Applid Phyic Rach; Vol 7, No 5; 5 ISSN 96-9639 -ISSN 96-967 Publihd by Caadia Ct of Scic ad ducatio A Ukow Phyical Cotat Miig fom Phyic Chudaiji Buddhit Tmpl, Iaki, Japa Kohu Suto Copodc: Kohu Suto, Chudaiji Buddhit Tmpl, 5-, Oot-Tow, Iaki, 37-8, Japa Tl: 8-7-39-98 -mail: kohu_uto9@mbiftycom Rcivd: Apil, Accptd: Augut, 5 Oli Publihd: Augut, 5 doi:5539/apv75p68 URL: http://dxdoiog/5539/apv75p68 Abtact Plack cotat i thought to blog to th uival cotat amog th fudamtal phyical cotat Howv, thi pap dmotat that, jut lik th fi-tuctu cotat α ad th Rydbg cotat R, Plack cotat blog to th mico matial cotat Thi pap alo idtifi th xitc of a cotat mall tha Plack cotat Thi w cotat i a phyical quatity with dimio of agula momtum, jut lik th Plack cotat Futhmo, thi pap poit out th poibility that a ukow gy lvl, which caot b xplaid with quatum haic, xit i th hydog atom Kywod: Plack cotat, Boh' quatum coditio, hydog atom, ukow gy lvl, fi-tuctu cotat, claical lcto adiu Itoductio I 9, wh divig a quatio matchig xpimtal valu fo black-body adiatio, M Plack popod th quatum hypothi that th gy of a hamoic ocillato with fqucy ν i quatizd ito itgal multipl of hν Thi wa th fit tim that Plack cotat h appad i phyic thoy Sic thi tim, Plack cotat ha b thought to b a uival cotat amog fudamtal phyical cotat Fudamtal phyical cotat play a tial pat i lmtay quatio dcibig atual phoma ad ca b boadly dividd ito uival cotat ad matial cotat Uival cotat iclud th pd of light i vacuum c, Nwtoia cotat of gavitatio G, ad Plack cotat h Matial cotat ca b dividd ito mico matial cotat ad maco matial cotat Alo, mico matial cotat ca b dividd ito phyical quatiti ad cotat Phyical quatiti blogig to th catgoy of mico matial cotat iclud th lcto t ma m, lmtay chag, ad lcto' Compto wavlgth λ C, ad iclud uch cotat a th fi-tuctu cotat α ad th Rydbg cotat R Th Boltzma cotat k ad th Avogado cotat N A a xampl of maco matial cotat Icidtally, i divig th quatio fo th gy lvl of th hydog atom, Boh aumd th followig quatum coditio icludig th Plack cotat: p π = π, =,, () Howv, th autho ha poitd out that quatio () i o mo tha a appoximatio (Suto, ) That i, p ( / ) / π = π + + α π () quatio () i a coditio divd fom th followig quatio fo th gy lvl of th hydog atom = m c + α /, =,,, (3) 68
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 quatio (3) divd by th autho i a quatio which ica th pciio of th quatio divd by Boh fo th gy lvl of th hydog atom (Howv, quatio (3) ha ot b uccfully galizd to a quatio icludig multipl quatum umb) Plack cotat do ot play a tial ol wh divig quatio (3) Thu, th xt ctio of thi pap xami whth Plack cotat ca tuly b calld a uival cotat Plack Cotat Divd fom Fudamtal Phyical Cotat Th followig i iti quatio xpig th quality of gy ad ma = () H, m i th ma of a objct o a paticl ad c i th pd of light i vacuum If m i th t ma of a lcto, a lcto ma gy ca b ptd by th followig quatio m c = (5) Mawhil, iti latioal xpio gadig light quata i a follow = hν (6) quatio () ad quatio (6) a taditioally thought to b ptativ quatio of th thoi of pcial lativity ad quatum haic, th foudatio of mod phyic, ad th two quatio hav b thought to hav imila impotac If ν c i th fqucy of a photo cayig a amout of gy quivalt to, th followig i tu = hν (7) C Nxt, lt u calculat th wavlgth of a photo with fqucy ν c Combiig qual fom quatio (5) ad quatio (7), w obtai: h C = ν (8) quatio (5) xp th gy pod by a lcto with t ma m Alo, quatio (7) idicat th latiohip btw photo fqucy ad gy Fudamtally th two typ of gy hav difft chaactitic, but fom a quatitativ ppctiv, it i poibl to combi thm a qual Thu, th photo fqucy ν c i xpd a follow Nxt, th photo wavlgth λ bcom: c h λ = = = λc ν C Thu, quatio (5) ca b tafomd a follow ν C = (9) h C C () = λν () I quatio (), λ C i th wavlgth of a photo, ot a lcto Howv, bcau th ight id of quatio () ad quatio (8) match, th followig latiohip hold tu i th ca of a photo a wll λ C = h () Now, lt u coid th ca wh th photo gy i ot m c If th t ma of th lcto dca by jut am th th gy a of th photo mittd fom that lcto i giv by th followig quatio Thi quatio ca alo b witt a follow a a, (wh a<) = < (3) 69
