B-field points into page

1. a g B-field points into page b 1900-01 Studying the deflection of these rays in magnetic fields, Becquerel and the Curies establish  rays to be charged particles

2. 1900-01 Using the procedure developed by J.J. Thomson in 1887 Becquerel determined the ratio of charge q to mass m for : q/m = 1.76×1011 coulombs/kilogram identical to the electron! : q/m = 4.8×107 coulombs/kilogram 4000 times smaller!

3. Noting helium gas often found trapped in samples of radioactive minerals, Rutherford speculated that  particles might be doubly ionized Helium atoms (He++) 1906-1909Rutherford and T.D.Royds develop their “alpha mousetrap” to collect alpha particles and show this yields a gas with the spectral emission lines of helium! Discharge Tube Thin-walled (0.01 mm) glass tube to vacuum pump & Mercury supply Radium or Radon gas Mercury

4. Status of particle physics early 20th century Electron J.J.Thomson 1898 nucleus ( proton) Ernest Rutherford 1908-09 a Henri Becquerel 1896 Ernest Rutherford 1899 b g P. Villard 1900 X-rays Wilhelm Roentgen 1895

5. Periodic Table of the Elements 26 27 28 Fe Co Ni 55.86 58.93 58.71 Atomic “weight” values averaged over all isotopes in the proportion they naturally occur.

6. C 6 Through lead, ~1/4 of the elements come in “single species” Isotopes are chemically identical (not separable by any chemical means) but are physically different (mass) The “last” 11 naturally occurring elements (Lead  Uranium) recur in 3 principal “radioactive series.” Z=82 92

7.    92U23890Th234 91Pa234 92U234      92U23490Th230 88Ra226 86Rn222 84Po218 82Pb214    82Pb21483Bi214 84Po214 82Pb210    82Pb21083Bi210 84Po210 82Pb206 “Uranium I” 4.5109 years U238 “Uranium II” 2.5105 years U234 “Radium B” radioactive Pb214 “Radium G” stable Pb206

8. Chemically separating the lead from various minerals (which suggested their origin) and comparing their masses: Thorite (thorium with traces if uranium and lead) 208 amu Pitchblende (containing uranium mineral and lead) 206 amu “ordinary” lead deposits are chiefly207 amu

9. Masses are given in atomic mass units (amu) based on 6C12 = 12.000000

10. Mass of bare hydrogen nucleus: 1.00727 amu Mass of electron: 0.000549 amu

11. number of protons number of neutrons

13. Starting from the defining relation of a Fourier transform: -i k g'(x) g(x)= e+ikx f(x) we can integrate this “by parts” f(x) is bounded oscillates in the complex plane over-all amplitude is damped at ±

14. Similarly, starting from:

15. And so, specifically for a normal distribution:f(x)=e-x2/22 differentiating: from the relation just derived: Let’s Fourier transform THIS statement i.e., apply: on both sides! 1 2 ~ ~ ~ F'(k)e-ikxdk 1 2 ~ ei(k-k)xdx ~  (k – k)

16. 1 2 ~ ei(k-k)xdx ~  (k – k) ~ selecting out k=k k k ' ' rewriting as: dk' dk' ' 0 0

17. Fourier transforms of one another Gaussian distribution about the origin Now, since: we expect: Both are of the form of a Gaussian! x  k 1/

18. x k  1 or giving physical interpretation to the new variable x px h