Blackbody Radiation the Quantum Hypothesis Max Planck Physics

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 3100 K (body temp) 58000 K (Sun’s surface) l peak 2. 9 x 10 -3 m = T(Kelvin) 2. 9 x 10 -3 m -6 m =9 x 10 3100 infrared light 10 -3 visible light 2. 9 x m -6 m =0. 5 x 10 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 2 x 1014 Hz e m a s e h on’s t t r t u c o le ab e the as KE Equant= hf =6. 6 x 10 -34 Jsx 1 Hz =6. 6 x 10 -34 J y ver tiny =(6. 6 x 10 -34 Js)x(2 x 1014 Hz) =(6. 6 x 2) x 10 -34+14 J =1. 3 x 10 -19 J

Typical energies in “ordinary” life Typical energy of a tot on a swing: Etot = mghmax 22 x 1 m 20 kgx ===20 kgx 10 m/s x = 200 kgm 2/s 2 = 200 J hmax much, much larger than Equant=6. 6 x 10 -34 J

Typical electron KE in an atom 1 “electron Volt” - - 1 V Energy gained by an electron crossing a 1 V voltage difference Energy = q V 1 e. V = 1. 6 x 10 -19 C x 1 V = 1. 6 x 10 -19 Joules similar Equant = 1. 3 x 10 -19 J for f 2 x 1014 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