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Published byDylan Willis Modified over 3 years ago

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

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

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peak vs Temperature peak = 2.9 x 10 -3 m T(Kelvin) T 310 0 K (body temp) 2.9 x 10 -3 m 310 0 =9x10 -6 m 5800 0 K (Suns surface) 2.9 x 10 -3 m 5800 0 =0.5x10 -6 m infrared light visible light

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Room temperature radiation

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Photo with an IR camera

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IR Cat

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IR house

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

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Plancks 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 E quantum = h f h = 6.6 x 10 -34 Js Plancks constant

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Other quantum systems

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The quantum of the US monetary system We dont worry about effects of quantization Because the pennys value is so small

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

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The quantum of the US Income tax system

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US Income tax with a $1 quantum Number of taxpayers

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US Income tax with a $1000 quantum All these guys dont have to pay anything Number of taxpayers Quantum effects are negligible to these taxpayers Quantum effects are huge to these guys

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

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Plancks quantum is small for ordinary- sized objects but large for atoms etc ordinary pendulum f = 1 Hz Hydrogen atom f 2x10 14 Hz E quant = hf=6.6x10 -34 Jsx1Hz =6.6x10 -34 J E quant = hf =(6.6x10 -34 Js)x(2x10 14 Hz) =(6.6 x 2) x 10 -34+14 J =1.3 x 10 -19 J very tiny about the same as the electrons KE

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Typical energies in ordinary life Typical energy of a tot on a swing: Etot = mgh max h max = 20kgx = 200 kgm 2 /s 2 = 200 J much, much larger than E quant =6.6x10 -34 J = 20kgx10m/s 2 x= 20kgx10m/s 2 x1m

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Typical electron KE in an atom 1 electron Volt Energy gained by an electron crossing a 1V voltage difference 1V -- - Energy = q V 1eV = 1.6x10 -19 C x 1V = 1.6x10 -19 Joules E quant = 1.3 x 10 -19 J similar for f 2x10 14 Hz

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

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