Ch 05-02 Blackbody Radiation

• Some empirical laws:
  • Wien's displacement law
             λ_max = 0.0029 m / (T/K)
             for T ~ 300 K,    λ_max ~ 10^-5m = 10 μm
                         3000 K                               1 μm
                         6000 K                               5000 Å
            
    
    
    
  • Stefan-Boltzmann law
             F = σT⁴ ,     σ =5.67 x 10^-5 erg sec^-1 cm^-2 K^-4
     
  • Wien's law (at short wavelengths)
             F_λ = 2πhc²λ^-5e^-hc/λkT   (erg sec^-1 cm^-2 cm^-1)
             (F = ∫ F_λdλ)
      
  • Rayleigh-Jeans law (at long wavelengths)
             F_λ = 2πcλ^-4 kT
     
• Planck's law (derived from the "quantum assumption of photons")
           F_λ = 2πhc²λ^-5(e^hc/λkT-1)^-1
           (F_ν = 2πhν³c^-2(e^hν/kT-1)^-1      F_νdν = F_λdλ)
   
• The "blackbody spectrum" is the photon distribution in a thermal equilibrium state.
  
  [The Sun as a blackbody]