Radiation Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton Atom

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1 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Radiation Equilibiu, Intia onts, and th Nuclus Radius in th Elcton-Poton Ato H. Vic Dannon Novb, 13 Rvisd July, 14 Abstact Boh s Ato solvs th aadox of th lost ngy that dos not lad to th Ato collas, by claiing that sinc th is no Atoic collas, th cannot b lost adiation. Accoding to Boh s Thoy, Elctodynaics dos not aly to th acclation of th lcton towads th oton. Th Quantizd Angula ontu lcton obits allow no adiation, and consquntly, no atoic ngy loss. Boh oosd that th lcton obits can dfy Elctodynaics bcaus thy hav angula ontus that a disct ultils of. Consquntly, th obits a occuid by standing wavs, 1

2 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon and no adiation taks lac in th. Howv, whil th standing wav agunt is u hyothsis, th adiation by an acclating chag is an xintal fact of lctodynaics. Boh s solution faild to tak into account th oton s adiation that consats fo th lcton s adiation loss. Thus, Boh agunt dos not guaant that th Ato will not collas. And it dos lac th lcton-oton Ato out of th laws of Physics, and Elctodynaics. Claly, th Poton has its own obits, in which it acclats towads th lcton, and adiats it. Thn, th lcton-oton syst satisfis a odifid Kl s 3 d law fo th iods of th lcton and th oton 3 ætlcton ö æ lcton lcton ö = çt è ø èç ø oton oton oton Nxt, w assu that th ow of th ngy adiatd by th oton into th lcton fild quals th ow of th ngy adiatd by th lcton into th oton fild. This lads to th quality of th Intia onts of th lcton, and th oton: A uly chanical condition.

3 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Naly, w show that Th lcton-oton Ato is lctodynaically stabl if and only if th lcton and oton intia onts a qual lcton lcton» oton oton This quality dtins th adius of th oton s obit, which is th Nuclus Radius of th Elcton-Poton Ato: -1»» Th Poton s Piod is aoxiatly - - T» T 4 1 / Th Poton s Angula Vlocity is aoxiatly W» w Th Poton s Quantizd Angula ontus a aoxiatly W 4 nn n» n (6.546) 3

4 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Kywods: Elctoagntic Radiation of Acclatd Chag, Rlativistic, Radiation Loss, Quantizd Angula ontu, Atoic Obits, Elcton, Poton, Ato, Nuclus Radius, Physics & Astonoy Classification Sch: 41.6-; 3; 3.1-f; B-; Contnts. Th Elcton Sialing onto th Poton 1. Photons Equilibiu and Radiation Equilibiu. Th Acclations of th Elcton and th Poton 3. Kl s 3 d Law fo th Elcton-Poton Ato 4. Radiation Equilibiu, Intia onts, and th Nuclus Radius 5. Th Poton s Piod, and Angula Vlocity 6. Poton s Obits with Quantizd Angula ontus Acknowldgnt Rfncs 4

5 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Th Elcton Sialing onto th Poton.1 Elcton s Acclation towads th Poton Th Elcton-Poton Ato is a lantay syst, wh th lcton obits th oton along so llis. Fo silicity, w consid a cicula obit of adius dtind by a balanc btwn th cntital foc v and th lctic attaction 1 4 That is, w = w,. 1 = 4 Thus, th lcton s acclation towads th oton is w 1 1 =. 4. Non-lativistic Elcton Th vlocity of th lcton in its obit is tangntial to th 5

6 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon obit, and ndicula to th lcton s acclation towads th oton. To s that th vlocity is non-lativistic, fa slow than light sd c, aoxiat th lcton obit s adius by t A wavlngth in th id otical sctu is l t. This wavlngth cosonds to th otical fquncy c 3 1 n = = 5 1 l cycls/sc. This fquncy cosonds to angula vlocity w = n = 3 1 adians/sc. Th lcton s vlocity is v = w t/sc Thus, v c 1 1, Thn, Lontz Facto 1 g () v =» 1 v 1 - c is non-lativistic. 5 6

7 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon.3 Th Elcton Sialing Ti onto th Poton Sinc v 1 =, 4 Th kintic ngy of th lcton in its cicula obit is 1 v 1 1 =. 4 Th lctic ngy of th Elcton-Poton Ato is Thfo, th total lcton ngy is and its at of chang is 1 1 -, 4 d ì 1 1 ü ï 1 1 í- ï ý = ïî 4 ïþ 4 d. dt dt This quals th at at which th lcton adiats ngy as it acclats towads th oton, wh th tadd ti is é êë a 3 6 c úû t- c t -» t - = t -» c ù, t, 7

