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

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

3. Temperature  avg KE

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

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

6. peak vs Temperature  peak = 2.9 x 10 -3 m T(Kelvin) T 310 0 K (body temp) 2.9 x 10 -3 m 310 0 =9x10 -6 m 5800 0 K (Sun’s surface) 2.9 x 10 -3 m 5800 0 =0.5x10 -6 m infrared light visible light

7. “Room temperature” radiation

8. Photo with an IR camera

9. IR Cat

10. IR house

11. 5800 o K =5x10 -7 m 300 o K =1x10 -5 m

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

14. Back to Planck, etc…

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

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 E quantum = 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 (~10 와 )

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 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

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

24. 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=6.6x10 -34 Jsx1Hz =6.6x10 -34 J E quant = hf =(6.6x10 -34 Js)x(2x10 14 Hz) =(6.6 x 2) x 10 -34+14 J =1.3 x 10 -19 J very tiny about the same as the electron’s KE

25. 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 =6.6x10 -34 J = 20kgx10m/s 2 x= 20kgx10m/s 2 x1m

26. Typical electron KE in an atom 1 “electron Volt” Energy gained by an electron crossing a 1V voltage difference 1V -- - Energy = q V 1eV = 1.6x10 -19 C x 1V = 1.6x10 -19 Joules E quant = 1.3 x 10 -19 J similar for f  2x10 14 Hz

27. 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

28. photons “Quantum Jump”

29. Photoelectric effect Vacuum tube

30. 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 0 0.5 1.0 1.5

31. 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 0 0.5 1.0 1.5

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

33. More intense light has bigger 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 Electron KE ( electron Volts) f0f0 0 0.5 1.0 1.5 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

36. 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

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

38. Photon Energy for red light Red light: f = 4.0x10 14 Hz E photon = hf = (6.6x10 -34 Js) x (4.0x10 14 Hz) = 2.6 x 10 -19 J 1eV 1.6 x 10 -19 J x = 2.6 1.6 eV =1.6 eV (Hz = 1/s)

39. Photon Energies for visible light color: freq E quant = hf Red 4.0x10 14 Hz 2.6x10 -19 J 1.6 eV Yellow 5.0x10 14 Hz 3.3x10 -19 J 2.1 eV Green 6.0x10 14 Hz 4.0x10 -19 J 2.5 eV Blue 6.7x10 14 Hz 4.4x10 -19 J 2.8 eV Violet 7.5x10 14 Hz 5.0x10 -19 J 3.1 eV

40. 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

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

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

43. 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

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

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

46. “particles” of light E=hf h p =

47. Two body collisions conservation of momentum

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

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

50. Photon “spectrum” Ultra- violet Infra- red X-rays  -rays micro waves radio waves TV/FM AM 4x10 -3 eV4x10 -11 eV4eV 4x10 3 eV 4x10 6 eV 4x10 -7 eV visible light 1.6 – 3.1eV

51. Wave? Particles??

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

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

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

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

56. Impossible to explain PE-effect and Compton scattering with waves Electron KE (electron Volts) red 0.5 1.0 1.5 yell ow blue violet

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

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

59. Photon photography