Gauge Institute Journal, Vol. 11, No. 3, August 2015

Transcription

1 Gaug Institut Jounal, Vol., o. 3, August 05 Th uton as a Collasd-Hydogn Atom: Zo Point Engy & ucla Binding Engy, X Rays & Gamma Rays, ucla Focs & Bonding utonic Elctons Oitals, and uton Stas vic0@comcast.nt May 05 Astact: A nuton may disintgat into a oton, an lcton, and an antinutino. In Gavitational Collas, lctons and otons comin into nutons. W stalish that th uton is a Collasd-Hydogn Atom comosd of an lcton and a oton: Th Elcton has -4 st Oit Radius m, Sd 5,558,34 m/sc, 3.5 (Sd in Hydogn).

2 Gaug Institut Jounal, Vol., o. 3, August 05 Fquncy cycls/scond, 9 3,7 (Hydogn Elcton Fquncy), in th ang of Had X Rays: Quantum of Angula Momntum ( ), Zo Point Engy -767 V, 564 (Hydogn s Zo Point Engy) with hoton fquncy cycls/sc. Th Poton has st Oit Radius m, Sd 7,905,45 m/sc, (Hydogn Poton Sd). ) Fquncy cycls/sc, 0 3,3 (Hydogn Poton Fquncy), in th ang of Gamma Rays: Quantum of Angula Momntum ( ), ucla Binding Engy -36, 308 V, Elcton Oit Radius 4.5 Poton Oit Radius, ) Had X Rays, and Gamma ays: 553 (Hydogn s ucla Engy Binding) Had X Rays, a du to a uton s xcitd lcton tuning fom a high ngy Oit to a low ngy Oit

3 Gaug Institut Jounal, Vol., o. 3, August 05 Gamma Rays a du to a uton s xcitd oton tuning fom a high ngy Oit to a low ngy Oit 3) Kl s 3 d Law fo th uton: T T M - 4» 8 m -, v, c V c is consistnt with th modl of th uton as a Collasd Hydogn 4) uton Sin Angula Momntum: ( ) Th Assumtion of (0.5) is off y 57% 5) Elctic Collas Vsus Gavitational Collas: Th Elctic Foc twn th lcton and th oton is (Gavitational Foc). Thus, a uton sta is catd y Elctic Collas. 6) Total Binding Engy: Th uton s Total Binding Engy is 7) ucla Foc: 553 (Hydogn s Total Binding Engy). Th uton s ucla Foc is 305,000 (Hydogn s ucla Foc), and 836 (uton s Zo Point Engy Foc) 8) Mini Molcula Bonding: 3

4 Gaug Institut Jounal, Vol., o. 3, August 05 A uclus comosd of a Poton and a uton is a Mini On-Elcton Molcul H +, with an lcton that oits th two otons. 9) uclus Bonding: Th utons suly lctons which Oitals aout th uclus ond th otons, and nsu th uclus Staility. 0) uton Stas Bonding: In uton Stas, th Gavitational Focs a ngligil comad to th ucla Bonding, which ks th sta ackd togth. ) utonic Elctons Oitals: uton s lctons oit th nuclus, and k th otons ondd Kywods: Suatomic, Photon, uton Radius, lcton Radius, Comosit Paticls, Quak, lcton, Poton, Poton Radius, uton, Gaviton, Radiation Engy, Kintic Engy, Gavitational Engy, Rotation Engy, Elctic Engy, Oital Magntic Engy, Sin Magntic Engy, Cntital Foc, Lontz Foc, Elctic Chag, Mass-Engy, Wav-aticl, Intia Momnts, ucla Stuctu, uclus Staility, ucla Foc, ucla Bonding, Oitals, ucla Binding Engy, Zo 4

5 Gaug Institut Jounal, Vol., o. 3, August 05 Point Engy, Elctomagntic Sctum, X Ray, Gamma Ray, Boh Modl, Hydogn Atom, Radiation Pow Equiliium, uton Sta, PhysicsAstonomyClassificationSchm: 4.0-c, 4.0.Dh, 4.60Cd, 4.60.Ef, 4.60.Fg, q, 4.65.Bt, 4.70.Bh, y, 47.3.C, , B, 6.05.J-, 6.05.fm, Contnts Th uton in Radioactivity, in Astohysics, and in th uclus. X Rays Lin Sctum Povs th xistnc of an Oiting Elcton in th uton. Th Elcton and Poton Oits 3. Radiation Pow Equiliium, and th uton s Intia Momnts Th Elcton s Zo Point Engy 6. Th Poton s ucla Engy 7. Th uton s Mass-Engy 8. Th Poton s Oit Radius 5

6 Gaug Institut Jounal, Vol., o. 3, August Th Poton s Sd 0. Th Poton s Fquncy. Th Elcton s Sd. Th uton s Radius 3. Th Elcton s Fquncy 4. Th Elcton s Quantum of Angula Momntum 5. Th Poton s Quantum of Angula Momntum 6. uton s Zo Point Engy 7. uton s ucla Engy Binding 8. ucla Foc and Zo Point Engy Foc 9. Gamma Rays Oigin is uton s Poton 0. Kl s 3 d law fo th uton is consistnt with th uton s Modl as a Collasd-Hydogn Atom. uton Sin Angula Momntum. Elctic Collas Vsus Gavitational Collas 3. uton s Binding Engy 4. ucla Focs, ucla Bonding, uclus Staility, and uton Stas Rfncs 6

