Electromagnetic radiation and steady states of hydrogen atom

Transcription

1 Elctromagtic radiatio ad stady stats of hydrog atom Jiaomig Luo Egirig Rsarch Ctr i Biomatrials, Sichua Uivrsity, 9# Wagjiag Road, Chgdu, Chia, Abstract. Elctromagtic phoma i hydrog atom ar cotrolld by th lctromagtic itractio of th movig chargd particls ad th iducd filds. Th ffcts of slf coctratio ad bd of propagatio of iducd filds will producd by pich ffct ad itractio of displacmt currts with icras of frqucy. Th groud stat of hydrog atom is th atural mchaical balac stat which th radiatio ractio o th chargd particl was coutractd by th radiatio actio of th othr. Th modal rspos of th orbits is stady stat of hydrog atom with high rgy, ad th modal quatio of groud orbit could b dducd by mas of stadig wav aalysis. Slctig th groud orbit of th hydrog atom as basic rfrc to dscrib th modal orbits, th modal quatio would b chagd ito th sam form with Schrödigr quatio. Thrfor, th modal rspos could b applid to xplai xcitd stats ad lctromagtic radiatio of hydrog atom. Ky words: Elctromagtic radiatio, Movig chargd particl, Pich ffct, Modal rspos, Stadig wav, Schrödigr quatio PACS m - Radiatio by movig chargs Cotts 1. Itroductio. Stability ad spotaous radiatio 3. Stability of th lctro orbit 5 4. Modal aalysis of hydrog atom 6 5. Discussio Coclusio 11 Rfrcs 1 1

2 1. Itroductio Light from hydrog atom, which is o kid of lctromagtic radiatio causd by movig chargd particls, is th most importat data to udrstad th structur of th atom. Although thr ar umrous modls to dscrib th lctromagtic phoma basd o quatum thory, classical lctrodyamics ad classical lctromagtics, but o of thm ca itrprt th radiatio of movig chargd particl idisputably ad compltly. At prst, th lctromagtic problms of a hydrog atom is tratd with th motio of sigl cotrolld by th ctr fild of th uclus, so th structur of hydrog atom is ustady bcaus of th rgy missio producd by acclratd lctro. Actually, radiatio is dtrmid by th iducd lctric fild producd by chag of magtic fild which rlats to th motios of two chargd particls. Clarly, th modl of sigl acclratd lctro ca ot dscrib this two chagig magtic filds causd by th two chargd particls, thrby; th currt udrstadig about th radiatio of hydrog atom is oly a icomplt or v icorrct dscriptio. I atomic ad molcular world, th chargd particls ar th ultimat sourcs of lctromagtic fild ad radiatio, ad thir motios ar dtrmid by th lctromagtic itractios amog thm. Hydrog atom is th simplst atom, which cosists of a proto ad a lctro, but is a vry complx lctromagtic systm. Excpt for th ordiary Lortz forcs, th lctromagtic itractio i a hydrog atom should iclud radiatio ractios, itractio btw radiatios causd by diffrt chargd particls, th ifluc of radiatio o motio of th othr chargd particls, ad th actio of iducd magtic fild o iducd lctric fild i radiatio wav tc. Ths ffcts ar importat factors for th motios of chargd particls i hydrog atom to b dscribd corrctly. Th ffct of spotaous radiatio o th motio of a acclratd chargd particl could b dscribd by th radiatio ractio o it. Accordig to cosrvatio of rgy, th radiatio ractio forc o a acclratd chargd particl should mak th rgy of th chargd particl loss cotiuously, so its dirctio must b i ivrs dirctio of its vlocity at ay tim. Abraham-Lortz quatio dscribs th radiatio ractio of th chargd particl dducd from Larmor s powr quatio, but th applicatio of th quatio is limitd by additioal coditios ad th problm ruaway solutio. A itgrodiffrtial