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 = a = aλν C C = λc a νc = hν () Fially, it wa poibl to cofim that quatio (6) hold i gal Th cutly kow valu fo m o λ C w ot dtmid though xpimtatio m wa dtmid though pci calculatio fom Rydbg cotat fomula, ad λ C wa obtaid by ubtitutig m i th fomula λ C =h/m c May fudamtal phyical cotat a big adjutd, bad o maud data fom thotical quatio o xpimt digd to pt th fudamtal law of phyic, to avoid coflict fom aiig btw th cotat Bcau th quatio fo dtmiig a lcto Compto wavlgth i λ C =h/m c, atually th modifid vio of thi quatio () i tu Accodig to taditioal claical quatum haic, Plack cotat xit a pioi a a uival cotat, ad thu it i thought that th gy of a photo ca b dtmid if it fqucy i kow, ad th wavlgth of a quatum ca b dtmid if it momtum i kow ( =hν ad λ=h/p) I thi pap, howv, a logical ca i mad that, ic th poduct of th momtum ad wavlgth of ay photo ca b xpd by th cotat m cλ C, Plack cotat oly com ito xitc wh m cλ C i placd with h I oth wod, quatio () ca b itptd to ma ot that th valu of m cλ C ad h match but itad to ma m cλ C i h I thi pap, w how that Plack cotat i ot a uival cotat but i itad jut a mico matial cotat o a pa with th fi-tuctu cotat α ad th Rydbg cotat R 3 A Ukow Phyical Cotat Miig fom Phyic I th claical quatum thoy of Boh, th gy lvl of th hydog atom ca b xpd with th followig quatio m,,, πε = = Wh Boh divd thi quatio, h aumd th quatum coditio i quatio () Fom quatio (), th poduct p of th miimum valu of th momtum p ad th miimum valu of th adiu i a follow p = (6) Icidtally, th autho ha divd a latio btw gy ad momtum, applicabl to th lcto i th hydog atom, fom th ppctiv of claical thoy (Suto, ) That i, (5) Alo,, ha b dfid a follow ( ) p c m c =,, (7), + =, = m c + (8), H,, i th lativitic gy of th lcto, ad th lcto gy i dcibd o a abolut cal Now, th followig quatio ca b divd by compaig dfid with quatio (8) ad quatio (3) /,, = + α, α = πε Nxt, if th ight id of quatio (9) i ubtitutd fo quatio (7), th th followig quatio ca b divd c (9) / α p = α + () 7
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 If i ubtitutd h fo i quatio (), p m c p i obtaid, ad thu i thi ca w will fid Fit, th gy of th hydog atom i giv by th followig quatio Du to thi quatio ad quatio (8), th lativitic gy = () = πε (), bcom a follow =, πε (3) H, th ight id of quatio (9) ad quatio (3) a coctd with a qual ig That i, If i foud fom that, / + α = πε ( α ) ( ) / + / / = = πε ( + α / ) + α H, i th claical lcto adiu Nxt, if i ubtitutd fo i quatio (5), () (5) = = πε (6) Fially, p i a follow du to quatio () ad quatio (6) ( Appdix) = = πε c (7) p Thi p valu i ot a appoximat valu Howv, a i cla fom quatio (), p i quatio (6) i a appoximat valu Thfo, thi pap coclud that th valu of thi p i a phyical quatity mo baic tha p i quatio (6) I thi pap, thi phyical quatity i ttativly calld ad poitiod a a cotat o a pa with Plack cotat That i, = (8) πε c A mall i ud a th ubcipt of Thi igifi that i a mall quatity tha Th latiohip btw ad, ad btw h ad h a a follow = α (9) h = αh (9) If, i quatio (9), ad α a mico matial cotat, th it i atual to gad i th am way If th latiohip i quatio (9) i ud h, th quatio (6) ca b witt a follow = hν (3) α 7
