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60 years ago…

60 years ago…. The explosion in high-tech medical imaging. & nuclear medicine. (including particle beam cancer treatments). The constraints of limited/vanishing fossils fuels in the face of an exploding population. The constraints of limited/ vanishing fossils fuels.

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60 years ago…

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  1. 60 years ago…

  2. The explosion in high-tech medical imaging &nuclear medicine (including particle beam cancer treatments)

  3. The constraints of limited/vanishing fossils fuels in the face of an exploding population

  4. The constraints of limited/ vanishing fossils fuels …together with undeveloped or under-developed new technologies

  5. will renew interest in nuclear power Nuclear

  6. Fission power generators will be part of the political landscape again as well as the Holy Grail of FUSION.

  7. …exciting developments in theoreticalastrophysics The evolution of stars is well-understood in terms of stellar models incorporating known nuclear processes. Applying well established nuclear physics to the epoch of nuclear formation - ~3 -15 minutes after the big bang - allows the abundances of deuterium, helium, lithium and other light elements to be predicted. The observed expansion of the universe (Hubble’s Law) lead Gamow to postulate a Big Bang which predicted the Cosmic Microwave Background Radiation as well as made very specific predictions of the relative abundance of the elements (on a galactic or universal scale).

  8. 1896 1899 a, b g 1912

  9. Henri Becquerel(1852-1908) 1903 Nobel Prize discovery of natural radioactivity Wrapped photographic plate showed distinct silhouettes of uranium salt samples stored atop it. 1896 While studying fluorescent & phosphorescent materials, Becquerel finds potassium-uranyl sulfate spontaneously emits radiation that can penetrate  thick opaque black paper  aluminum plates  copper plates Exhibited by all known compounds of uranium (phosphorescent or not) and metallic uranium itself.

  10. 1898Marie Curie discovers thorium (90Th) Together Pierre and Marie Curie discover polonium (84Po) and radium (88Ra) 1899Ernest Rutherfordidentifies 2 distinct kinds of rays emitted by uranium  - highly ionizing, but completely absorbed by 0.006 cmaluminum foil or a few cm of air  - less ionizing, but penetrate many meters of air or up to a cm of aluminum. 1900P. Villard finds in addition to  rays, radium emits  - the least ionizing, but capable of penetrating many cm of lead, several ft of concrete

  11. 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

  12. m R v F or

  13. 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!

  14. V R C A

  15. Number surviving Radioactive atoms What does  stand for?

  16. Number surviving Radioactive atoms logN time

  17. for x measured in radians (not degrees!) What if x was a measurement that carried units?

  18. Let’s complete the table below (using a calculator) to check the “small angle approximation” (for angles not much bigger than ~15-20o) which ignores more than the 1st term of the series Note: the x or(in radians) = (/180o)(in degrees) Angle (degrees)Angle (radians)sin  0 0 0.000000000 1 0.017453293 0.017452406 2 0.034906585 3 0.052359878 4 0.069813170 6 8 10 15 20 25 0.034899497 0.052335956 0.069756473 0.104719755 0.104528463 0.139173101 0.173648204 0.258819045 0.342020143 0.422618262 0.139626340 0.174532952 0.261799388 0.349065850 0.436332313 25o 97% accurate!

  19. y = x y = x - x3/6 + x5/120 y = x3/6 y = x5/120 y = sinx y = x - x3/6

  20. Any power of e can be expanded as an infinite series Let’s compute some powers of e using just the above 5 terms of the series 0 0 0 1 e0 = 1 + 0 + + + = e1 = 1 + 1 + 0.500000 + 0.166667 + 0.041667 2.708334 e2 = 1 + 2 + 2.000000 + 1.333333 + 0.666667 7.000000 e2 = 7.3890560989…

  21. violin Piano, Concert C Clarinet, Concert C Miles Davis’ trumpet

  22. Similarly A Fourier series can be defined for any function over the interval 0  x 2L where Often easiest to treat n=0 cases separately

  23. Compute the Fourier series of the SQUARE WAVE function f given by p 2p Note:f(x)is an odd function ( i.e.f(-x) = -f(x)) so f(x)cosnxwill be as well, whilef(x)sinnxwill be even.

  24. change of variables: x  x'= x- periodicity: cos(X+n) = (-1)ncosX for n = 1, 3, 5,…

  25. for n = 2, 4, 6,… for n = 1, 3, 5,… change of variables: x  x'= nx IFf(x) is odd, all an vanish!

  26. periodicity: cos(X±n) = (-1)ncosX for n = 1, 3, 5,…

  27. for n = 2, 4, 6,… for n = 1, 3, 5,… change of variables: x  x'= nx for odd n for n = 1, 3, 5,…

  28. y 1 2 x

  29. Leads you through a qualitative argument in building a square wave http://mathforum.org/key/nucalc/fourier.html Add terms one by one (or as many as you want) to build fourier series approximation to a selection of periodic functions http://www.jhu.edu/~signals/fourier2/ Build Fourier series approximation to assorted periodic functions and listen to an audio playing the wave forms http://www.falstad.com/fourier/ Customize your own sound synthesizer http://www.phy.ntnu.edu.tw/java/sound/sound.html

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