quatio was iducd to rplac it, but is cotrary to th traditioal cocptio of causality bcaus of th pracclratio prdictd by this quatio[1]. So, th radiatio ractio is still a difficult problm to b solvd. I trms of magtic forc of Ampr law, magtic forc btw two lctric currts is dtrmid by two lctric currts ad thir distac, th magtic fild of a movig chargd particl could b udrstood with th ffct of th lctric currt lmt. For circular orbit motios of chargd particls i hydrog atom, magtic filds will chag with rotatio of th chargd particls, ad whil iduc lctric filds. Th chag of magtic forc dpd o th chags of magtic filds, so it is possibl to build a rlatio btw th iducd th itsity of lctric filds at th chargd particls ad th rat of th chag of magtic forc by lctromagtic laws. Elctromagtic radiatio is th propagatio of variabl iducd lctric fild with iducd magtic fild i spac, ad th variabl iducd fild could b rgardd as displacmt currt by mas of Maxwll s thory. Clarly, th radiatio filds causd by th chargd particls i hydrog atom will act ach othr ad could b udrstood by displacmt currts. I additio, by th cocptio of pich ffct of plasma, th chargd particls i plasma will b pichd by slf magtic fild. So, th displacmt currt which could b rgardd

3 as th ffct of movig displacmt chargs will crtaily b pichd by slf iducd magtic fild. Thrfor, th itractio btw iducd lctric filds ad pich ffct will obviously affct th distributio ad th propagatio of th radiatio i hydrog atom. I this articl, accordig to classical lctromagtic, th lctromagtic radiatio from hydrog atom was discussd i dtail basd o aalysis of th lctromagtic itractios btw th two variabl lctric currt lmts causd by movig lctro ad movig uclus, ad th th stability of hydrog atom was also ivstigatd. Fially, th modal rspos of th groud stat orbit of hydrog atom wr aalyzd by mas of statioary wav approach. Spotaous radiatio of hydrog atom I a hydrog atom, rotatig aroud th ctr of mass o itslf circular orbit, th dirctios of th vlocity ad acclratio of th lctro ad th proto ar rotatig with th sam frqucy υ, but th magituds of thm kp ivariabl. Figur 1 shows th lctro ad th uclus rotat coutrclockwis aroud ctr of mass o pla xy, th ctr-of-mass is at th origi O of th frams. Th Lortz s forcs o th lctro ad uclus provid th ctriptal forc to kp th balac of circl orbits. Th lctric currt lmts of thm (J ad J ) will b rotatig with th two chargd particls ad producig a chagig magtic fild, as wll as iducig th lctric filds. v F & m y F r F m r F m v x O F & m Fr Figur 1. Elctromagtic itractio of th two movig chargd particls i hydrog atom with circl orbit. Th ctr of mass of hydrog atom is at th origi O of th fram; subscript ad rprst lctro ad uclus. r is th distac btw uclus ad lctro; F m ad V rprst magtic forc ad vlocity, rspctivly; F & is th rat of th chag of m F m ; F r is radiatio ractio; dash li rprst th orbit of th particl. Accordig to classical lctromagtics thory, th magtic forc itractig btw th lctro ad th proto is rlatd to th product of two lctric currt lmts J ad J, ad cotrols th chags of magtic filds producd by J ad J, so th radiatios of th two chargd particls should rlat to this product. At ay tim, th magtic forcs actig o th lctro F m ad o th uclus F m ar sam i magituds but opposit i dirctio, ad th rats of chags of th physical quatitis rlatd to vlocity ar πν tims of thm i magitud ad prpdicular i dirctio, such as J, J, F m ad F m. Bcaus of rotatio, th additioal lctric currts wr producd ad could b dscribd by th rats of J ad J that is J & ad J & as show i figur, whil a additioal forc was actig o th chargd particl. By magtic forc of Ampr law, th additioal forcs o th lctro F r ad o uclus F r could b dscribd as follow. F = J & B r 3

