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Suppose we have a silicon crystal and we add phosphorus atoms to make it n‑type. The doping concentration is 1 x 10^15 atoms per cm³. Each phosphorus atom contributes one free electron. Step 1: Find the number of free electrons per cm³ (n). n = 1 x 10^15 cm⁻³. Step 2: Assume the electron mobility (μ_n) is 1350 cm²/V·s. Step 3: Use the conductivity formula σ = q·n·μ_n, where q = 1.6 x 10⁻¹⁹ C. σ = (1.6 x 10⁻¹⁹) × (1 x 10^15) × 1350 = 2.16 x 10⁻³ S/cm. Thus the doped silicon now conducts electricity with a conductivity of about 2.2 mS/cm, much higher than pure silicon (≈10⁻⁶ S/cm). This shows how a tiny amount of dopant creates many free carriers and changes the material’s behavior.