7 Gaug Institut Jounal, Vol., o. 3, August 05 Th uton in Radioactivity, in Astohysics, and in th uclus 0. Th uton in Radioactivity It is wll-stalishd that in th wak intaction, a nuton disintgats into a oton, an lcton, and an antinutino. This may suggst that a uton is comosd of ths th stal aticls. But if such suggstion was v mad, it has no tac in Atomic Physics Txtooks. 0. Th uton in Astohysics It is fimly livd that in th Gavitational Collas of a sta into a uton Sta, lctons and otons comin into nutons. Again, this may suggst that a uton is a Collasd-Hydogn Atom, comosd of an lcton, and a Poton. But such suggstion has no tac in Astohysics Txtooks. 0.3 Th uton as a Collasd-Hydogn Atom Thus, th dscition of uton as a Collasd-Hydogn Atom dwlls in th ackgound of majo Physics discilins, and may 7

8 Gaug Institut Jounal, Vol., o. 3, August 05 not considd a Hyothsis. It may dscid tt as a fact that has to sustantiatd, and xlod. Th fundamntal thoy of th uton is dismissd y assuming th uton to a vaiation of th Poton. Howv, X Rays Emission, and Comutations confim that th uton is a Collasd-Hydogn Atom. This Modl of th uton oints to th oigin of X Rays, vals th souc of th ucla Focs, and offs a lival xlanation to th Staility of th uclus. 0.4 ucla Focs ucla focs w suggstd to account fo th inding of th otons and th nutons in th nuclus. But no ogss was mad in th undstanding of ths focs. As Quaks w suggstd as su-nuclons, thi inding was attiutd to a su-nucla foc, and th inding of nuclons was attiutd to lftov su-nucla focs. This amounts to u sculation aout involvd xchang of gluons, quaks, and a Pion fo luck [Wikidia, ucla Focs]. At th nd, it mains uncla. What a th focs? Lftovs of th stong foc do not tll us much. 8

9 Gaug Institut Jounal, Vol., o. 3, August 05. How do thy oat? Exchang of this, and that dos not claify how th focs oat. 3. How th lctic ulsion twn otons is solvd? At th distanc twn th otons in th uclus, th lctic foc is fomidal too. 4. How do utons contiut to th staility of th nuclus? W cannot tll th diffnc if in th Wikidia animatd faiytal aout th xchang of Quaks, and Gluons, and Pion, th uton will lacd with a Poton. 0.5 ucla Stuctu It is livd that th mo otons in th nuclus, th mo nutons a ncssay to k it stal. But th is no xlanation to how that gat staility is achivd. In aticula, non of th modls fo th nuclus [Wikidia, ucla Stuctu] accounts fo th ulsion twn th otons, and fo th nign lctic nutality of th nutons. How dos th nutal uton hl to dcas th ulsion twn th otons? 0.6 ucla Radiation It is livd that X-Rays oiginat in th nuclus, ut th ocss 9

10 Gaug Institut Jounal, Vol., o. 3, August 05 y which thy a oducd is not cla, [Wikidia, X Ray]. In fact, X Rays Emission ovs th xistnc of an oiting lcton in th uton, and Gamma Ray Emission ovs th xistnc of an oiting oton in th uton. 0

11 Gaug Institut Jounal, Vol., o. 3, August 05. X-Rays Lin Sctum Povs th Existnc of an Oiting Elcton in th uton It has n osvd that X Rays a mittd whn a matial is omadd with a am of lctons o ions. Continuous lctomagntic sctum indicats that som lctons in th am dclat y lctons in th atomic shlls, and som may acclat towads th otons in th nuclus But aks of a lin sctum that show u in th X Ray Sctum a oducd just as th Otical sctum is gnatd: Elctons in th am ush an lcton to a high oit, and whn that xcitd lcton tuns to a low oit, it mits a hoton of X Ray Radiation. It is cla that lin sctum of X Rays Emission mandats an oiting lcton. What is disutd is that this lcton may in th nuclus itslf. Evn th lcton that coms out of a disintgating nuton, is

12 Gaug Institut Jounal, Vol., o. 3, August 05 not nough vidnc fo th livs that th cannot any lcton in th nuton. Thus, th lcton that mits an X Rays hoton has n sculatd to long to th inn shlls of th havy lmnts which omadmnt gnats X Rays, and Gamma Rays Howv, thos inn shlls lctons don t mov fast nough: Th lcton shlls suounding th nuclus a not ngtic nough to yild mo than otical fquncis, and at most, soft X Rays. Ou comutations ov that Gound Oit Elcton Dos not Radiat Gamma Rays. And vn Had X Rays must oiginat in th uclus. Gamma Rays mission quis oiting otons in th uclus.