4 F = J & B (1) r Whr, B is th itsity of magtic fild of th uclus at th positio of th lctro, ad B is th itsity of magtic fild of th lctro at th positio of uclus. Th dirctios of F r ad F r ar i th oppsit dirctio of thir vlocitis, ad th magituds of thm ar sam. Bcaus F r ad F r ar th ffct producd by th chagig magtic fild, so should b ifluc of iducd lctric fild o th chargd particls i trms of th cocpt of lctromagtic iductio. With rotatig, F r ad F r will do gtiv work to th chargd particls ad mak thm slowdow, thus ar th radiatio ractio forcs. Th itsity of iducd lctric filds at th poit of th chargd particls could b dscribd with F r ad F r dividd by thir chargs, ad oly occur i th frot of th chargd particls. Th lctro ad th proto possss th sam magitud of charg but oppsit lctrical proprty, th th iducd lctric filds of thm ar sam i magitud but i oppsit dirctio. J & J E r J & O y E r J x Figur. Elctromagtic itractio by th two lctric currt lmts. subscript ad rprst lctro ad uclus. E r th itsity of iducd lctric fild by movig chargd particl; J is th lctric currt lmt ad J & is th rat of th chag of J; dash li rprst th orbit of th particl. Accordig th iductio of Faraday s law, th iducd lctric fild E r should b proportioal to F& m /, whr th charg of lctro is -, E r th magitud of itsity of E r at th poit of th lctro could b writt as F& m Er = ki () Whr, k i is a cofficit rlatd to lctric iductio. Ad th magitud of F & m is as follow, Whr, F & = πνj B = πν F (3) m Fm m is th magitud of magtic forc o lctro, Combiig formula () ad (3), th magitud of E r is dscribd as πk iυ Er = Fm (4) Bcaus th ctriptal forc of th circl motio of th lctro is providd by th ordiary Lortz s forc which is ctr forc, ad is ivrsly proportioal to r th squar distac btw th lctro ad uclus, ad th frqucy ν of orbit of th lctro is dirctly proportioal to r -3/. So, th radiativ ractio forc F r 4

5 ad th itsity of iductio lctric fild E r will icras rapidly with th dimiutio of distac r, ad th spd of icras of thm is sharplir tha that of Lortz s forc. Accordig to Maxwll s lctromagtic wav thory, a chagig lctric fild iducs a magtic fild rotatig it, ad could b udrstood as a displacmt currt producd by movig displacmt chargs. Bcaus th vacuum spac is lctrically utral, th displacmt currt could b itrprtd as th motio ffct by th sam amout of th gtiv ad positiv displacmt chargs which mov i oppsit dirctio. This dscriptio is similar to th pichd-plasma, th pich ffct of plasma is that th distributio ad motio of chargd particls i plasma ar strogly rstrictd i a crtai rgio by slf magtic fild, ad th itsity of th pich ffct is proportioal to th squar of slf lctric currt [1]. Thrfor, w could giv th dductio that th iducd magtic fild would rstrict th propagatio ad distributio of iducd lctric fild lik pihd plasma, ad mak th lctromagtic wav radiats i vry arrow ara i frot of movig chargd particl at high frqucy, as wll as th ara of radiatio will rapidly shrik with icras of frqucy. Thrfor, th sprad charactristics of th priodic iducd lctric fild is diffrt from that of lctrostatic of magtostatic fild bcaus of pich ffct, ad could radiat to far distac without dcras of itsity of ltromagtic fild. y J d r O J r x Figur 3. Itractio of displacmt currts with diffrt radius of circl orbit. subscript ad rprst lctro