5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS

Transcription

1 5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870 s) had alady shown using lctochmisty that amounts of lctic cunt popotional to amounts of som substancs could b libatd in an lctolytic cll. Th tm lcton was suggstd as a natual unit of lcticity. But Thomson xpimntally obsvs lctons as paticls with chag & mass. y = displacmnt inducd by dflcto voltag ξ Cathod Anod Dflcto plats Phospho scn Thomson found that sults a indpndnt of (1) cathod matial (2) sidual gas composition lcton is a distinct paticl, psnt in all matials! Classical mchanics foc on lcton du to dflcto voltag: F y = ξ dv y (foc stats at tim t = 0 whn lcton nts gion btwn plats) = m dt ( F = ma ) Intgating v y = dv y = ξ dt m m ξt [Not vy (t = 0) = 0]

2 5.61 Fall 2007 Lctu #2 pag 2 Intgating again sinc v y = dy and y t = 0) = 0 y = ξt 2 f ( dt m 2 t f = total tim lcton is btwn th plats (asily calculatd) St voltag ξ, calculat tim t f, masu displacmnt y Modn day valu is m = 1.758x1011 C/kg = 1x1011 C/kg m (b) 1909 Millikn oil dop xpimnt dtmins, m spaatly mist of micon-siz oil doplts in ai Gavitational foc downwad: F g = Mg M = mass of doplt, g = gavitational constant F g Fictional foc upwad du to ai: = 6π ηv = adius of doplt, η = ai viscosity, v = doplt vlocity Sinc v, tminal vlocity v t is achd whn focs balanc 6π ηv t = Mg gt doplt mass M = 6π ηv t g Now us x-ays o γ-ays to add som chag ( n) to th doplts Voltag ξ acoss plats xts Coulomb foc F c = ξn on th chagd doplt x-ays n- F c F g

3 5.61 Fall 2007 Lctu #2 pag 3 Adjust voltag until dop stops falling: v = 0 = 0, F c = F g ξn = Mg Dtmin n = Mg ξ Mullikn did this fo lots of doplts i = 1,2,3,... Thy all had diffnt chags (n i ) but all intg multipls of chag ( ) Dtmind lmntay chag as = 1.59x10 19 C (vy clos to today s valu = 1.602x10 19 C ) Combining valus fo ( m m = 9.11x10 31 kg ) and ( ) Hydogn mass was known: m H = 1.66x10 27 kg lcton is subatomic!! (c) Wh a th lctons? What s th stuctu of th atom? Angstom (10-10 m) atomic siz scal alady infd fom gas kintics Fist jllium modl didn t last long (jlly) n + Ruthfod backscatting xpimnt Au foil H 2 + H 2 + (no lctons) 98% undflctd 2% scatt back (1) H 2+ nuclus vy small, << m (Ruthfod stimatd m) (2) Au atoms a mostly mpty!

4 5.61 Fall 2007 Lctu #2 pag 4 Ruthfod plantay modl: classical mchanical modl of atomic stuctu Coulomb attaction plays th ol of gavity +Z 2 m v cntiptal foc F c = v Z 2 Coulomb foc F C = 4πε0 2 fo stabl obit m v 2 Z 2 Z 2 = = 4πε 0 2 4πε 0 m v 2 This is stabl compad to spaatd lcton & nuclus 1 Z 2 1 Z 2 E = K.E. + P.E. = m v 2 + = < 0 2 4πε 0 2 4πε 0 BUT modl not consistnt with classical lctodynamics: Acclating chag mits adiation! (cntiptal acclation = v 2 /) And sinc light has ngy, E must b gtting mo ngativ with tim must b gtting small with tim! Elcton spials into nuclus in ~ s! Also, as dcass, v should incas Fquncy ν of mittd light = fquncy of otation ν (Hz = cycls/s) = v (m/s) 2π (m/cycl) cicumfnc of obit atom should mit light at all fquncis that is it should poduc a continuous spctum

5 5.61 Fall 2007 Lctu #2 pag 5 BUT mission fom atoms was known to b disct, not continuous! Fo H: n 1 = 3 n 1 = 2 n 1 = 1 n 2 = n 2 = ,000 30,000 50, ,000 (cm -1 ) Fo th H atom, Rydbg showd that th spctum was consistnt with th simpl fomula: 1 1 ν (cm -1 ) = R 2 2 n 1 n 2 with n 1 = 1, 2, 3,... and n 2 = n 1 + 1, n 1 + 2, n 1 + 3,... R = 1.097x10 5 cm -1 (Rydbg constant) n 1 = 1 Lyman sis n 1 = 2 Balm sis n 1 = 3 Paschn sis visibl & UV lins wll known Summay: Ruthfod s modl of th atom (1) Is not stabl lativ to collaps of lcton into nuclus (2) Dos not yild disct mission lins, (3) Dos not xplain th Rydbg fomula