13 Gaug Institut Jounal, Vol., o. 3, August 05. Th Elcton and Poton Oits Th lcton oits th oton to gnat th cntital foc that counts th lctic attaction twn th lcton and th oton. That attaction acclats th lcton towads th oton, and th lcton adiats ngy, that could caus it to sial onto th oton, and hav th atom collas In [Dan4] w xlaind that to comnsat fo th adiation ngy lost y th lcton, and vnt its sialing onto th oton, th oton must oiting th lcton, acclating towads it, and adiating it with ngy that ks th Atom in quiliium, and in xistnc. Th lcton s oit is lag than th oton s oit, and to find th lcton s oit, and sd, w assum that th oton is at st with sct to th lcton. Thus, th quations fo th lcton s oit and sd, in which th oton s motion will nglctd, a only aoximat. Closd Oits To stay within th nuton s oundais, 3

14 Gaug Institut Jounal, Vol., o. 3, August 05 th lcton, and th oton should hav closd oits.. Cntal Focs By [Routh,. 74], a closd oit sults fom a cntal foc that is ootional to th invs squa of th distanc,(such as th Coulom lctic foc) o dictly to th distanc(such as th cntital foc). Th lcton s chag, and th oton s chag suly th lctomagntic focs to clos thi oits..3 Oits Staility By [Routh,.80] Cntal Foc oits a stal. That is, thy a oundd in a ing twn two cicls. Th staility of th nuton indicats a stal lcton oit, and a stal oton oit..4 Plana Motion Sinc th lctic foc is invs squad law foc, Th lcton s oit, and th oton s oit will stay in th sam lan, and will not gnat a sh Th lan of motion of a aticl tuns aound to gnat a sh only und a non-invs squad law foc. 4

15 Gaug Institut Jounal, Vol., o. 3, August 05 [Chandaskha,. 95]..5 Sds, and Oits Radii Dnot th oton sd in its oit y V V c. / Th adius of th oton s oit is. Th lcton s sd in its oit v v / c Th adius of th lcton s oit, which is th nuton adius,.. 5

16 Gaug Institut Jounal, Vol., o. 3, August Radiation Pow Equiliium, and th uton s Intia Momnts Th lcton is attactd to th oton y th foc m - a 4 0. It is acclatd towads th oton y a - m 40, and adiats hotons into th oton fild. 3. Th Elcton s Radiation Pow is æ - ö ç 6 6 ç ø a ç 3 3 0c m 0c çè 40 Th Poton has an oit within th lcton s oit, with adius, fa small than th lcton s oit adius. Th oton is attactd to th lcton, with acclation 6

17 Gaug Institut Jounal, Vol., o. 3, August 05 A - M 4 0, and adiats hotons into th lcton s fild. 3. Th Poton s Radiation Pow is æ ö - A c 6 M 0c ç 0 è ø At quiliium, th Radiation Pow asod y th oton, quals th Radiation Pow asod y th lcton. æ æ ö - ö - 3» 3 6 m 0c M 0c èç ø ç 0 è ø H, w us» caus ach fomula assums that on aticl is moving whil th oth aticl is stationay. This Elctodynamics quality lads to a suisingly uly mchanical condition: th quality of th Rlativistic Intia Momnts of th lcton and th oton. That is, 3.3 Th uton s Intia Momnts Balanc 7

18 Gaug Institut Jounal, Vol., o. 3, August 05 Th uton is Elctodynamically stal if and only th Intia Momnts of its lcton and oton a qual m M» - - 8

19 Gaug Institut Jounal, Vol., o. 3, August Th uton s Foc Balanc Poof: m M Th Foc alanc quation fo th lcton is Dividing oth sids y c, 40 m v -. m - 40c m 0, 4, 0 7, 9

20 Gaug Institut Jounal, Vol., o. 3, August 05 m Th Foc alanc quation fo th oton is Dividing oth sids y c, - 40 M V M - 4 0c, 0 7, Thfo, m M M » Poof: Dividing th uton s Intia Momnts Balanc 3.3, m M» - -, 0

21 Gaug Institut Jounal, Vol., o. 3, August 05 y th uton s Foc alanc 4., w otain m M - -»,,». M may stimatd oughly y m, as in [Dan4]. 4.3 M m» 4.5 Poof: Fom th Intia Momnts Balanc, 3.3, m M» - - M -» 4 m Evn if 0.5, and 0., thn, -., 4 - -»

22 Gaug Institut Jounal, Vol., o. 3, August 05 In fact, w ll hav» 0.73,» , and 4 - -» 0.99». Thfo, M 0.99» m » 4.5.

23 Gaug Institut Jounal, Vol., o. 3, August Th Elcton's Zo Point Engy 5. Th Elcton s Elctic Binding Engy U lctic c 5. Th Elcton s Magntic Engy U magntic m 4 0 n (4 ) m 0v Poof: Th cunt du to th lcton s chag that tuns n cycls/scond is I n Th Magntic Engy of this cunt is [Bnson,.486] By [Fisch,.97] L LI. 0 m 0 m. Thus, th magntic ngy du to th lcton chag is 3

24 Gaug Institut Jounal, Vol., o. 3, August 05 m0( n ) m 4 0 n w 4 m 0v. (4 ) 5.3 Th Elcton s Magntic Engy in its uton s Oit Poof: is ngligil comad to its Elctic Engy U U magntic lctic m 0v (4 ) 4 v 4 c 4 0 In th following w ll aoximat» Thfo, »» Th Elcton s Rotation Engy m c v

