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Black-body Radiation & the Quantum Hypothesis Max Planck Physics 100 Chapt 20 Black-body Radiation Light intensity l peak UV IR 2.9 x 10-3 m = T(Kelvin) lpeak vs Temperature T 3100K (body temp) 58000K (Sun’s surface) l peak 2.9 x 10-3 m = T(Kelvin) 2.9 x 10-3 m -6m =9x10 3100 infrared light 10-3 visible light 2.9 x m -6m =0.5x10 58000 “Room temperature” radiation Photo with an IR camera IR Cat IR house the UV catastrophe Theory & experiment disagree wildly Pre-1900 theory Planck’s solution EM energy cannot be radiated or absorbed in any arbitrary amounts, but only in discrete “quantum” amounts. The energy of a “quantum” depends on frequency as Equantum = h f h = 6.6 x 10-34 Js “Planck’s constant” Other “quantum” systems The quantum of the US monetary system We don’t worry about effects of quantization Because the penny’s value is so small Suppose the quantum were a $1000 bill A quantum this large would have an enormous effect on “normal” transactions The quantum of the US Income tax system Number of taxpayers US Income tax with a $1 quantum Number of taxpayers US Income tax with a $1000 quantum Quantum effects are huge to these guys All these guys don’t have to pay anything Quantum effects are negligible to these taxpayers How quanta defeat the UV catastrophe Without the quantum With the quantum high frequency, large quantum, huge effects Low frequency, small quantum, Negligible effects Planck’s quantum is small for “ordinarysized” objects but large for atoms etc “ordinary” pendulum f = 1 Hz Hydrogen atom f 2x1014 Hz Equant= hf Equant= hf =6.6x10-34Jsx1Hz =6.6x10-34J =(6.6x10-34Js)x(2x1014Hz) =(6.6 x 2) x 10-34+14J =1.3 x 10-19J Typical energies in “ordinary” life Typical energy of a tot on a swing: Etot = mghmax 22x1m 20kgx ===20kgx10m/s 20kgx10m/s x = 200 kgm2/s2 = 200 J hmax much, much larger than Equant=6.6x10-34J Typical electron KE in an atom 1 “electron Volt” - - 1V Energy gained by an electron crossing a 1V voltage difference Energy = q V 1eV = 1.6x10-19C x 1V = 1.6x10-19 Joules similar Equant = 1.3 x 10-19J for f 2x1014 Hz Classical vs Quantum world In everyday life, quantum effects can be safely ignored This is because Planck’s constant is so small At atomic & subatomic scales, quantum effects are dominant & must be considered Laws of nature developed without consideration of quantum effects do not work for atoms