VISUAL PHYSICS ONLIN BOHR MODL OF TH ATOM Bhr typ mdls f th atm giv a ttally icrrct pictur f th atm ad ar f ly histrical sigificac. Fig.. Bhr s platary mdl f th atm. Hwvr, th Bhr mdls wr a imprtat stp i th dvlpmt f quatum mchaics. Quatum mchaics is a mathmatical thry t accut fr th atmic rlatd bhaviur f ur physical wrld. I quatum mchaics, th lctrs bud t a atm ar dscribd i trms f wavs. N lgr ca talk abut th path f a lctr mvig arud th uclus, but ly abut th prbability f fidig a lctr at a crtai lcati.
Nils Bhr prpsd th Bhr Mdl f th Atm i 93. Bcaus th Bhr mdl is a mdificati f th arlir Ruthrfrd Mdl, sm ppl call Bhr's Mdl th Ruthrfrd-Bhr Mdl. Ulik arlir mdls, th Bhr mdl xplais th Rydbrg frmula fr th spctral missi lis f atmic hydrg. Rviw: atmic spctra Th Bhr mdl is a platary mdl i which th gativlychargd lctrs rbit a small, psitivly-chargd uclus bcaus f th Culmb frc btw th psitivly-chargd uclus ad th gativly-chargd lctrs. H dvlpd his thry basd up assumptis that wuld lad t a xplaati f th li spctra mittd frm atms ad t a drivati f th Rydbrg quati fr hydrg-lik atms. Bhr usd th idas f Plack ad isti that radiati is mittd ad absrbd i discrt amuts ad ths idas lad t th ccpt f th pht.
Mai Pits f th Bhr Mdl Bhr usd th Ruthrfrd mdl f th atm as his startig pit. His mdificatis ivlvd tw pstulats that wr simply ackwldgmts f xprimtal facts rlatd t th spctral missis. Ths pstulats wr at dds with th idas f classical physics. Th Bhr pictur f th atm was f a ctral psitiv uclus with a lctr i allwd circular stabl rbit such that th lctr s agular mmtum was quatisd. Th lctr i a stabl rbit did t ls rgy by th missi f lctrmagtic radiati. Bhr assumd that classical lctrmagtic thry was t cmpltly valid fr atmic systms.
Pstulat A atm ca xist i crtai allwd r statiary stats, with ach stat havig a dfiit valu fr its ttal rgy. Wh th atm is i f ths stats it is stabl ad ds t radiat rgy. Th ttal rgy f a rbitig lctr is quatisd such that th lctr s agular mmtum L has a st f discrt valus giv by quati () () h L mv r =,, 3, m mass f lctr v rbital vlcity f lctr r rbital radius h L Plack s cstat h = 6.63x0-34 J.s agular mmtum
Pstulat A atm mits r absrbs rgy ly wh a lctr mvs frm stabl stat t athr. I a trasiti frm its iitial stat t its fial stat, a pht is ithr mittd r absrbd ad th rgy f th pht is qual t th diffrc i th rgy f th tw stats (quati ) () f i h f rgy lst r gaid by atm hf rgy f mittd r absrbd pht h f i f Plack s cstat h = 6.63x0-34 J.s frqucy f lctrmagtic radiati (pht) ttal rgy f lctr i iitial stat i ttal rgy f lctr i fial stat f Fig.. Bhr s mdl f th atm.
W ca driv a quati fr th radii f th stabl circular bits (quati 3) ad th ttal rgis f th allwd stats (quati 4) usig th idas f classical lctrmagtic thry ad Bhr s quatisati f agular mmtum pstulat. Th allwd radii r f th stabl stats ar (3) h r r q m 0 h ttal rgis f th lctr ( = K + P ) ar (4) 4 m q 8 h 0 0 prmittivity f fr spac 0 = 8.85x0 - C.N -.m - h Plack s cstat h = 6.63x0-34 J.s q lctr charg =.60x0-9 C m lctr mass m = 9.x0-3 kg pricipl quatum umbr =,, 3,
Drivati f Bhr s quatis fr th hydrg atm Statiary rbit ttal rgy is cstat = K + P attractiv frc btw p + ad - circular rbit F q mv Culmb frc = ctriptal frc 4 r r Pttial rgy f - P 4 q r Kitic rgy f - K mv ()(4 ) q r Ttal rgy f - ()(4 ) q r agular mmtum - quatizd L m v r h Radius f statiary stat, pricipl quatum umbr r h mq Bhr radius, = h r r r 5.6 0 m mq Ttal rgy f - 4 mq 3.6 V 8 h 3.6 V mq 8 4 h
Ngativ sig lctr bud t uclus Iizati rgy 3. 6 V = -3.6 V = - 3.4 V 3 = -.5 V 4 = -0.85 V 5 = - 0.54 V V =.600-9 J Hydrg spctral lis f i h f hc f i agrmt with Rydbrg quati
Prblms with th Bhr Mdl A fatal shrtcmig fr ay thry is that it shuld t agr with xprimtal rsults. Th discrpacis btw prdictd ad masurd wavlgths fr li spctra thr tha hydrg wr ugh t idicat that mdificatis wuld hav t b mad t Bhr s thry f th atm. Athr difficulty lay i th atur f th pstulats. Th quatisati rul fr agular mmtum was cmpltly arbitrary ad thr was a ccptual difficulty with hw th lctrmagtic wavs mittd by a atm wr prducd ad what was th scillati that dtrmid th frqucy f th mittd radiati. It vilats th Hisbrg Ucrtaity Pricipl bcaus it csidrs lctrs t hav bth a kw radius ad rbit. Th Bhr Mdl prvids a icrrct valu fr th grud stat rbital agular mmtum. It maks pr prdictis rgardig th spctra f largr atms. It ds t prdict th rlativ itsitis f spctral lis. Th Bhr Mdl ds t xplai fi structur ad hyprfi structur i spctral lis. It ds t xplai th Zma ffct.
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