ad uclus. J d is th displacmt currt; r is th radius of th hydrog atom; dash li rprst th orbit of th particl. It is ot difficult to fid th displacmt currts causd by radiatio ar paralll ad i th sam dirctio, ad at th positios of th chargd particls ar i sam dirctio with th currts by thir motios, So th propagatio of iducd lctric fild of o chargd particl will b flxd by th magtic forc producd by th othr chargd particl, whil th radiatio will tak away a part of rgy of th movig chargd particls ad mak radius of th orbit shrik. With th dcras of radius of th orbit, th magitud of th vlocity, frqucy ad th displacmt currt will icras sharply, whil th curvig iducd lctric fild of o chargd particl will gradually approach to ad act o th othr chargd particl. Fially, th iducd lctric fild will mt with th othr chargd particl ad push it ahad, ad th push forc will coutract th radiatio ractio actig o th chargd particl, th th propagatio of th iducd lctromagtic fild will d at th chargd particl, as show i figur 3. Thus, hydrog atom will ot radiat rgy to outsid, ad th orbits of th lctro ad th uclus will b stady. This ffct could b calld radiatio coupl of pair of charg, th frqucy of th orbit could b calld cutoff frqucy of radiatio υ c, ad th cutoff radius of th lctro orbit quals to r c. Wh υ>υ c or r < r c, th curvd iducd lctric filds will pass througth th ara btw th lctro ad th uclus, th magtic forcs btw th movig chargd particls ad th displacmt currts ar rpllt ad will mak th distac btw th two chargd particls icras. Thrfor, ulss th radius of th chargd particls qual th cutoff radius, hydrog atom will b ustady. Of cours, th cutoff radius r c should b coicidt with Bohr radius a 0 of hydrog atom. For th ocircular closd orbits, th dirctios of lctric currt lmts th two movig chargd 5

6 particls ar paralll ad chag priodically, ad th rat of th chags of th radial compots of th two currt lmts ar always i th sam dirctio o a sam li at ay tim. Th iducig lctric filds by thm ar always i sam dirctio ad chag sychroistically, ad th radiatio fild which is th summatioof thm will loss th rgy of hydrog atom. Thus, th ocircular closd orbit is ustady stat with lctromagtic radiatio. 3 Stability of hydrog atom For a isolatd hydrog atom, th groud stat which th lctro ad th uclus rotat alog thir circular orbits with th cutoff frqucy υ c is th uiqu stady structur, th lctro movig o highr rgy orbit will automatically com back to groud stat orbit by spotaous radiatio basd o th discussio abov. Clarly, this rsult satisfis to th lowst rgy pricipl. Wh a hydrog atom was disturbd by th outr fild, th orbits of chargd particls would chag to rspos ad balac to th outr ifluc. A importat cssary coditio for th stability of th orbit is that a stady orbit is rst ad closd. That is, startig from a arbitrary poit of a stady orbit, th chargd particls will go back to th startig poit with th sam stat aftr a cycl. Th rsoac of th groud orbit of hydrog atom is o of stady rspos to th outr lctromagtic vibratig fild, bcaus th rsoat orbit of th chargd particls satisfis th closdss coditio. Wh th chargd particl absorbs th rgy of outr vibratig fild with th sam frqucy with th groud orbit of hydrog atom, th rsoac of th groud orbit will tak plac, ad th radiatio of th lctromagtic fild producd by th rsoat orbit will balac with th outr fild. Aothr rspos of th orbit is to chag to a w orbit with a diffrt frqucy ad absorbs th vibratig fild rgy with th spcial frqucy which is part of th outr disturbig fild. Clarly, this