Ogs of Quatu Thoy Masuts of sso of lght (EM adato) fo (H) atos foud dsct ls 5 4 Abl to ft to followg ss psso ν R λ c λwavlgth, νfqucy, cspd lght RRydbg Costat (~09,7677.58c - ),,, +, +,..g.,,.6, 0.6, (Lya Ss, 906), 656.5, 486., 44.,. (Bal, 885) Boh Modl- Copyght 009 by Jy M. Stza. All ghts svd. Boh Modl of Ato Boh (9) plaato fo dsct ls. atos cosst of havy uclus (postv chag) ad lght lcto (gatv chag). lctos obt uclus; oly cta dsct obts allowd that a stabl statoay quatu stats qud to pla why th s o adato (gy loss) by lcto obt (classcally, qud fo acclatg lcto). EM adato (gy) ttd/absobd wh obt chags ad fqucy s νδe/h Boh Modl- Copyght 009 by Jy M. Stza. All ghts svd.
Obtals Boh s d postulat lads to assupto that agula otu s quatzd h Plack s Costat L v ω h π quatu ub Cob wth lctostatc attacto foc balacd by ctfugal foc v Sphcal Elcto Obtals st Boh ad. H ato v o,,... L ucla chag ( H) (toducd by h 900) (photo plaato Est 905) Boh Modl- Copyght 009 by Jy M. Stza. All ghts svd. Boh Modl-4 Copyght 009 by Jy M. Stza. All ghts svd. Egy Lvls Elcto obt has ktc (KE) ad pottal (PE) gy Lt PE 0 as (zo PE dfto) PE v E v E Boh th usd Plack/Est thos ΔE j hν j 4 ν π c h c R hν
Boh s H Egy Lvls E 4 ν π λ c h c Pobls ffctv Rydbg costat dfft fo o-bal ss data hgh soluto spcta show dvdual ls actually ultpl closly spacd ls, l splttg (.g., ach Bal ls actually ls) Good agt wth Bal ss (H) data, Boh Modl-5 Copyght 009 by Jy M. Stza. All ghts svd. Modfcatos to Boh Ato. Iclud oto of lcto about ato ct of ass ( ct of uclus) us ducd ass (fo classcal ch.) of two-body syst ucl μ + μh ato 0.99945 + ucl 4 π μ chags R but dos ot pla splttg R h c. Noccula obts llptcal obts ca also satsfy balac of attacto/ctfugal focs Sofld s galzd (chacs) postulat. Spcal Rlatvty fo Est, ffctv s fucto of vlocty Boh Modl-6 Copyght 009 by Jy M. Stza. All ghts svd.
Boh Modl-7 Ellptcal Obts: Sofld Us galzd ota p Sofld Acto Itgal (ov pod of oto) p dq ach g l. o. odat quatzd KE.g., -d: KE v ; v d dt v p v -d (, θ) azuthal cood. Copyght 009 by Jy M. Stza. All ghts svd. KE q& sa as Boh pθ dqθ θ h assupto ( v θ )( dθ ) θ h L θ h () π Lag. o. Ldθ θ h 0 θ k,,,... π Lcostat fo L dθ θ h 0 ls lcto solatd sys. 0 sd uclus d/dt of gal coodat (.g., vlocty dcto) azuthal quatu ub Boh Modl-8 Ellptcal Obts: Sofld -d (, θ) adal cood. p d () 0,,,... fo ccula obt, p 0 Cob azuthal ad adal p p g l. soluto of () ad () s llptcal obt a b k L k π So quatu # s, but EE(): o splttg Copyght 009 by Jy M. Stza. All ghts svd. h a μ b h μ k pcpal quatu ub k + k,,,..., sallst fo gv k s k ccula obt adal quatu ub 0 s ccula obt k 4 a b k 4 4
Spcal Rlatvty Est showd ass dpds o vlocty, st ( v ) c lctos ovg quckly, so potat Iclud gy of obtg lcto sult 4 π μ α E, k + h k Boh Modl-9 ow obts wth sa but dfft k hav dfft gy l splttg Copyght 009 by Jy M. Stza. All ghts svd. 4 α ~ 0.007 hc F Stuctu Costat Boh Modl-0 Boh-Sofld Obts Egy dpds paly o pcpal quatu ub () sall ffct fo dfft k ultpl tastos (ls) wth sa Δ but dfft k at dfft λ.g., Bal ls ( ) Lss ls foud th possbl slcto uls (Δk±) Thoy succssful at pdcto spcta of H-lk atos (H, H +, L ++, ); hlpd buld podc tabl qus so ad hoc assuptos pobls wth ultlcto atos ptus fo quatu chacs Copyght 009 by Jy M. Stza. All ghts svd. lk- 5