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

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

lpeak vs Temperature T l peak = 3100K 58000K 2.9 x 10-3 m T(Kelvin) (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

“Room temperature” radiation

Photo with an IR camera

IR Cat

IR house

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

Planck’s solution h = 6.6 x 10-34 Js “Planck’s constant” 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

US Income tax with a $1 quantum Number of taxpayers

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

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

Planck’s quantum is small for “ordinary-sized” objects but large for atoms etc 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 =(6.6 x 2) x 10-34+14J very tiny =6.6x10-34J =1.3 x 10-19J

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

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

Classical vs Quantum world 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