25 Gaug Institut Jounal, Vol., o. 3, August 05 Poof: Fom th alanc twn th Cntital and Elctic focs on th lcton in its uton oit, - 40 m v m v - 4 Sustituting c m0, and 4 m 0, c. 0,. 5.5 Th Elcton s Total Binding Engy ( Zo Point Engy) U» 0 lcton inding 7 c 4 0 Poof: c lcton inding» U c c

26 Gaug Institut Jounal, Vol., o. 3, August Th Elcton s Total Engy Ulcton» mc + c 7 0 mc

27 Gaug Institut Jounal, Vol., o. 3, August Th Poton's ucla Engy 6. Th Poton s Elctic Binding Engy U lctic c 6. Th Poton s Magntic Engy U magntic m 4 0 n (4 ) 0 m V Poof: Th cunt du to th Poton s chag - that tuns n cycls/scond is I - n Th Magntic Engy of this cunt is [Bnson,.486] By [Fisch,.97] L LI. 0 m 0 m. 7

28 Gaug Institut Jounal, Vol., o. 3, August 05 Thus, th magntic ngy du to th Poton s chag is 4 m 0 ( n) m 0 n W 4 m 0V (4 ). 6.3 Th Poton s Magntic Engy in its uton Oit is ngligil comad to its Elctic Engy Poof: U U magntic lctic m 0V (4 ) 4 0 V 4 c 4 Aoximating» , U U magntic -5 lctic »» Th Poton s Rotation Engy 8

29 Gaug Institut Jounal, Vol., o. 3, August 05 M c - 0 V 7 Poof: Fom th alanc twn th Cntital and Elctic focs on th Poton in its uton oit, M V - 4 0, M - 4 V 0. Sustituting c m0, and 4 m 0, c Th Poton s Total Binding Engy is th ucla Engy U» 0 oton inding 7 c» 4 0 Poof: c oton» U c 9

30 Gaug Institut Jounal, Vol., o. 3, August 05 c Th Poton s Total Engy Uoton» Mc + c 7 0» Mc U U oton inding lcton inding» 4.5 Poof: U U oton inding 0 0 lcton inding 7 7 c c»

31 Gaug Institut Jounal, Vol., o. 3, August Th uton s Mass-Engy 7. Th uton s Mass-Engy Equation Poof: æ ö M -M - m» ç çè ø Dm M c Unu ton, Dividing y c, U + U oton lcton, Mc c mc 7 c 7 0 0» æ ö M -M - m» 7 0 ç + çè ø. 3

32 Gaug Institut Jounal, Vol., o. 3, August Th Poton s Oit Radius 8. Sustituting 7 æ ö» + 0 Dm çè ø C, -7 M» Kg, -7 M» Kg, -3 m» Kg, ( ) 0» D m By 4.3,» » ( ) »

33 Gaug Institut Jounal, Vol., o. 3, August Th Hydogn Poton Oit Radius is 553 (uton s Poton Oit Radius) Poof: By [Dan4,.], th Hydogn Poton Oit Radius is in H m M in H in »

34 Gaug Institut Jounal, Vol., o. 3, August Th Poton s Sd 9. æ 4 ö æ ö ç ç 7 7 ç0 M è ø çè0 M ø +ç -ç» 0 Poof: Fom th Foc Balanc, 4., M - 7 0» 7 0 M - æ 4 ö æ ö ç ç 7 7 ç0 M è ø çè0 M ø +ç -ç» 0. Sustituting C, -7 M» Kg, -5» m -38 ( ) 0» 0 M

35 Gaug Institut Jounal, Vol., o. 3, August 05 æ ö ç ç 7 çè0 M ø ç» » Using MAPLE > with(rootfinding): > > » Th uton s Poton s Sd Poof: V c» ( )c V 7, 905,45 m/sc. 35

36 Gaug Institut Jounal, Vol., o. 3, August 05» 7, 905,45 m/sc. 9.6 Th Hydogn Poton s Sd V 330, 40 m/sc. in H Poof: In Hydogn Atom, v H H 40 H m. mv HHv H 4 w HH 0, w in H w H a» 37 c, H 40 c c adians/sc By [Dan4,.], th Hydogn Poton Angula Vlocity is M W 4 -in-h» w-in-h. m

37 Gaug Institut Jounal, Vol., o. 3, August 05 V W -in-h -in-h -in-h 7» , 40 m/sc 9.7 Th uton s Poton Sd is Poof: 4 ( Hydogn Poton Sd) V V -in- -in-h 7, 905,45 330, 40» 4. 37

38 Gaug Institut Jounal, Vol., o. 3, August Th Poton Fquncy 0. Th uton s Poton Angula Vlocity V W adians/sc Poof: V W» 7, 905,45 m/sc m adians/sc. 0. Th Hydogn Elcton Angula Vlocity 6 w H adians/sc Poof: In th Hydogn Atom, v H H 40 H m. mv HHv H 4 w HH 0, 38

39 Gaug Institut Jounal, Vol., o. 3, August 05 w H a» 37 c, H 40 c c adians/sc 0.3 Th Hydogn Poton Angula Vlocity 7 W H adians/sc Poof: By [Dan4,.], th Hydogn Poton Angula Vlocity M W 4 H» wh. m Th uton s Poton Fquncy W Poof: W adians/sc 39

