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Black-body Radiation & the Quantum Hypothesis

Black-body Radiation & the Quantum Hypothesis. Physics 100 Chapt 20. Max Planck. Black-body Radiation. 2.9 x 10 -3 m T(Kelvin). l peak =. Light intensity. UV. IR. l peak vs Temperature. 2.9 x 10 -3 m T(Kelvin). T. l peak =. 310 0 K (body temp). 2.9 x 10 -3 m 310 0.

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Black-body Radiation & the Quantum Hypothesis

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  1. Black-body Radiation & the Quantum Hypothesis Physics 100 Chapt 20 Max Planck

  2. Black-body Radiation 2.9 x 10-3 m T(Kelvin) l peak = Light intensity UV IR

  3. lpeak vs Temperature 2.9 x 10-3 m T(Kelvin) T l peak = 3100K (body temp) 2.9 x 10-3 m 3100 =9x10-6m infrared light 58000K (Sun’s surface) visible light 2.9 x 10-3 m 58000 =0.5x10-6m

  4. “Room temperature” radiation

  5. Photo with an IR camera

  6. IR Cat

  7. IR house

  8. the UV catastrophe Theory & experiment disagree wildly Pre-1900 theory

  9. 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”

  10. Other “quantum” systems

  11. The quantum of the US monetary system We don’t worry about effects of quantization Because the penny’s value is so small

  12. Suppose the quantum were a $1000 bill A quantum this large would have an enormous effect on “normal” transactions

  13. The quantum of the US Income tax system

  14. US Income tax with a $1 quantum Number of taxpayers

  15. US Income tax with a $1000 quantum Number of taxpayers All these guys don’t have to pay anything Quantum effects are negligible to these taxpayers Quantum effects are huge to these guys

  16. How quanta defeat the UV catastrophe Without the quantum With the quantum Low frequency, small quantum, Negligible effects high frequency, large quantum, huge effects

  17. Planck’s quantum is small for “ordinary-sized” objects but large for atoms etc “ordinary” pendulum f = 1 Hz Hydrogen atom f2x1014 Hz about the same as the electron’s KE Equant=hf =(6.6x10-34Js)x(2x1014Hz) Equant=hf =6.6x10-34Jsx1Hz =(6.6x2)x 10-34+14J very tiny =6.6x10-34J =1.3 x 10-19J

  18. Typical energies in “ordinary” life Typical energy of a tot on a swing: Etot = mghmax = 20kgx = 20kgx10m/s2x1m = 20kgx10m/s2x hmax = 200 kgm2/s2 = 200 J much, much larger than Equant=6.6x10-34J

  19. Typical electron KE in an atom Energy gained by an electron crossing a 1V voltage difference 1 “electron Volt” Energy = q V - - - 1eV = 1.6x10-19Cx1V 1V = 1.6x10-19 Joules similar Equant =1.3 x 10-19J for f  2x1014 Hz

  20. Classical vs Quantumworld At atomic & subatomic scales, quantum effects are dominant & must be considered In everyday life, quantum effects can be safely ignored Laws of nature developed without consideration of quantum effects do not work for atoms This is because Planck’s constant is so small

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