phomo could b udrstood as vibratio rspos of th orbits of hydrog atom, ad b dtrmid by th mchaical proprtis ad th structur of groud orbit of hydrog atom. By th kowldg of structural mchaics, modal vibratio is a commo atural phomo for a lastic objct to rspos th outr priodic disturbs, ad th modal frqucis ar rlatd to th atural frqucy which is dtrmid by th shap ad lastic proprty of th lastic objct. Th groud hydrog atom could b cosidrd as a o-liar lastic structur which is cotrolld by ctr fild forc causd by th itractio btw th lctro ad th uclus. Thrfor, th w orbits ar oly th highr rgy orbits which satisfy modal rspos of groud orbit of hydrog atom, ad th modal frqucis could b dscribd with th atural umbr ad th frqucy of groud orbit. Th rgy of th w orbits ar crtaily discrt, th radiatio ad absorptio of lctromagtic wav of th hydrog atom could b xplaid with th missio ad absorptio of priodic lctromagtic wav by th trasitio amog modal orbits. Th groud circular orbit of hydrog atom could b dscribd with th compoud motio of two orthogoal vibratios with th sam amplitud ad frqucy, th modal rspos of th groud orbit could b solvd by th vibratio aalysis. I trms of wav, th groud circular orbit of hydrog atom could b udrstood as a tsd strig, th modal rspos of it could b dscribd by th statioary wavs. Thus, thr ar svral mathmatical approachs to b slctd to trat th modal rspos of groud stat hydrog atom, ad to itrprt th structur ad radiatio of it. 4. Modal aalysis of hydrog atom 6

7 I hydrog atom, thr ar thr kid itractios btw th lctro ad th uclus, such as coulombic forc, magtic forc ad radiatio ractio causd by faradic lctric fild, ad th magtic forc is vry wak compard with coulombic forc. So th ffct of magtic forc was cosidrd as modificatio for th rsult. Usig th rlativ coordiat of th lctro rlativ to th uclus, th two-body systm of hydrog atom could b rducd o-body. Rplacig lctro mass with rd ucd mass μ, μ=mm/m+m, M is th mass of uclus, ad m is th mass of th lctro. Th lctro motio rlativ to uclus could dscrib th motio ad pottial rgy of hydrog atom. z A H O H H E H θ A E 0 x r 0 A 1 O a E 1 y Figur 4. Vibratio of th circular lctro orbit alog its ormal dirctio. E 0 is th iitial orbit (dash circl) with radius r 0 ; E 1 is th lctro trajctory (solid llips) with trasvrs a; E H is th vibratig orbit (dash circl); A H is th farthst poit of orbit E 1 ; O H is th ctr of orbit E H, H is rsoat amplitud of orbit E 0 quals to th distac from O to O H. A 1 ad A ar th itrsctios of E 0 ad E 1, ad also ar th ods of stadig wav. Figur 4 shows a circular orbit with rgy E 0 ad radius r was put o xy pla ad uclus was as origi of fram. It was rsoatig alog its ormal dirctio with atural frqucy. E 1 was trajctory of th lctro ad was similar to llips, which could b cosidrd as a stadig wav basd o E 0, th wav satisfid coditio πr=λ, =1, that is th primtr of th orbit E 0 quals to wavlgth λ of th wav. Orbit E H is th highst pottial rgy vibratig orbit of E 0, Slctig curv coordiats of orbit E 0 ad axis z, th axis OE 0 starts at od A 1, passs through od A ad ds at od A 1. As th frqucy of orbit E 1 is sam with that of orbit E 0 ad kps ivariabl, th orbit E 1 should b a harmoic wav with variabl amplitud, ad is similar to th stadig wav of ts strig as show i figur 5. Th approach of stadig wavs aalysis for ts strig could b itroducd to dscrib th modal rspos of lctro orbit i hydrog atom. z A H H Orbit E 1 OE 0 A 1 πr A πr A 1 Figur 5. Harmoic wav of orbit E 1 rlativ to orbit E 0. A 1 ad A ar th ods of wav; A H is th farthst poit of orbit E 1 7

