Black-body Radiation & the Quantum Hypothesis

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

2. Thermal atomic motion Air solid Heat energy= KE and PE associated with the random thermal motion of atoms

3. Temperature  avg KE

4. Temperature scales Fahrenheit 212 F 80 F 300oK room temp 27o C 32 F -459 F

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

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

7. “Room temperature” radiation

8. Photo with an IR camera

9. IR Cat

10. IR house

11. 5800oK l=1x10-5m l=5x10-7m 300oK

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

14. Back to Planck, etc…

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

16. 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”

17. Other “quantum” systems

18. The quantum of the US monetary system We don’t worry about effects of quantization Because the penny’s value is so small (~10와)

19. Suppose the quantum were a $1000 bill A quantum this large would have an enormous effect on “normal” transactions

20. The quantum of the US Income tax system

21. US Income tax with a $1 quantum Number of taxpayers

22. 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

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

24. Planck’s quantum is small for “ordinary-sized” objects but large for atoms etc “ordinary” 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 =(6.6x2)x 10-34+14J very tiny =6.6x10-34J =1.3 x 10-19J

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

26. Typical electron KE in an atom Energy gained by an electron crossing a 1V voltage difference 1 “electron Volt” Energy = q V - - - 1eV = 1.6x10-19Cx1V 1V = 1.6x10-19 Joules similar Equant =1.3 x 10-19J for f  2x1014 Hz

27. Classical vs Quantumworld 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

28. photons “Quantum Jump”

29. Photoelectric effect Vacuum tube

30. 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

31. Experimental results For light freq above f0, the KE of electrons that leave the cathode increases with increasing freq Electron KE (electron Volts) f0 But does not change With light intensity 0 0.5 1.0 1.5

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

33. More intense light hasbigger E-fields E E E And, therefore Larger acceleration

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

35. 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 f0 0 0.5 1.0 1.5

36. Einstein’s explanation Light is comprised of particle-like quanta each with energyEquant = 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 quantum energy in excess of f becomes electron KE f KEelectron = hf - f

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

38. Photon Energyfor red light Red light: f = 4.0x1014Hz (Hz = 1/s) Ephoton = hf = (6.6x10-34 Js)x(4.0x1014Hz) 1eV 1.6x10-19 J x = 2.6x10-19 J 2.6 1.6 eV = =1.6 eV

39. Photon Energiesfor visible light color: freq Equant = hf Red 4.0x1014Hz 2.6x10-19J 1.6eV Yellow 5.0x1014Hz 3.3x10-19J 2.1eV Green 6.0x1014Hz 4.0x10-19J 2.5eV Blue 6.7x1014Hz 4.4x10-19J 2.8eV Violet 7.5x1014Hz 5.0x10-19J 3.1eV

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

41. For E Electron KE (electron Volts) violet blue yellow red KE KE 0 0.5 1.0 1.5

42. Photons are weird particles v=c (always) 1 1 – v2/c2 1 1 – c2/c2 g = = 1 1 – 1 =  (always) =

43. What is the photon’s rest mass? E c2 E=mc2  m= m  m g m =gm0 = =0  m0=  Rest mass=0 m0=0

44. Photon’s momentum For any particle: p=mv E c2 for a photon: m= & v=c E c E c2 p = c =

45. Photon energy & momentum E = hf h l E c hf c = p= = f c 1 l c f Wavelength:l =  =

46. “particles” of light h l p = E=hf

47. Two body collisions conservation of momentum

48. Compton scattering Scatter X-rays from electrons p=h/li - Recoil electron & scattered photon conserve momentum p=h/lf

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

50. Photon “spectrum” Infra- red Ultra- violet radio waves micro waves X-rays g-rays TV/FM AM 4x10-11eV 4x10-7eV 4x10-3eV 4eV 4x103eV 4x106eV visible light 1.6 – 3.1eV