Black Body Radiation and the experimental basis for Quantum Theory Josef Stefan (1835-1893) • Total energy radiated proportional to T4 Question: Suppose temperature raised from 300K (room temp) to 6000K (sun) By what factor does the energy radiated increase? A. 16 B. 16,000 C. 90,000 D. 160,000 Josef Stefan (1835-1893) • Total energy radiated proportional to T4 Question: Suppose temperature raised from 300K (room temp) to 6000K (sun) By what factor does the energy radiated increase? A. 16 B. 16,000 C. 90,000 D. 160,000 Answer: (6000/300)4 = 204=160,000 Steam Radiator 400K IR Very Hot Stove 900K Dull Red (transition to visable) Lava ~2000K Glowing (most radiation still in IR) Sun 6000K Most radiation visable Wilhelm Wien Wilhelm Wien (18643-1928) Nobel Prize 1911 Example of Black Body Spectra for different temperatures Below is a photo of three stars. The light emitted by these stars is thermal radiation. Which of these stars is the hottest? The coolest? A. Red, yellow B. Red, blue C. Yellow, blue D.Blue, red E. Blue, yellow © 2007 W.W. Norton & Company, Inc. 9 Physics for Engineers and Scientists Below is a photo of three stars. The light emitted by these stars is thermal radiation. Which of these stars is the hottest? The coolest? A. Red, yellow B. Red, blue C. Yellow, blue D.Blue, red E. Blue, yellow © 2007 W.W. Norton & Company, Inc. 10 Physics for Engineers and Scientists Spectrum of high energy particle radiation from space does not follow a black body spectrum Cosmic Ray Flux Above 1020 eV Very low flux ~ 1 particle per 2 km /sr/century 1 Joule What is the best known example of a black body source? What is the best known example of a black body source? Hint Temperature = 2.7 K Cosmic Microwave Background (Radiation from Big Bang! T=2.725K. The theoretical curve obscures the data points and the error bars. Astrophysical Journal, 473, 576 Black Body Radiation and the experimental basis for Quantum Theory What is the energy of a “quanta” of RED light? 660 nm wavelength in units of electron volts? E=hν h=6.62x10-34 Js What is the energy of a “quanta” of E=hν RED light? 660 nm wavelength in units of h=6.62x10-34 Js electron volts? ν=c/λ=3x108m/s/660x10-9m =4.54x1014 s-1 E= 6.62x10-34Js x 4.54x1014 s-1 E= 3.01 x 10-19 J 1eV= 1.602 x10-19 J E=3.01x10-19J/1.602x10-19J/eV E=1.88 eV What is the energy of a “quanta” Easier Way to Solve this of RED light? 660 nm wavelength in units of E=hc/λ electron Volts hc=1240 eV nm (useful constant to remember) E=(1240/660)eV E= 1.88 eV Question: What is the energy quantization of a grandfather clock? Hint: Question: What is the energy quantization of a grandfather clock? Hint: E=nhν for n=1, ν=1Hz=1s-1 E= 6.6x10-34J E=nhν for n=1, ν=1Hz=1s-1 E= 6.6x10-34J How is the quantization realized? E=nhν for n=1, ν=1Hz=1s-1 E= 6.6x10-34J How does this quantization translate into quantization of the pendulum displacement (height)? E=nhν for n=1, ν=1Hz=1s-1 E= 6.6x10-34J How does this quantization translate into quantization of the pendulum displacement (height)? E=mgH=6.6x10-34J H=6.6x10-34J/(1kg 10m/s2)=6.6x10-35m H Too small to measure (size of an atom is about 10-8 m) .