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 Thi pap pdict that quatio (3) will b a impotat quatio jut lik quatio (6) Nomally, th gy of a photo i thought to b popotioal to th photo' fqucy Howv, quatio (6) do othig mo tha igify that th photo gy i xpd by th poduct of h ad ν (Sic h ha dimio, it caot b aid that h i a cotat of popotioality) I quatio (3), i cotat, /α bcom th cotat of popotioality, ad thu it i poibl to itpt th photo gy a vayig i popotio to h ν Alo, h i a cotat, ad thu th fact that gy i popotioal to h ν ha th am maig a gy big popotioal to ν That i, h = hν ν hν α = α = (3) So, i th xpimtal data uppotig th icluio of amog phyical cotat? To olv thi poblm, thi pap aum, o a tial bai, that th i a ukow gy lvl i th hydog atom Th a quatio fo th ukow i divd by uig a coditio imila to th Boh quatum coditio Th th valu obtaid fom th quatio a compad with xpimtal data to dtmi whth o ot thy match If th thoy of quatum haic i complt, th hould b o match btw xpimtal data ad th valu pdictd by th quatio fo th ukow Howv, if th i a match btw th thotical valu ad obvd data, thi ca b gadd a powful vidc uppotig icluio of amog th phyical cotat Divatio of quatio fo Ukow gy Lvl If it i aumd that a ukow gy lvl xit i th hydog atom, what i th bt mthod of divig a quatio fo it? Th followig cofim that pocdu It i difficult to div a ukow quatio, ad thu w bgi by pdictig a appoximatio of th ukow quatio, whil fig to Boh quatum coditio At that tim, it i aumd that th followig latio hold, which i imila to Boh quatum coditio α p π = π = π, =,, (3) Takig ito accout th fact that th appoximatio of quatio (3) i Boh quatio (5), i thi ca th oigial quatio i divd by pocdig backwad fom th divd appoximatio Lt u uppo that a atomic uclu i at t bcau it i havy, ad coid th ituatio wh a lcto (lctic chag, ma m ) i obitig at pd v alog a obit (adiu ) with th atomic uclu a it ct A quatio dcibig thi motio i a follow: mv = (33) πε Th followig quatio i divd by multiplyig both id of th abov quatio by 3 ad uig quatio (3) α,,, m = πε = (3) To ag with o th light id, i addd to o th lft id Nxt, th followig quatio i divd wh thi i ubtitutd ito quatio () ad th ubcipt i attachd to m πε α =, =,, H, gy i tak to b i od to ditiguih fom xitig quatio of quatum haic Icidtally, Boh quatio (5) ca b witt a follow (35) 7
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 I cotat, quatio (35) ca b witt a follow m,,, πε = = α = = α, =,, (37) α Nxt, w cofim that quatio (5) i a appoximatio fo quatio (3) Fit, quatio (3) ca b witt a follow (36) H, / = + α / ( α / ) ( + α / ) ( α / ) = / / / / α α =,,,, = α / ad thfo, (38) (38) (383) / α That ma quatio (383) ca b witt a follow / α, =,,, Th Taylo xpaio of thi fomula i a follow (39) () / α α α m = c + 8 Th cod ad ubqut tm i th path ca b gadd a zo, ad thu if oly th fit tm i ud, th ult i a follow α, =,, () Th abov dmotat that Boh quatio (5) i a appoximatio of quatio (3) Now, thi tim w will apply th logic ud thu fa to quatio (37) quatio (36) ud oly th fit tm i path i quatio () Thfo, fig to quatio (), w ca pdict that th Taylo xpaio of th quatio to b foud will b a follow / α α α m c + (3) α α 8α If th latiohip btw quatio () ad quatio (383) i tak ito accout h, th it ca b pdictd that quatio (3) i a appoximatio of th followig quatio () 73
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 / / = If th fact that quatio (383) i divd fom quatio (38) i tak ito coidatio, quatio () ca b witt a follow / ( / ) ( + / ) ( / ) = / / Raagig thi quatio, th followig quatio ca b divd / =,,,, = (6) + Thi i th quatio fo th ukow gy lvl of th hydog atom which thi pap i popoig a a pigboad fo dicuio 5 Compaio of Thotical ad Maud Valu I thi ctio, w ach oth pap fo xpimtal data matchig thotical data obtaid fom quatio (6) Howv, compaio of thotical valu ad xpimtal data i ot do i od to pov th coct of quatio (6) Thi compaio i caid out to obtai vidc uppotig cogitio of a a phyical cotat quatio (6) do ot caily hav to b coct i od to cogiz a a phyical cotat v if it i ttativly aumd that th