Black-body Radiation & the Quantum Hypothesis Micro-world Macro-world Lect 13 Max Planck

Thermal atomic motion Heat energy = KE and PE associated with the random thermal motion of atoms Airsolid

Temperature  avg KE

Temperature scales Fahrenheit 212 F 32 F F room temp 27 o C 300 o K 80 F

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

peak vs Temperature  peak = 2.9 x m T(Kelvin) T K (body temp) 2.9 x m =9x10 -6 m K (Sun’s surface) 2.9 x m =0.5x10 -6 m infrared light visible light

“Room temperature” radiation

Photo with an IR camera

IR Cat

IR house

5800 o K =5x10 -7 m 300 o K =1x10 -5 m

Light absorbtion in the atmosphere Visible light T=300o Infrared light

Back to Planck, etc…

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

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 E quantum = h f h = 6.6 x 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 (~10 와 )

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 All these guys don’t have to pay anything Number of taxpayers Quantum effects are negligible to these taxpayers Quantum effects are huge to these guys

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

Planck’s 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=6.6x Jsx1Hz =6.6x J E quant = hf =(6.6x Js)x(2x10 14 Hz) =(6.6 x 2) x J =1.3 x J very tiny about the same as the electron’s KE

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 =6.6x J = 20kgx10m/s 2 x= 20kgx10m/s 2 x1m

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

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 Planck’s constant is so small Laws of nature developed without consideration of quantum effects do not work for atoms

photons “Quantum Jump”

Photoelectric effect Vacuum tube

Experimental results Electron KE ( electron Volts) f0f0 For light freq below f 0, no electrons leave the cathode Even if the light Is very intense

Experimental results Electron KE ( electron Volts) f0f0 For light freq above f 0, the KE of electrons that leave the cathode increases with increasing freq But does not change With light intensity

What does Maxwell’s theory say? E E E Electrons in cathode are accelerated by the E-field of the light wave

More intense light has bigger E-fields E E E And, therefore Larger acceleration

Electron KE should depend on E-field strength  light intensity Electron’s motion Not what is observed

But that’s not what is observed Electron KE ( electron Volts) f0f Above f 0,the KE only depends on freq, & not on the light’s intensity Below f 0, no electrons jump out of the cathode no matter what the light’s intensity is

Einstein’s explanation  KE electron = hf -  Light is comprised of particle-like quanta each with energy E quant = hf The quanta collide with electrons & Transfer all their energy to them Each electron needs a minimum energy to escape the cathode. This is called  If E quant is less than , the electron can’t escape If E quant is greater than , the electron escapes & the quantum energy in excess of  becomes electron KE

Light quanta  “photons” Einstein’s light quanta were given the name “photons” by Arthur Compton

Photon Energy for red light Red light: f = 4.0x10 14 Hz E photon = hf = (6.6x Js) x (4.0x10 14 Hz) = 2.6 x J 1eV 1.6 x J x = eV =1.6 eV (Hz = 1/s)

Photon Energies for visible light color: freq E quant = hf Red 4.0x10 14 Hz 2.6x J 1.6 eV Yellow 5.0x10 14 Hz 3.3x J 2.1 eV Green 6.0x10 14 Hz 4.0x J 2.5 eV Blue 6.7x10 14 Hz 4.4x J 2.8 eV Violet 7.5x10 14 Hz 5.0x J 3.1 eV

Producing photoelectrons with photons   2.1eV - Not enough energy to get over the barrier Red photon - Clears the barrier with energy to spare KE=0.7eV Blue photon Surface barrier 1.6eV 2.8eV inside the metal outside of the metal

For E Electron KE ( electron Volts) red yellow blue violet KE

Photons are weird particles v=c (always) 1  1 – v 2 /c 2   (always) 1  1 – c 2 /c 2  1  1 – 1   

What is the photon’s rest mass? E=mc 2  m= Ec2Ec2 m =  m 0  m 0 = mm = mm = 0 = 0 m 0 = 0  Rest mass = 0

Photon’s momentum For any particle: p=mv for a photon: m= Ec2Ec2 & v = c p = c Ec2Ec2 = EcEc

Photon energy & momentum E = hf p = EcEc = hf c Wavelength: = cfcf = h  = fcfc 1

“particles” of light E=hf h p =

Two body collisions conservation of momentum

Compton scattering Scatter X-rays from electrons Recoil electron & scattered photon conserve momentum p=h/ i p=h/ f -

Compton’s expt proved the existence of photons & won him the 1927 Nobel Prize (Physics)

Photon “spectrum” Ultra- violet Infra- red X-rays  -rays micro waves radio waves TV/FM AM 4x10 -3 eV4x eV4eV 4x10 3 eV 4x10 6 eV 4x10 -7 eV visible light 1.6 – 3.1eV

Wave? Particles??

Maxwell Light is a wave of oscillating E- and B-fields James Clerk Maxwell E B

Einstein Light is comprised of particle-like quanta called photons E=hf h p =

Who’s right?? Waves explain diffraction & interference Photons explain photoelectric effect & Compton scattering

Impossible to explain interference with particles With 2 slits open no light goes here Block off one slit Now light can go here

Impossible to explain PE-effect and Compton scattering with waves Electron KE (electron Volts) red yell ow blue violet

Make an interference pattern with low intensity light One photon at a time goes through the two-slit apparatus

-Light behaves like a wave when it propagates through space -And as a particle when it interacts with matter

Photon photography