40 Gaug Institut Jounal, Vol., o. 3, August Th Hydogn Poton Fquncy W H cycls/sc Poof: W 7 H cycls/sc Th uton s Poton Fquncy is 3,3 ( Hydogn Poton Fquncy) Poof: W in WH W in H W ,3. 40

41 Gaug Institut Jounal, Vol., o. 3, August 05. Th Elcton s Sd. æ 8 ö æ ö m ç ç 0 m è ø è ø» 0 Poof: Fom th Foc alanc fo th lcton, 4., m - 7 0, Sustituting fom 4., Squaing oth sids, 7 0 m -,»,» - m 7 0, æ 8 ö æ ö m ç ç 0 m è ø è ø» 0. Sustituting -5» , , 4

42 Gaug Institut Jounal, Vol., o. 3, August ( ) m ( ) m æ ö ç. çè ø ( ) -( )» ( ) -( ) 0 Dnoting º x, w sk th zos of th olynomial f ( x) x + ( ) x -( ) twn x 0, and x. Using wton s Itations x j+ xj - f ( x ) j f '( x ) j x xj - j+ xj x j ( ) ( ) x W osv that If x j > 0.05, thn x j + < x j. That is, th itations dcas. j 4

43 Gaug Institut Jounal, Vol., o. 3, August 05 Stating with x 0.05, and otaind with a calculato x» 0.04 x 3» x 4» x 5» Mal Root-Finding Pogam quis zo. W took x 0.0 Mal Inut and Outut follow: > with(rootfinding): > x to to th ight of th >

44 Gaug Institut Jounal, Vol., o. 3, August 05.5 Th uton s Elcton Sd v 5,558,34 m/sc. Poof: c c 5,558,34 m/sc..6 Th Hydogn Elcton Sd v B a c,89, 78 m/sc.» 37 Poof: In th Hydogn Atom, v H H 40 H m. mv HHv H 4 0, v H 4 c, c 0 a» 37,89,78 m/sc..7 Th uton s Elcton Sd is 3.5 ( Hydogn Elcton Sd) Poof: 5,558,34 3.5,89, 78». 44

45 Gaug Institut Jounal, Vol., o. 3, August 05. Th uton s Radius. -» Poof: Sustituting , , Th Hydogn Radius is ~563 (uton Radius) Poof: Poof: M M -» 4» m - m, caus 4 - -»

46 Gaug Institut Jounal, Vol., o. 3, August Th Elcton s Fquncy 3. Th Elcton s Angula Vlocity v 0 w adians/sc Poof: w» v 5,558,34 m/sc m adians/sc. 3. Th Elcton s Fquncy w Poof: n w adians/sc

47 Gaug Institut Jounal, Vol., o. 3, August Th Hydogn Elcto n Angula Vlocity vh 6 w adians/sc H H Poof: w H v H H»,89,78 m/sc m adians/sc. 3.4 Th Hydogn Elcton Fquncy w H cycls/sc Poof: wh cycls/sc. 3.5 Th uton s Elcton Fquncy is 3,7 (Hydogn Elcton Fquncy) 47

48 Gaug Institut Jounal, Vol., o. 3, August 05 Poof: w w H w w H ,

49 Gaug Institut Jounal, Vol., o. 3, August Th Elcton s Quantum of Angula Momntum Th Elcton s Quantum of Angula Momntum is th Angula Momntum of th lcton s st oit 4. Th Elcton s Quantum of Angula Momntum m - v By dict comuting (with many aoximat valus), w otain 4. ( ) Poof: - -( ) m - v -3-4 ( )( )0 (5,558,34)( )0-34 ( )0 ( ). 49

50 Gaug Institut Jounal, Vol., o. 3, August 05 Altnativly, w hav m v a,» wh a 4 c» 37 0 is th Fin Stuctu Constant Poof: - 40 m v. m c - Angula Momntum, 4 c 0 4 c a 0 37 a. In th ocdings w usd th valu 4.4 ( ) 50

51 Gaug Institut Jounal, Vol., o. 3, August Th Poton s Quantum of Angula Momntum Th Poton s Quantum of Angula Momntum is th Angula Momntum of th Poton s st oit 5. Th Poton s Quantum of Angula Momntum M - V ( ) 5. M a V, -» ( ) wh a 4 c» 37 0 is th Fin Stuctu Constant Poof: - 40 M V. 5

52 Gaug Institut Jounal, Vol., o. 3, August 05 M c - Angula Momntum, 4 c 0 4 c a 0 37 a. 5

53 Gaug Institut Jounal, Vol., o. 3, August uton s Zo Point Engy Th lctical inding ngy will xist at tmatu zo, wh all thmal motions cas, and is calld Zo Point Engy. If th oton s motion is nglctd, th Zo Point Engy is th lcton s total inding ngy. 6. Poof: Elcton Binding æ a w ö h 40 ç è ø -U c w 40 40c w a / a w æ a w ö h ç è ø. 6. Th uton s st lcton oit has hoton s ngy æ a w ö - h ç è ø. 53

