2. Quantum Theory Micro-world Macro-world Lecture 14

3. Light propagates like a wave, & interacts as a particle E=hf h p =

4. Louis deBroglie If light behaves as particles, maybe other “particles” (such as electrons) behave as waves h p =Photons: hphp  = particles: hphp  = Wave-particle duality is a universal phenomenon  “ deBroglie wavelength”

5. Ordinary-sized objects have tiny wavelengths 0.2kg 30m/s hphp  = h mv = 6.6x10 -34 Js 0.2kg x 30 m/s = 6.6x10 -34 Js 6.0 kg m/s = 1.1x10 -34 m = Incredibly small

6. the wavelength of an electron is not so small 9x10 -31 kg 6x10 6 m/s hphp  = h mv = 6.6x10 -34 Js 9x10 -31 kg x 6x10 6 m/s = 6.6x10 -34 Js 5.4x10 -24 kg m/s = 1.2x10 -10 m = - About the size of an atom

7. Send low-momentum electrons thru narrow slits See a diffraction pattern characteristic of wavelength =h/p as predicted by de Broglie

8. or through a small hole “Diffraction” rings

9. Matter waves (electrons through a crystal) “Diffraction” rings

10. Electron waves through a narrow slit acquire some p y pypy pypy yy x y

11. Waves thru a narrower slit wider pypy pypy yy When the slit becomes narrower, the spread in vertical momentum increases x y

12.  y/2 x y /2 

13. Heisenberg Uncertainty Principle  y  p y > h Uncertainty in location Uncertainty in momentum in that direction If you make one of these smaller, the other has to become bigger

14. Heisenberg tries to measure the location of an atom For better precision, use a shorter wavelength But then the momentum change is higher  x  p x > h

15. Localize a baseball 0.2kg  x  p x > h  p x > hxhx Suppose  x= 1x10 -10 m  p x > 6.6x10 -34 Js 1x10 -10 m  v x > = 6.6x10 -24 kgm/s A very tiny uncertainty About the size of a single atom pxmpxm 6.6x10 -44 Js 0.2 kg = = 3.3x10 -23 m/s

16. Localize an electron  x  p x > h  p x > hxhx Suppose  x= 1x10 -10 m  p x > 6.6x10 -34 Js 1x10 -10 m  v x > = 6.6x10 -24 kgm/s Huge, about 2% of c About the size of a single atom pxmepxme 6.6x10 -24 Js 9x10 -31 kg = = 7x10 6 m/s - m e =9x10 -31 kg

17. uncertainty is inherent in the quantum world

18. The Bohr-Rutherford Atom Physics 100 Chapt 23 Nils Bohr Ernest Rutherford

19. 1895 J.J. Thomson discovered electron + - - - - + cathode anode “cathode rays” Vacuum flask

20. Cathode rays have negative charge and very small mass + - - - - + cathode anodeN S m=0.0005M Hydrogen

21. Plum pudding? - - -- - - - - - 10 -10 m + + + + + + + + + + + + + + + + Positively charged porridge Negatively charged raisins (plums)

22. Planetary-like? 10 -10 m + - - - - - Positively charged dense central nucleus Negatively charged orbiting electrons

23. Rutherford Experiment Vacuum flask  -rays

24. What’s in the box? Is all the mass spread throughout as in a box of marshmallows”? or is all the mass concentrated in a dense “ball-bearing”?

25. Figure it out without opening (or shaking) Shoot bullets randomly through the box. If it is filled with marshmallows, all the bullets will go straight through without (much) deflection

26. Figure it out without opening (or shaking) If it contains a ball-bearing most the bullets will go straight through without deflection---but not all Occasionally, a bullet will collide nearly head-on to the ball-bearing and be deflected by a large angle

27. Rutherford used  -ray “bullets” to distinguish between the plum- pudding & planetary models - - -- - - - - - + + + + + + + + + + + + + + + +     no way for  -rays to scatter at wide angles Plum-pudding:

28.     + - - - - - Occasionally, an  -rays will be pointed head-on to a nucleus & will scatter at a wide angle distinguishing between the plum- pudding & planetary models

29. Rutherford saw ~1/10,000 a-rays scatter at wide angles     + - - - - - from this he inferred a nuclear size of about 10 -14 m

30. Rutherford atom + 10 -14 m 10 -10 m Not to scale!!! If it were to scale, the nucleus would be too small to see Even though it has more than 99.9% of the atom’s mass

31. Relative scales Aloha stadium Golf ball Atom Nucleus 99.97% of the mass x10 -4

32. Classical theory had trouble with Rutherford’s atom Orbiting electrons are accelerating Accelerating electrons should radiate light According to Maxwell’s theory, a Rutherford atom would only survive for only about 10 -12 secs

33. Fraunhofer discovered that some wavelengths are missing from the sun’s black-body spectrum sola Other peculiar discoveries: Solar light spectrum:

34. Other discoveries… Low pressure gasses, when heated, do not radiate black-body-like spectra; instead they radiate only a few specific colors

35. bright colors from hydrogen match the missing colors in sunlight Hydrogen spectrum Solar spectrum

36. Bohr’s idea “Allowed” orbits

37. Hydrogen energy levels + 1 3 4

38. + 1 2

39. What makes Bohr’s allowed energy levels allowed? Recall what happens when we force waves into confined spaces:

40. Confined waves Only waves with wavelengths that just fit in survive (all others cancel themselves out)

41. Electrons in atoms are confined matter waves ala deBroglie This wave, as it goes around, will interfere with itself destructively and cancel itself out However, if the circumference is exactly an integer number of wavelengths, successive turns will interfere constructively Bohr’s allowed energy states correspond to those with orbits that are integer numbers of wavelengths

42. Bohr orbits

44. Quantum Mechanics Erwin Schrodinger Schrodinger’s equation

45. Matter waves are “probability” waves  Probability to detect the electron at some place is   2 at that spot Electrons are most likely to be detected here or here Electrons will never be detected here

46. Electron “clouds” in Hydrogen

47. Nobel prizes for Quantum Theory 1918 Max Planck E=hf 1921 Albert Einstein photons 1922 Niels Bohr atomic orbits 1929 Louis de Broglie matter waves 1932 Werner Heisenberguncertainty principle …