8 Rfrrig to th statioary wav quatio for a tsd strig, th spac dpdc sgmt of wav quatio is as follow: u( x) k + u( x) = 0 (5) x T Or Ad u( x) π + x λ k T p p π = λ u( x) = 0 k = ρ m ω (8) Whr, k is lastic cofficit, u(x) ad T p rprst rspctivly th wav fuctio of strig ad th tsio actig o th strig. ρ m is th mass pr uit lgth of strig, ad ω is th agular frqucy. Th lctro of hydrog atom is cotrolld by coulombic forc, magtic forc ad actig of faradic fild. Th quivalt lastic cofficit ad tsio of th lctro should b vry complx, ad it is difficult to gt th xact mathmatical xprssio of thm. A practicabl way is to cosidr th mai actio of coulombic forc, th to modify th gott rsult by th othr two actios. For ay lctro circular orbit, th ctrifugal forc quals to th ctriptal forc, so th rsultat forc F(r) should b zro ad th tsio T p actig o th lctro quals to th coulombic forc: 1 Tp = f = (9) 4πε r 0 V T F ( r) = + = 0 (10) r r For th circl orbit, th lastic cofficit k(r) is th drivativ of F(r) ad could b dducd from th quatio (10) df( r) V T k ( r) = = = (11) dr r r Th circular lctro orbit of groud stat hydrog atom is th foudatio to aalyz its mods, ad could b cosidrd as a stadig wav with wavlgth λ=πr ad with a ivariabl amplitud. Th tsio actig o th lctro T w should qual to T p, lastic cofficit k w is as follow. 1 Tw = Tp = (1) 4πε r 1 T k w = k( r) = πr πr r Rfrcig to formula (5), (9) ad (13), u( x) 4π ε 0 + T u( x) = 0 x πr 0 (6) (7) (13) (14) 8

9 Th abov formula is th wav quatio of th circular orbit of hydrog atom. Bcaus th orbit could b at arbitrary dirctio i spac, so th spatial stadig wav quatio should b iducd to dscrib th circular orbit of th lctro orbit. 4π ε 0 ϕ ( x, y, z) + T ϕ( x, y, z) = 0 (15) πr Whr, = + + x y z Comparig quatio (15) to formula (6), th wav lgth λ would b dscribd as: h λ = (16) P Whr, P is momtum of th lctro, ad μπr h = (17) ε 0 4π μ ϕ ( x, y, z) + T ϕ( x, y, z) = 0 (18) h Formula (17) ad (18) is th mathmatical xprssio i form statioary wav for groud circular orbit of hydrog atom, but it is difficult to apply thm to solv th structur of hydrog atom. So, it is cssary for th mathmatical xprssio to b tratd for applicatio. By th cocptio of statioary wav, ay poit o th statioary wav is at rst, th rgy of a statioary wav oly icluds pottial rgy. Th circular orbit could b udrstood as a tsd strig, ad th motio of th lctro producs ctrifugal forc for th balac of th orbit. Th rlatio amog th rgy E of th statioary wav ad th pottial rgy V, kitic rgy T of movig lctro alog orbit could b dscribd as follow. E = V = T = 4π μυ r (19) From formula (17) ad (19), th rgy of statioary wav is rwritt as E = hυ (0) Hydrog atom is th simplst atom, th structur of othr atoms could b udrstood th problms that th lctros mov i ctr fild as lik hydrog atom. Th tratmt ad solutio of modal rspos of hydrog atom could b usd as rfrc to dscrib th othr atoms. By th kowldg of modal rspos, th high trm modal frqucis, rgis ad radius could b dscribd with atural umbr ad that of groud stat. So, Bohr radius a 0 of groud stat hydrog atom could b trat as a costat, th πa μ 0 h = (1) ε 0 Calculatig h with rlativ physical costats i formula (1), th rsult of h is 34 h = J S () Clarly, h is vry clos to Plak s costat. Rplacig kitic rgy T with subtractio of pottial rgy V from total rgy E, (E-V), formula (18) is writt as. 9