54 Gaug Institut Jounal, Vol., o. 3, August Th uton Gound stat Engy is Zo Point Engy æ a w ö h ç è ø. 6.4 uton s Zo Point Engy Poof: a - w V V 8-0 a w 37 é(6.580)0 V ù( )0 ( ) êë úû V -38 c ( ) 0 V Joul ( )0 ( )0 Joul V 6.5 Th Zo Point Engy Fquncy 767V cycls/scond h 54

55 Gaug Institut Jounal, Vol., o. 3, August 05 a w cycls/scond 8 Poof: 767V 767V h V cycls/scond a w ( ) cycls/scond uton s Zo Point Engy is 564 (Hydogn s Zo Point Engy) Poof:

56 Gaug Institut Jounal, Vol., o. 3, August uton s ucla Engy Binding Most of inding is du to th oiting oton s, and th Poton s inding Engy is th actual Zo Point Engy. 7. uton s ucla Engy Binding c a W Poof: a W W c W a c 7. uton s ucla Engy Binding is 4.5(uton s Zo Point Engy Binding) Poof: c 0 c

57 Gaug Institut Jounal, Vol., o. 3, August uton s ucla Engy Binding is (uton s Total Engy Binding) Poof: a W -36,68 V Poof: - -36, 308 V 8 0 a 37 é(6.580)0 V ù( )0 ( ) ë û -6 W ê ú 36, V -38 c ( ) 0 V Joul ( )0 ( )0 Joul 36, V 7.5 Hydogn s ucla Binding Engy 57

58 Gaug Institut Jounal, Vol., o. 3, August 05 æ a ö æacö 4 W ç çè ø H 0 H è in H ø H Poof: c æ a ö W H H 40 H 40c HH W. W çè in H ø a / in H æac ö ç è ø. H 7.6 Poof: 4 7 v æm H ö W H ( )0 adians/sc ç» çèm ø H M H w æ ö W H ç çèm ø v H H 4 c 37 ( ) - ( )0 4 ( ) æac ö V ç è ø H V 8 0 H 58

59 Gaug Institut Jounal, Vol., o. 3, August 05 c é(6.580)0 V ù ê ë ú û(.73735)0 ac H V c ( ) 0 V Joul H 0 (.73735)0 ( )0 Joul V. 7.8 uton s ucla Engy Binding is 553 (Hydogn s ucla Engy Binding) Poof: 36, 308 V V. 59

60 Gaug Institut Jounal, Vol., o. 3, August ucla Foc and Zo Point Engy Foc 8. uton s ucla Foc Hydogn s ucla Foc 4 0 H 8.3 uton s ucla Foc is 305,467(Hydogn s ucla Foc) Poof: H 0 H æ ö ç. çè ø By [Dan4, 4.4], H»

61 Gaug Institut Jounal, Vol., o. 3, August 05 æ ö ç -5 è ø 305, uton s ucla Foc is 836(uton s Zo Point Engy Foc) Poof: M m 0»

62 Gaug Institut Jounal, Vol., o. 3, August Gamma Rays Oigin is uton s Poton Soft X Rays a hotons at fquncis Had X Rays stat at 8 0 cycls/sc. 9 0 cycls/sc Th uton s Elcton Fquncy is in th ang of Had X Rays. Gamma Rays stat at Th uton s Poton Fquncy W wn cycls/sc, 0 0 cycls/sc n 0 is in th ang of Gamma Rays cycls/scond, Thus, th xistnc of Gamma Rays Radiation ovs that th uton is a condnsd Hydogn Atom, comosd of an lcton, and a oton. 6

63 Gaug Institut Jounal, Vol., o. 3, August 05 That is, 9. a uton s Poton xcitd fom its oit into a high oit, tuns to a low uton s Oit, and mits a Gamma Ray Photon 63

64 Gaug Institut Jounal, Vol., o. 3, August Kl s 3 d Law fo th uton, is Consistnt with th uton s Modl as a Collasd-Hydogn Atom wton s Gavitational foc on a lant oiting th sun at adius, with iod T is w Thfo, O, m M Plant Sun m w G. Plant Plant w GM. 3 Plant T Sun 4, GM 3 Constant which is Kl s 3 d Law fo Gavitation. Sinc th Sun too, oits th systm s cnt of Gavitation with a small adius Sun, m w GM m M W 3. 3 Plant Plant Plant Sun Plant Sun Sun Sun 64

65 Gaug Institut Jounal, Vol., o. 3, August 05 O, 3 æt ö m Plant æ ö Plant Plant ç è T ø M èç ø. Sun Sun Sun Fo th Elcton and Poton that comos th uton, 0. m M 3 3 w 4 W Poof: caus m - M - w 4 0 W 4 0,. 0. Kl s 3 d Law fo th uton is 3 - m æt ö æ ö T M ç çè ø - è ø Poof: Sustitut in 0. w ; W. T T 65

66 Gaug Institut Jounal, Vol., o. 3, August W M - w T 4» 8 T m - Poof: By 0., m æt ö ç - ç çèt ø M -. Sustituting fom 3.3, m M» - -, æt ö ç ç» çèt ø» M m Th Poton s Angula Vlocity Poof: M W» - 4 w m - Coma with Th discancy of is du to ou ounding os, and th calculato 66

