom: 1
Formula used:
ρ = density, M = molar mass, n = number density
Example Calculation: Copper
Given Values
Material: Copper (Cu)
Density (ρ): 8,960 kg/m³
Molar Mass (M): 63.546 g/mol
Free Electrons per Atom (Z): 1
Avogadro Number (N_A): 6.022 × 10²³ mol⁻¹
Calculation Steps
n = (N_A × Z × ρ) / M
n = (6.022×10²³ × 1 × 8,960) / (63.546 × 10⁻³)
n = 5.394×10²⁷ / 0.063546
n = 8.491 × 10²⁸ carriers/m³
Result
Copper has approximately 8.49 × 10²⁸ charge carriers per cubic meter, which explains its excellent electrical conductivity.
Common Conductors
Physics Constants
Conductivity Categories
Physics Tips
Higher carrier density = better conductivity
Metals have free electrons as carriers
Temperature affects carrier mobility
Semiconductors have much lower density
Formula: n = (N_A × Z × ρ) / M
Understanding Number Density
What is Number Density?
Number density (also called charge carrier density) is the number of charge carriers per unit volume in a material. It's a fundamental property that determines electrical conductivity. In metals, charge carriers are typically free electrons that can move through the crystal lattice.
Formula Derivation
n = (N_A × Z × ρ) / M
n: Number density (carriers/m³)
N_A: Avogadro number (6.022×10²³ mol⁻¹)
Z: Free electrons per atom
ρ: Material density (kg/m³)
M: Molar mass (kg/mol)
Physical Interpretation
Step 1: Atoms per Volume
Calculate how many atoms fit in a unit volume using density and molar mass
Step 2: Free Electrons
Multiply by the number of free electrons each atom contributes
Step 3: Total Carriers
Result is the total number of charge carriers per unit volume
Applications
Electrical Engineering
Design conductors, calculate resistance, optimize current flow
Materials Science
Compare conductivity of different metals and alloys
Semiconductor Physics
Understand doping effects and carrier concentrations
Key Relationships
Conductivity
σ = n × e × μ (conductivity = density × charge × mobility)
Current Density
J = n × e × v (current = carriers × charge × drift velocity)
Hall Effect
Used to measure carrier density experimentally