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Black-body Radiation & the Quantum Hypothesis Max Planck Micro-world Macro-world Lect 13 Thermal atomic motion Air solid Heat energy= KE and PE associated with the random thermal motion of atoms Temperature avg KE Temperature scales Fahrenheit 212 F room temp 27o C 300oK 80 F 32 F - 459 F Black-body Radiation Light intensity l peak UV IR 2.9 x 10-3 m = T(Kelvin) lpeak vs Temperature T 3100K (body temp) 58000K (Sun’s surface) l peak 2.9 x 10-3 m = T(Kelvin) 2.9 x 10-3 m -6m =9x10 3100 infrared light 10-3 visible light 2.9 x m -6m =0.5x10 58000 “Room temperature” radiation Photo with an IR camera IR Cat IR house 5800oK 300oK Visible light Light absorbtion in the atmosphere T=300o Infrared light Back to Planck, etc… 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 (~10와) 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 2x1014 Hz Equant= hf Equant= hf =6.6x10-34Jsx1Hz =6.6x10-34J =(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 22x1m 20kgx ===20kgx10m/s 20kgx10m/s x = 200 kgm2/s2 = 200 J hmax much, much larger than Equant=6.6x10-34J Typical electron KE in an atom 1 “electron Volt” - - 1V Energy gained by an electron 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 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 photons “Quantum Jump” Photoelectric effect Vacuum tube Experimental results Electron KE (electron Volts) For light freq below f0, no electrons leave the cathode f0 Even if the light Is very intense 0 0.5 1.0 1.5 Experimental results For light freq above f0, the KE of electrons that leave the cathode increase with increasing freq Electron KE (electron Volts) f0 0 0.5 But does not change With light intensity 1.0 1.5 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 But that’s not what is observed Above f0,the KE only depends on freq, & not on the light’s intensity Electron KE (electron Volts) Below f0, no electrons jump out of the cathode no matter what the light’s intensity is 0 f0 0.5 1.0 1.5 Einstein’s explanation Light is comprised of particle-like quanta each with energy Equant = 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 f If Equant is less than f, the electron can’t escape If Equant is greater than f, the electron escapes & the f quantum energy in excess of f becomes electron KE KEelectron = hf - f Light quanta “photons” Einstein’s light quanta were given the name “photons” by Arthur Compton Photon Energy for red light Red light: f = 4.0x1014 Hz (Hz = 1/s) Ephoton = hf = (6.6x10-34 Js) x (4.0x1014 Hz) = 2.6 x 10-19 J = 2.6 eV 1.6 x 1eV 1.6 x 10-19 J =1.6 eV Photon Energies for visible light color: Red Yellow Green Blue Violet freq 4.0x1014 Hz 5.0x1014Hz 6.0x1014 Hz 6.7x1014Hz 7.5x1014 Hz Equant = hf 2.6x10-19J 3.3x10-19J 4.0x10-19J 4.4x10-19J 5.0x10-19J 1.6 eV 2.1 eV 2.5 eV 2.8 eV 3.1 eV Producing photoelectrons with photons Clears the barrier with energy to spare - - 1.6eV KE=0.7eV outside of the metal f=2.1eV 2.8eV - - - - inside the metal Not enough energy to get over the barrier For E Electron KE (electron Volts) violet blue yellow red KE 0 0.5 KE 1.0 1.5 Photons are weird particles v=c (always) g= 1 1 – v2/c2 = 1 1 – 1 1 1 – c2/c2 = = (always) What is the photon’s rest mass? E=mc2 m = g m0 m0 = 0 m0 = E c2 m= m g = m =0 Rest mass = 0 Photon’s momentum For any particle: p=mv for a photon: m= E2 c p = E2 c c & v=c E = c Photon energy & momentum E = hf p = E c = Wavelength: l = c f hf c = h l f c = 1 l “particles” of light p = E=hf h l Two body collisions conservation of momentum Compton scattering Scatter X-rays from electrons p=h/li - Recoil electron & scattered photon conserve momentum Compton’s expt proved the existence of photons & won him the 1927 Nobel Prize (Physics) 4x10-11eV g-rays X-rays Ultraviolet Infrared micro waves TV/FM AM radio waves Photon “spectrum” 4x10-7eV 4x10-3eV 4eV 4x103eV visible light 1.6 – 3.1eV 4x106eV Wave? Particles?? Maxwell E B James Clerk Maxwell Light is a wave of oscillating E- and B-fields Einstein p = h l E=hf Light is comprised of particle-like quanta called photons 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) yell ow red 0.5 violet blue 1.0 1.5 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