A furnace at 1500 K is viewed through a small hole (a blackbody). (a) Where does its spectrum peak? (b) Compare the Rayleigh-Jeans prediction with Planck's at lambda = 100 nm (ultraviolet). Solution: (a) Wien: lambda_max = 2.898x10^-3/1500 = 1.93 x 10^-6 m = 1930 nm (infrared). (b) At 100 nm, nu = 3 x 10^15 Hz; h nu/kT = (6.626x10^-34)(3x10^15)/((1.38x10^-23)(1500)) = 96. Rayleigh-Jeans gives u_RJ proportional to nu^2 kT (large), while Planck suppresses it by 1/(e^96 - 1) ~ 10^-42 - the catastrophe's infinity versus quantum reality.