67 Gaug Institut Jounal, Vol., o. 3, August 05 M - 4 w 8 m - W» 0 w adians/sc M 4 ( ) m»» »» W» ot that W in 0. was otaind fom ou uton s Mass- Engy Equation, 7.. That Mass-Engy quation yildd, with which w otaind, V c, and W. V / Thn,, and w usd to otain,, u c, and w u /. Thus, W in 6.4 dnds on th Mass-Engy Equation. vthlss, th clos sults of 0., and 0.4, stalish 0.5 Kl s 3 d Law fo th uton is consistnt with th uton s Mass-Engy Equation, and with th Modl of th uton as a Collasd-Hydogn Atom 67

68 Gaug Institut Jounal, Vol., o. 3, August 05. uton Sin Angula Momntum. uton Sin is th Sum of th Elcton and th Poton Angula Momntums m M æ ö +» 37 ç çè ø c c Poof: Th Foc on th uton s lcton is - 40 m c ( ) Th Angula Momntum of th Elcton gnats th Sin. m - c 4 c 0, m c 0 4 c c 0 7 Sustituting m c ha, wh a» 0 37 a. 68

69 Gaug Institut Jounal, Vol., o. 3, August 05 Similaly, th Angula Momntum of th Poton in its uton Oit, gnats th Sin M - Th uton Sin is th Sum c a m M æ ö + a ç çè ø c c a a / 37 / 37 +» +» Consquntly,. Th Assumtion that th uton s Sin is (0.5) is off y 57% 69

70 Gaug Institut Jounal, Vol., o. 3, August 05. Elctic Collas Vsus Gavitational Collas. Th Gavitational Foc twn th lcton and th Poton in th Hydogn Atom, o in th uton is ngligil with sct to th Elctical Foc twn thm Poof: Fo th uton, mm G c G mm Similaly, fo th Hydogn, ( ) 0 mm G H c G H mm

71 Gaug Institut Jounal, Vol., o. 3, August 05 Consquntly,. uton Stas a Catd y Elctic Collas. Gavitational Focs a ngligil in th Collas. 7

72 Gaug Institut Jounal, Vol., o. 3, August uton s Binding Engy 3. Th uton s Total Binding Engy c 0 7 æ ö ç +» ( - - çè M M m) c ø ( )MV Poof: By 7., th Binding Engy is c 0 7 æ ö ç +» ( - - çè ø ) M M m c Dm J Sinc Joul 0 V, 60, MV (m c )MV Th Hydogn Atom Total Binding Engy c 0 æ ö ç 7 ç çè H ø ç V 7

73 Gaug Institut Jounal, Vol., o. 3, August 05 Poof: Sustituting fom [Dan4,.], H c æ ö ( ) 0 ( ) ç H - è ø J ( )0 V V. 3.3 Th uton s Total Binding Engy is aout 553 (Hydogn Total Binding Engy) Poof: V V». 73

74 Gaug Institut Jounal, Vol., o. 3, August ucla Focs, ucla Bonding, uclus Staility, and uton Stas Ov th shot distanc twn th uton s lcton and Poton, th lctic foc is nomous comad to th Hydogn lctic Foc: 4. Th Poton-Elcton Elctic Foc in th uton is 37,000 (Poton-Elcton Foc in th Hydogn) Poof: Sustitut H Hydogn Radius m -4» uton Radius m 0 H è 0 H æ ö ç ø æ ö ç -4 è ø 74

75 Gaug Institut Jounal, Vol., o. 3, August 05» 37, 000. This lctic foc is th souc of th ucla Foc that inds th otons in th uclus. Fo instanc, 4. A uclus mad of a Poton and a uton is a Mini On-Elcton Molcul H +, with two otons and on lcton that oits th two otons just as it dos in th H + molcul. Fo such Molcula Bonding s [Gil,.70]. This sot of Molcula Bonding in th uclus nsus th staility of th uclus amly, 4.3 ucla Bonding is a Mini Molcula Bonding Though Oitals of Elctons Sulid y th utons in th uclus. Hnc, 75

76 Gaug Institut Jounal, Vol., o. 3, August In uton Stas, th Gavitational Focs a ngligil comad to th uton s ucla Bonding, which ks th sta ackd togth 76

77 Gaug Institut Jounal, Vol., o. 3, August 05 Rfncs [Aaatzis] Thodo Aaatzis Rsnting Elctons, A Biogahical Aoach to Thotical Entitis U. of Chicago Pss, 006. [Bis] Athu Bis Concts of Modn Physics Fifth Edition, McGaw Hill, 995. [Bnson], Bnson Walt, Hais John, Stock Host, Lutz Holg, Handook of Physics, Sing, 00. [Chandaskha] S. Chandaskha, wton s Pinciia fo th Common Rad Clandon Pss, Oxfod, 995. [Bohm] David Bohm, Th Scial Thoy of Rlativity Routldg, 996. [Bon] Max Bon, Atomic Physics Blacki, 7 th Edition, 96. [Budn], Richad Budn, and Douglas Fais, umical Analysis, Fouth Edition, PWS-KET, 989. [CRC] CRC Handook of Chmisty and Physics CRC, 995. [Dan], Dannon H. Vic, Wav-Paticl Duality: d Bogli Wavs and Unctainty Gaug Institut Jounal Of Math and Physics, Vol., o. 4, ovm 006. [Dan], Dannon H. Vic, Photon s Sin, Diffaction, and Radius. Th On Photon Hyothsis, and Stod Photon Gaug Institut Jounal Of Math and Physics, Vol. 9, o., Fuay 03. [Dan3], Dannon H. Vic, Zo Point Engy and th Chag-Radiation Equation in Boh s Atom Gaug Institut Jounal Of Math and Physics, Vol. 8, o. 4, ovm 0. [Dan4], Dannon H. Vic, Radiation Equiliium, Intia Momnts, and th uclus Radius in th Elcton-Poton Atom Gaug Institut Jounal Of Math and Physics, Vol. 0, o. 3, August

