notesonly.in

Step 1: Identify the energy of one mode of a photon in a cavity. Let ε = 2.0×10⁻²⁰ J. Step 2: Choose a temperature, say room temperature T = 300 K. Step 3: Use the Bose–Einstein distribution for photons (μ = 0): ⟨n⟩ = 1/(exp(ε/(kT)) – 1). Step 4: Compute the exponent: ε/(kT) = 2.0×10⁻²⁰ / (1.38×10⁻²³ × 300) ≈ 4.83. Step 5: Find exp(4.83) ≈ 125.6. Step 6: Calculate the average occupation: ⟨n⟩ = 1/(125.6 – 1) ≈ 0.008. Result: On average, about 0.008 photons occupy this energy mode at 300 K.