Special Event!

1. Special Event! “The Universe is a Strange Place” Frank Wilczek Feshbach Professor of Physics, MIT Winner of the 2004 Nobel Prize in Physics Today, 3:00pm LeMay Auditorium

2. So what is an atom? • Typical size: 10–10 m • Alternate name: 1 Angstrom (Å) • But what are they? • Maybe small, solid, indivisible lumps? • What gives them different chemical properties? Shapes, maybe? • Or, do atoms have pieces that can be taken apart? • If so, what are the pieces? • How are they put together? • Are the pieces made of even smaller pieces??

3. Electric Charges • Electrolysis – the separation of compounds into constituent atoms using an electric current – showed that atoms could become electrically charged • Objects that are charged exert forces on each other • Like charges repel, opposites attract • Basic phenomena known since ancient times • For example, rub a piece of amber in fur  static electricity • There seemed to be a basic “unit” of charge, i.e. a standard chunk of charge e, so that any amount of charge is just some multiple of e • So 1e,2e , 3e, … but never 1.25e, for example

4. Cathode Rays • Phenomenon of “cathode rays” known since around 1865 • A sort of beam (“ray”) produced by an electrical discharge in a tube of gas at low pressure • Basically like the picture tube on your TV • But what are they?! Thomson’s cathode ray tube J.J. Thomson

5. The Electron • J. J. Thomson showed (1897) that cathode rays were particles with electric charge – “electrons” • Argued that electrons came from the gas atoms • Measured the ratio of their charge to their mass "...we have in the cathode rays matter in a new state, a state in which the subdivision of matter is carried very much farther than in the ordinary gaseous state: a state in which all matter – that is, matter derived from different sources such as hydrogen, oxygen, etc. – is of one and the same kind; this matter being the substance from which the chemical elements are built up." – J.J. Thomson (1897), "Cathode Rays," Philosophical Magazine 44, 295

6. The Electron • Later, Robert Millikan measured the charge of the electron directly • A student at Oberlin College • Later professor at U. of Chicago, then Caltech • Led to the determination of the mass of the electron • About 1/2000 the mass of hydrogen (!) • Showed that all charges, positive and negative, come in multiples of the basic e

7. Millikan’s Paper

8. Models of the Atom • So atoms do have pieces – electrons, at least • These pieces don’t account for much of the mass of an atom, though! • Atoms are electrically neutral; since electrons are negative, there must be something positive as well • Thomson proposed a “plum pudding” model • Electrons are embedded like plums in a pudding, or blueberries in a muffin • But how to test it??

9. Scattering • Basic idea: bombard atoms with projectiles • Depending on what’s inside, the projectiles will be deflected in various ways • Reconstruct the internal structure of the atom from the pattern of scattered objects • Still the way we study small systems today!

10. ErnestRutherford • Born to a poor family in New Zealand • A student of J. J. Thomson at Cambridge • Spent time at McGill University in Canada and the University of Manchester • Later returned to Cambridge as head of the Cavendish Lab • Nobel Prize in chemistry (1908) • Supervised an unusually large number of future Nobel winners • Known for his somewhat caustic wit "All science is either physics or stamp collecting."

11. Rutherford’s Experiment (1910) • With Hans Geiger and Ernest Marsden • Shot “ particles” at a thin gold foil •  particle = nucleus of helium • 8000 times as heavy as an electron • About 50 times lighter than a gold atom • Positive charge • Looked at pattern of scattered ’s

12. Outgoing  particle Incoming  particle 1-2 degrees What did he expect to find? • If Thomson’s picture is correct, we expect very little scattering • Since  particles are much heavier than electrons, the electrons just get brushed aside – we can ignore them! • Positive charge “the muffin” is very spread out, diffuse • The incoming  particle should just blow right through it • Very little net deflection, on average • Theory suggests a few degrees at most

13. What did he find? • Most (99.99%)  particles are deflected only slightly • Some, however, are deflected through very large angles! Outgoing  particle Incoming  particle "It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

14. What does it mean? • Most of the atom is empty space • Because most of the  particles were not deflected significantly • The positive charge in the atom is concentrated in a tiny nucleus • Only a high concentration of charge can produce the large scatterings seen occasionally • The nucleus has a large mass, almost the entire mass of the atom in fact • Otherwise the  particle would brush it out of the way A very unexpected result, basically the opposite of Thomson’s model!