10 8π μ ϕ ( x, y, z) + ( E V ) ϕ( x, y, z) = 0 (3) h Formula (0) ad (3) ar th quatios usd to solv th stady orbit of hydrog atom, ad ar i sam form with Plak s quatum hypothsis, Schrödigr quatio. So, th solutio about hydrog atom by Formula (0), () ad (3) is crtaily coicidt to that by Schrödigr quatio. 5. Discussio Classical lctromagtis is a prfct thory to itrprt th lctromagtic phoma by macroscopic chargd objct ad lctric currt. Th ffct of lctric currt lmt of movig chargd particl ad th displacmt lctric currt ar importat cocptio to udrstad th lctromagtic fild ad wav. So, i this work, th radiatio from hydrog atom has b discussd with itractio btw th two variabl lctric currts lmt of th lctro ad th proto, ad th pich ffct of plasma was itroducd to dscrib th propagatio of th iducd lctromagtic fild. Th tratmt ad cosquc should b satisfid to th classical lctromagtics thory. I atomic ad molcular systm, th chargd particls ar th ultimat sourcs of th lctromagtic fild ad radiatio, th motio of a chargd particl is dtrmid by th itractio btw it ad th othr. Ad th radiatio is compltly cotrolld by itractio amog th chargd particls, ad th actio o a chargd particl icludig radiatio ractio is producd by th lctromagtic fild ad could b applid to dscrib itsity ad proprty of lctromagtic fild of th poit it locat. So, th radiatio ad th stability of movig chargd particl could b dscribd by mas of mchaical aalysis. Th cocptio of displacmt currt was itroducd by Maxwll for dductio of Maxwll quatios of lctromagtic fild. Elctromagtic wav is a importat cosquc from th quatios, ad had b coformd by Hrtz xprimt. I additio, lctromagtic wav could b itrprtd as propagatio of chagig lctric fild with chagig magtic fild by mutual iductac, ad could b udrstood as th displacmt currt with slf magtic fild sprads i spac i trms of cocptio of displacmt currt. Accordig to th pich ffct of plasma, th distributio ad motio of chargd particls i plasma will b rstrictd by slf magtic fild. So, th propagatio of chagig lctric fild will b pichd by iducd magtic fild, ad th agl of radiatio of lctromagtic wav will b cotrolld by this pich ffct. For a priodic orbital motio of chargd particl i ctr lctric fild, th frqucy will ifluc itsivly o th radiatio ad pich ffct. At a lowr frqucy th ifluc of pich ffct of lctromagtic wav could glctd, but at a highr frqucy such as visibl light, th propagatio of radiatio could b compltly cotrolld by pich ffct ad travls i a tubular spac with ivariabl radius. I this situatio, visibl light could sprad to far distat i vacuum without attuatio of fild itsity. Clarly, th pich ffct of lctromagtic fild is hlpful to udrstad th wav-particl duality of light. At prst, quatum mchaics provids a xact ad complt thory to udrstad th structur ad th lctromagtic radiatio of atom ad molcul. Schrödigr quatio [] which is wav mchaics vrsio of quatum mchaics has brought about outstadig cosqucs ad provids a prcis mathmatical basis to xplai th phoma of atomic, molcular ad solid-stat structur [3]. Th importat foudatio of quatum mchaics icluds Plack s quatum hypothsis [4] ad th d Brogli wav [5], but th dbat about th itrprtatio of th d Brogli wav has vr calmd dow ad v xtds to th philosophic domai. 10