8 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon and th acclation of th lcton is [ vg( v)] v a =». Thfo, th Elcton s Radiation at is æv ö æ 1 1 ö 6 c» 6 c. çè ø çè 4 ø 3 3 Sinc it quals th at of chang of th lcton s ngy, / æ 1 1 ö 1 1 /» 6 // c ç 4 4 // 3 è ø æ 3 ö ç 4 3 dt» c ç d 4 çè ø d dt, Thfo, th lcton will sial into th oton in - 11 = = 3» æ ç4 = ö = t c ç 4 çè ø æ ö 3» c ( ) ç çè ø - c c sc ( )» 1 1 (1.6 1 ) 8

9 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon (9.11)» (1.6) -13» sc..4 Boh s Rsolution avoiding Elctodynaics Boh claid that sinc th is no Atoic collas, th cannot b lost adiation. Accoding to Boh, th lcton that acclats towads th oton in its obit, dos not adiat lctoagntic ngy, dfying Elctodynaics. Boh oosd that th lcton obits hav angula ontus that a disct ultils of. Consquntly, accoding to Boh, th obits a occuid by standing wavs, and no adiation taks lac in th. Claly, th standing wav agunt is u hyothsis. On th oth hand, th adiation by an acclating chag is an xintal fact of Elctodynaics. Thus, Boh s agunt lacs th lcton-oton Ato out of th laws of Physics, and Elctodynaics..5 Th Poton s Loss balancs th Elcton s loss Claly, th Poton has its own obits, in which it acclats 9

10 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon towads th lcton, and adiats it. Thn, w ll assu that th lcton and th oton xchang qual aounts of ngy btwn th, and balanc ach oths loss. 1

11 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon 1. Photons Equilibiu and Radiation Equilibiu 1.1 Equilibiu of Exchangd Photons Th oton shows th lcton with hotons that consat fo th hotons ngy lost by th lcton, vnt th sialing of th lcton onto th oton, and k th ato stabl. Claly, that xchang of hotons btwn th lcton and th oton taks lac along th lin that saats th. 11

12 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Howv, w do not hav a foula that involvs th nub of hotons xchangd, and th adii of th obits. To div such foula, w hav to dscib th xchangd hotons as xchangd adiation. 1. Equilibiu of Exchangd Radiation Th lctoagntic adiation of an acclating chag is in a lan ndicula to its obit. Thus, th adiation of th lcton and th oton a along cicls ndicula to thi obits W shall assu that th ow of th ngy adiatd by th oton into th lcton fild quals th ow of th 1

13 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon ngy adiatd by th lcton into th oton fild. Each consats fo th oth s loss, to k th obits ngis in a dynaic quilibiu. Rquiing th d Pow = { adiation ngy} dt adiatd by th acclating oton into th lcton fild, to qual th Pow lost by th acclating lcton, lads to an stiat fo th adius of th oton s obit. Th lcton with acclation a lcton adiats th ow 6 c 3 a lcton. Th oton with acclation A oton adiats th ow 6 c 3 A oton Th quality of th two yilds an stiat fo th oton s obit, which is th nuclus adius.. 13

14 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon. Th acclations of th Elcton and th Poton Dnot = lcton s ass, =oton s ass, = lcton s obit adius, = oton s obit adius, w =lcton s angula vlocity in its obit W=oton s angula vlocity in its obit a =lcton acclation in its obit towads th oton A =oton acclation in its n th obit towads th lcton g () v = 1 v 1 - c = Lontz Facto fo th Elcton obit g ( V ) = 1 V 1 - c = Lontz Facto fo Poton obit Du to th nonlativistic sd of th lcton, g () v» 1, 14

15 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon v ()». W aoxiat th oton in its obit by a chag + concntatd at th cnt of th lcton s obit. Thn, th lctic attaction on th lcton 1 4 is balancd by th cntital foc w. Thfo, th balanc of focs on th Elcton is, Hnc, w 1 =, 4.1 Th Elcton Acclation in its Obit is a = w = 1 4 Siilaly, w aoxiat th lcton in its obit by a chag - concntatd at th cnt of th oton s obit. Thn, th lctic attaction on th oton 4 1, is balancd by th cntital foc 15

16 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon W. Thfo, th balanc of focs on th oton is Hnc, 1 W =, 4. Th Poton acclation in its Obit is A =W =

17 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon 3. Kl s 3 d Law fo th Elcton-Poton Ato Nwton s Gavitational foc on a lant obiting th sun at adius, with iod T = is w Thfo, G Plant Sun w =. Plant Plant 3 w = G = constant. Plant Sun O T 4 = = k 3, G 3 which is Kl s 3 d Law fo Gavitation. Fo two lants, w = G = w Sun O 3 æt ö 1 æ1 ö = ç èt ç ø è ø. 17

18 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Fo th Elcton-Poton Ato, lcton w lcton = 1 4 yild PotonW Poton = w = = W 4 Hnc, 3. Kl s 3 d Law fo th Elcton-Poton Ato is æ 3 T ö ç lcton æ ö = T èç ø èç ø oton 18