15. Animation

16. A New Model • Rutherford’s analysisshowed that the size of the nucleus is about 100,000 times smaller than the atom as a whole • About 10–10 / 105 = 10–15 m • If we could scale up the atom so that the nucleus was the size of a golf ball, the atom would be about five miles across! • Atom = nucleus plus electrons • Nucleus is heavy, positively charged • Electrons are light and negatively charged • How is it put together?? • Analogy: the solar system

17. Planetary Orbits • Solar system contains planets plus the sun • Sun is much more massive than any planet • Force of gravity holds them in orbit • Planets are attracted to the sun • Force falls off like the square of the distance from the planet to the sun

18. Q2 Q1 d Electrical Attraction • Interestingly, the force of attraction between electric charges has almost the same form! Compare to: Hmmm...

19. “Planetary Model” of the Atom • Atom like a miniature solar system – electrons orbiting nucleus • Electrical attraction holds it together • Opposites attract • Same type of orbits as for planets, even • A dynamic atom, not static • Chemical properties perhaps connected to electron orbits?

20. A Problem • It won’t work! • There are (three) additional equations describing electrical and magnetic phenomena – Maxwell’s equations • Unify electric, magnetic, and optical phenomena • Light is an electromagnetic wave • An electron moving in an orbit would give off light • The light carries energy away from the electron • The electron spirals closer to the nucleus and eventually crashes into it • This would all happen in much less than a second!

21. So what’s the answer? • Rutherford and his contemporaries had no solution to this problem • Solving it required an entirely new type of physics theory – Quantum Mechanics • In this theory, the electrons don’t really “orbit,” rather, they are “spread out” in a sort of cloud around the nucleus • You always find whole electrons, though! • In a sense, the electron is nowhere (everywhere?) until we look for it • Weird, but QM is the most precisely tested scientific theory of all time!

22. “Hard Cylinder” Scattering • A (relatively!) simple model that is analogous to Rutherford’s experiment and analysis • Consider scattering of steel balls (say) off a heavy, perfectly elastic cylinder Ball ( particle) Cylinder (Nucleus)

23. Analysis • Let’s determine the pattern of scattered particles in this case, i.e. how they deflect • If we see this pattern, we could conclude that the nucleus is cylindrical (round) • Also that the scattering (interaction) is of “hard cylinder” type • In this simple case, the scattering behavior can be determined from the geometry alone • In the real-world case, the scattering pattern follows from knowing the force between the  particle and nucleus • Just the electrical repulsion • A bit more complicated…

24. Outgoing direction These angles are equal!  R Basic Setup Scattering angle b So we can determine what  is for any b

25. Result • This geometry exercise is not terribly interesting  • Result: (For the record, I have neglected the size of the ball compared to R in this.) • Gives b for any , or vice versa:

26. b Check #1 • If b = 0 we should get  = 180   = 180

27. Does the formula work? • If b = 0 then • Thus Yep!

28.  = 0 b = R b Check #2 • If b = R we should get  = 0 

29. Does it work? • If b = R then • Thus Yep!

30. Putting it to Use • Assume that we couldn’t see the heavy cylinder! • Scatter balls off it for lots of different b’s • Note the outgoing directions  of the scattered particles • If we find that b and  obey the relation then we conclude the nucleus is round and the scattering of “hard sphere” type!

31. Size of the Nucleus • The formula says that b is proportional to cos(/2) • So if we plot b versus cos(/2) we should get a straight line with slope equal to R b Allows us to determine the size R of the “nucleus”! cos(/2)

32. Sample Data

33. “Nuclear” Size Determination Slope = 2.95 so R = 2.95 cm