78 Gaug Institut Jounal, Vol., o. 3, August 05 [d Bogli], Louis d Bogli, Hisng s Unctaintis and th Poailistic Inttation of Wav Mchanics Kluw Acadmic, 990. [Fynman] Richad Fynman, Th Fynman Lctus of Physics, Edison Wsly, 965. [Fisch] Fisch-Cis, A., C., Th Physics Comanion, IoP, 003. [Gil] Victo Gil, Oitals in Chmisty: A Modn Guid fo Studnts Camidg, 000. [Gigoiv], Igo S. Gigoiv, and Evgnii Z. Milikhov, Handook of Physical Constants, CRC, 997. [Kovtz] Attay Kovtz, Elctomagntic Thoy, Oxfod, 000. [Mac Ggo] Malcolm Mac Ggo Th Enigmatic Elcton Kluw, 99 [Maion] Jy Maion; Mak Hald, Classical Elctomagntic Radiation, Scond Edition, Acadmic Pss, 980. [Mackintosh], Ray Mackintosh, Jim Al-Khalili, Bjon Jonson, Tsa Pna, uclus: A ti into th Hat of Matt Scond Edition, Johns Hokins, 0. [Millikan], Millikan, Rot, Andws, Elctons (+ and -), Potons, Photons, utons, Msotons, and Cosmic Rays U. of Chicago, Rvisd Edition, 947. [ol] B. ol, umical Mthods: Itation Pogamming and Algaic Equations Oliv & Boyd, 964. [Panofsky] Wolfgang Panofsky; Mla Phillis, Classical Elcticity and Magntism, Scond Edition, Addison Wsly, 96. [Pak] Syil P. Pak, McGaw-Hill Encyclodia of Physics, Scond Edition, McGaw-Hill, 993. [PDG] Paticl Data Gou, at LBL, and CER () July 00 PARTICE PHYSICS BOOKLET, IOP Pulishing() Physical 78

79 Gaug Institut Jounal, Vol., o. 3, August 05 Rviw D, Paticls, Filds, Gavitation, and Cosmology, July 0, Pat I, Rviw of Paticl Physics, Volum 86, um, Amican Physical Socity. [Polyanin] Andi Polyanin; Alxi Chnoutsan, A Concis Handook of Mathmatics, Physics, and Engining Scincs, CRC, 0. [Pool] Chals P. Pool, Th Physics Handook Fundamntals and Ky Equations, Wily, 998. [Richadson], O.W. Richadson, Th Elcton Thoy of Matt Scond Edition, Camidg Univsity Pss, 96. [Rindl], Wolfgang Rindl, Rlativity Scial, Gnal, and Cosmological, Oxfod, 00. [Routh] Edwad, John Routh A Tatis on Dynamics of a Paticl, Stcht, 898. [Simulik], Volodimi Simulik, dito, What is th Elcton Aion, 005. [Skinn], Ray Skinn, Rlativity fo Scintists and Engins, Dov, 98. [Smith] Glnn S. Smith, An Intoduction to Classical Elctomagntic Radiation Camidg, 997. [Sigl] Sigl, Muay, Thotical Mchanics McGaw Hill, 967. [Stannad], Russll Stannad, Rlativity, Stling, 008. [Thomson] J. J. Thomson, Byond th Elcton Camidg U. Pss, 98. [Thomson] G. P. Thomson, Conduction of Elcticity Though Gass Volum I, Camidg U. Pss, 98. [Wagon] Rot Wagon, Poduction of Factional Chag in a Zo: w Fontis of Physics ditd y J.D. Faiank, B.S. Dav, C.W.F. Evitt, and P. F. Michlson, Fman, 988 [Woan] Woan, Gaham, Th Camidg Handook of Physics Fomulas, 79

80 Gaug Institut Jounal, Vol., o. 3, August 05 Camidg 000. htt://n.wikidia.og/wiki/lontz_tansfomation htt://n.wikidia.og/wiki/rlativity_thoy htt://n.wikidia.og/wiki/uton htt://n.wikidia.og/wiki/ucla_foc htt://n.wikidia.og/wiki/ucla_stuctu htt://n.wikidia.og/wiki/x_ay htt://n.wikidia.og/wiki/poton htt://n.wikidia.og/wiki/elcton htt://n.wikidia.og/wiki/hydogn_atom htt://n.wikidia.og/wiki/boh_modl htt://n.wikidia.og/wiki/uclon htt://n.wikidia.og/wiki/elctomagntic_sctum htt://uload.wikimdia.og/wikidia/commons/8/8a/elctomagn tic-sctum.ng 80