# Black-body Radiation & the Quantum Hypothesis Black-body Radiation & the Quantum Hypothesis Max Planck Physics 100 Chapt 20 Black-body Radiation Light intensity peak

U IR 2.9 x 10-3 m = T(Kelvin) peak vs Temperature T 3100K (body temp)

58000K (Suns surface) peak 2.9 x 10-3 m = T(Kelvin) 2.9 x 10-3 m -6 =9x10 m

0 310 infrared light visible light 2.9 x 10 m -6 =0.5x10 m 0 5800

-3 Room temperature radiation Photo with an IR camera IR Cat IR house the UV catastrophe Theory & experiment disagree wildly

Pre-1900 theory 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 Equantum = h f

h = 6.6 x 10-34 Js Plancks Other quantum systems The quantum of the US monetary system We dont worry about effects of quantization Because the pennys value is so small Suppose the quantum were a

\$1000 bill A quantum this large would have an enormous effect on normal transaction 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 dont 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 Plancks quantum is small for ordinarysized objects but large for atoms etc ordinary pendulum f = 1 Hz Hydrogen atom f 2x1014 Hz

e m a s e th E t K u s

o s a b n a o r t c e l

e e th Equant= hf Equant= hf=6.6x10 Jsx1Hz y n i t

=6.6x10-34J ery v -34 =(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 22

20kgx ===20kgx10m/s 20kgx10m/s x1m x hma = 200 kgm2/s2 x = 200 J

much, much larger than Equant=6.6x10-34J Typical electron KE in an atom 1 electron - - 1V Energy gained by an Voltelectron 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 Plancks 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