11 Currtly, th Cophag itrprtatio dvlopd by Bohr ad his collagus, icludig th purly probabilistic itrprtatio of wav fuctio [6, 7], dis classical causality, causs th particl trajctory to disappar, ad causs uprdictability i th obsrvatio of quatity. Not oly wr its foudrs dply prturbd, today som of th lumiaris of scic rmai dissatisfid with its foudatio ad its itrprtatio, v i spit of ackowldgig its stuig powr [8]. Eisti [9] ad Schrödigr [10] arousd srious objctios to th purly probabilistic itrprtatio, ad Eisti blivd that th thory was icomplt to dscrib th physical systm [11], ad vr accptd quatum thory. Modal rspos of lastic structur is a commo phomo i atur. Atom ad molcul could b cosidrd as o-liar lastic structur systm cotrolld by Lortz s forc ad radiatio itractio amog th chargd particls, ad is th stady balac systm of mchaics ad radiatio. Modal frqucis ar discrt, ad th rgis ad radius of th modal orbits of th lctro ar discrt too. Thrfor, modal rspos is th root caus which producs quatum phomo i atomic ad molcular world. I this work, Plack s hypothsis ad Schrödigr quatio hav dducd from th modal aalysis of groud stat of hydrog atom, th mathmatic rlatio E =hυ was achivd udr th coditio that Bohr radius of hydrog atom must b a costat. Thrfor, it is cssary for tratmt of th structur of atom ad molcular to us th stady stat of hydrog atom as rfrc. 6. Coclusio Th lctromagtic radiatio from hydrog atom is producd by th lctromagtic itractio btw th two chagig lctric currt lmts by th movig lctro ad th movig proto. Th radiatio ractio o th chargd particls is th iductio ffct, ad could b dducd from th chag of magtic itractio forc. Th radiatio is th opposit ffct to radiatio ractio, ad th th itsity of th iducd lctric fild at th locatio of th chargd particl could b dscribd with radiatio ractio. Th distributio ad th propagatio of th iducd fild ar dtrmid by pich ffct ad itractio btw th displacmt currts. So, th radiatios ar rstrictd by th motios of th chargd particls, ad could act o thm. Ths importat physical phoma ca ot b glctd for th comprhsio about th lctromagtic ffcts by movig chargd particls i hydrog atom. Th stady orbits of th chargd particls must satisfy th closdss coditio, i.. th orbit is closd ad rst i th ctr of mass fram of th atom. Th groud stat of hydrog atom is dtrmid by th radiatio coutractio of th pair of charg, ad is th atural stat of a isolatd hydrog atom. Th orbits with highr rgy ar ot stady bcaus of spotaous radiatio of movig chargd particls, oly if thr is appropriat disturbac of outr factors, ad th stady orbits with high rgy would xist possibly. Th rsoat absorptio ad modal trasitio of groud orbit ar th importat way for hydrog atom trs i high rgy stats. Thr ar svral mathmatical approachs to trat th physical phomo, ad with th wavs th modal rspos of groud orbit of hydrog atom is dscribd asily. Slctig th groud orbit of hydrog atom as basic rfrc, th mathmatical xprssio of modal rspos was simplid for tratmt. Th rlatio btw rgy ad frqucy, ad modal quatio i form of wav sparatly ar i th sam form with Plack s quatum ad Schrödigr quatio. Thrfor, th modal rspos of hydrog atom could b usd to itrprt th xcitig stats ad th liar spctrum of hydrog atom. 11

12 Rfrcs 1. Jackso J. D., Classical Elctrodyamics, Joh Wily & Sos, Ico., p.30-38, , (196).. Plack M., A. Physik, 4:553 (1901). 3. d Brogli L., A. Phys., 3: (195) 4. Schrödigr E., A. Physik, 79:361, 489, 734; 80:473, 81:109 (196). 5. Slatr J., Quatum Thory of Atomic Structur, McGraw-Hill Book Compay, Ic. p., (1960) 6. Bor M., Z. Physik, 40:167 (196). 7. Bor M. ad Fork V., Z. Physik, 51:165 (198). 8. Klppr D., ad Jackwi R., Scic, 89, 893 (000) 9. Eisti A., Podolsky B. ad Ros N., Phys. Rv., 47, 777 (1935). 10. Schrödigr E., Naturwissschaft, 3:787, 83 ad 844 (1935) 11. Schilpp P. A., Albrt Eisti: Philosophr-Scitist, Th Library of Livig Philosophrs, Ic. Evasto, III. P. 666, (1949). 1