19 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon 4. Radiation Pow Equilibiu, Intia onts, and th Nuclus Radius W consid an lcton obiting th oton in a cicl with adius. Th lcton is attactd to th oton with acclation a = and adiats hotons into th oton fild. Thfo, 4.1 Th Elcton s adiation Pow is æ 1 1 ö = 6 c 6 c ç çè 4 ø a 3 3 Th Poton in th Elcton-Poton Ato, has an obit within th lcton s obit, with adius, fa sall than th lcton s obit adius. 19

20 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Th oton is attactd to th lcton, with acclation A = 1 1 4, and adiats hotons into th lcton s fild. Thfo, 4. Th Poton s Radiation Pow is æ 1 1 ö = 6 c 6 c ç 4 çè ø A 3 3 At quilibiu, th Radiation Pow absobd by th oton, quals th Radiation Pow absobd by th lcton. æ 1 1 ö æ 1 1 ö 6» ç 4 6 ç 4 è ø è ø 3 3 c c H, w us» bcaus of th slightly lativistic chaact of th sds and th asss. This lctodynaic quality lads to a suisingly uly chanical condition: th quality of th Intia onts of th lcton and th oton. That is,

21 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon 4.3 Th lcton-oton Ato is Elctodynaically stabl if and only if th intia onts of th lcton and th oton a qual» Consquntly, 4.4 Th oton obit adius, which is th nuclus adius is W cout »»»» Thfo, -11 = / = Th Nuclus Radius of th Elcton-Poton Ato -1»»

22 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon 5. Poton s Piod, and Angula Vlocity By Kl s 3 d Law fo th Elcton-Poton Ato, æ 3 T ö ç æ ö = çt ç è ø è ø = æ ö ç çè ø 3 That is, = 5.1 Th Elcton and th Poton Piods W 1 T =»» 4» w T 4 ( ) Th Poton Piod is T» T 4

23 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon To aoxiat T, and T, not that a wavlngth in th id otical sctu is -7 l 6 1 t. This wavlngth cosonds to th otical fquncy 8 c n = = 5 1 cycls/sc. l This fquncy cosonds to a iod Thfo, T lcton = = 1 sc/cycl n Th Poton s Piod is aoxiatly - - T» T 4 1 / Th fquncy n cosonds to th angula vlocity wlcton = n = 3 1 adians/sc. Thfo, 5.4 Th Poton s Angula Vlocity is aoxiatly W» w

24 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon 6. Poton s Obits with Quantizd Angula ontus Th lcton s obits dtin th oton s cosonding obits, with Quantizd Angula ontus: 3 3 Sinc by 3.1, w = W, Th Poton s Quantizd Angula ontus a n n nn wn n W = n w W n n 4 n Th Poton s Quantizd Angula ontus a aoxiatly W n (6.546) n n 4

25 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Acknowldgnt I thank th Aican Association Physics Tachs ting aticiants who lt snt a liinay vsion of y attts, and citiqud it, on July 14, in innaolis, innsota. Rfncs [Boh] David Boh, Th Scial Thoy of Rlativity Routldg, [Fynan] Richad Fynan, Th Fynan Lctus of Physics, Edison Wsly, [Kovtz] Attay Kovtz, Elctoagntic Thoy, Oxfod,. [aion] Jy aion; ak Hald, Classical Elctoagntic Radiation, Scond Edition, Acadic Pss, 198. [Panofsky] Wolfgang Panofsky; lba Phillis, Classical Elcticity and agntis, Scond Edition, Addison Wsly, 196. [Pak] Sybil P. Pak, cgaw-hill Encyclodia of 5

26 14 AAPT SUER EETING innaolis N, July 3, 14 H. Vic Dannon Physics, Scond Edition, cgaw-hill, [Polyanin] Andi Polyanin; Alxi Chnoutsan, A Concis Handbook of athatics, Physics, and Engining Scincs, CRC, 11. [Pool] Chals P. Pool, Th Physics Handbook Fundantals and Ky Equations, Wily, [Rindl], Wolfgang Rindl, Rlativity Scial, Gnal, and Cosological, Oxfod, 1. [Skinn], Ray Skinn, Rlativity fo Scintists and Engins, Dov, 198. [Sith] Glnn S. Sith, An Intoduction to Classical Elctoagntic Radiation Cabidg, [Stannad], Russll Stannad, Rlativity, Stling, 8. [Woan] Gaha Woan, Th Cabidg Handbook of Physics Foulas, Cabidg,. htt://n.wikidia.og/wiki/lontz_tansfoation htt://n.wikidia.og/wiki/rlativity_thoy htt://n.wikidia.og/wiki/rlativity_thoy 6

UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.

UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM Solution (TEST SERIES ST PAPER) Dat: No 5. Lt a b th adius of cicl, dscibd by th aticl P in fig. if, a th ola coodinats of P, thn acos Diffntial