i o xpimtal data matchig th thotical data, that i ot a ao to jct th coidatio i ctio 3 Alo, covly, v if thotical valu ad xpimtal data match, that i ot cocluiv vidc that th xpimtal data i a taitio gy btw th gy lvl at iu h Fo th abov ao, thi pap u th impl mthod of a Itt ach to ach fo xpimtal data I additio, th compaio of thotical valu ad xpimtal data i pfomd by limitig to th followig ag Tak Fit, th gy lvl i quatio (6) i calculatd fom = to 6 Th it i chckd whth o ot that thotical valu i actually obvd Sachig i pfomd with th tm: hydog atom, gy lvl, ad th thotical valu to b chckd Tak It i cofimd whth o ot a valu i actually obvd which match th taitio gy btw difft gy lvl ad m H,, m = m, ( m, > m ) Thi tak i pfomd i th followig th gy ag Sachig i pfomd with th tm: hydog atom, taitio gy, ad th thotical valu to b chckd ) gy ag fom to ) gy ag fom 7 to 79 Howv, thi iclud foud fom quatio (3) 3) gy ag fom 5 to 553 Howv, thi iclud foud fom quatio (3) Fit, fo Tak, it wa cofimd that th i xpimtal data umically matchig th gy lvl fom to 6 (Howv, that maumt valu do ot pov th xitc of th ptit gy lvl) Nxt, Tabl -3 ummaiz th ult of Tak (S Tabl,, 3) Bad o th abov compaio, thi pap ha dtmid that th xit xpimtal data umically matchig thotical valu (Howv, v thi ca i ot cocluiv vidc that th maud valu a th ptit taitio gi) Howv, o vidc wa obtaid that quatio (6) i a mitak Thu, i thi pap it wa dtmid that th i o poblm with cogizig a a phyical cotat Th dicuio i thi pap do ot ach a cocluio gadig whth quatio (6) i coct o ot Howv, thi pap pdict that i th hydog atom th i a gy lvl low tha th gy lvl pdictd by quatum haic () (5) 7
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 Tabl Taitio gy cofimd i th gy ag fom to Th maud valu i thi tabl almot match th thotical valu Thi tabl wa oigially log i th hoizotal dictio Howv, fo ao of pag pac, th oigial tabl wa dividd h by cuttig it vtically i th ct of th lft-ight dictio Th th ight half of th tabl wa placd ud th lft half Th dottd li o th top ight dg ad th dottd li at th low lft dg ovlap i th oigial tabl Alo, i th paid umical valu i th tabl, th top figu i th thotical valu Th bottom figu i a valu obtaid by a ach, ad i a maumt valu clo to th thotical valu (Th am mak apply to Tabl ad 3 blow) = 5MV 5MV = 85MV 8 MV = 97 MV 5 MV 3 = 858 k V 858k V = 5395k V 539k V 5 = 3655k V 365k V 6 = 6k V 6k V 7 = 966 k V 97 k V 8 = 56k V 53k V 9 = 7 k V k V = 993k V 3 85MV 9MV 363MV 36MV 5MV 5MV 57MV 75MV 75MV 7MV 88MV 85MV 93MV 9MV 957MV 96MV 988MV 99MV 5MV 38MV 33MV 967MV 97MV 85MV 9MV 59MV 6MV 563MV 56MV 68MV 63MV 67MV 67MV 73MV 7MV 76MV 6385kV 638kV 957kV 957kV 3MV 3MV 3MV 3MV 3MV 3MV 3MV 3MV 375MV 375MV 397MV 387kV 39kV 97kV 93kV 596kV 596kV 666kV 66kV 757kV 76kV 7365kV 737kV 759kV 7kV 7kV 77kV 77kV 39kV 33kV 3869kV 387kV 78kV 8kV kv 99k V 5MV 73MV MV 759kV kv 5 6 7 8 9 6,5 = 33k V 33k V 7,5 = 689k V 689k V 8,5 = 9k V 9k V 9,5 = 38k V 38k V,5 = 663k V 663k V 656kV 656kV 97kV kv 5kV kv 63kV 63kV kv kv 793kV 75kV 9738kV 97kV 389kV 38kV 533kV 533kV 5kV 5kV 75
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 Tabl Taitio gy cofimd i th gy ag fom 7 to 79 Th maud valu i thi tabl almot match th thotical valu 7 7 7 73 7 7 = 9 V V 7 = 395V 39 V 7 = 383V 38V 73 = 37 V 37V 7 = 36 V 36V = 365V 365V 75 = 353V 35V 76 = 36 V 3 V 77 = 339 V 33 V 78 = 33V 3 V 79 = 39 V 33V 3V 5V 5V 36V 36V 63V 6V 3V 3V 55V 55V 69V 63V 6995V 7V 795V 795V 8898V V V 3V 3V 33V 33V 3V 3V 9V V 996V 5V 5963V 596V 699V 69V 7865V V V 9V V 8V 8V 997V 3V 3975V 397V 9V 9V 5898V 59V 68V 999V V 7V 7V 987V 99V 965V 96V 393V 393V 888V 89V 583V 7V 7V 988V 99V 966V 97V 93V 93V 3889V 389V 835V 39V 89V 787V 68V 583V 8V 75 76 77 78 79 75, = 97 V 97V 76, = 89 V 89V 77, = 86V 86V 78, = 387 V 38V 79, = 76 V 76V 977V 98V 9V 9V 9V 9V 387V 385V 967V 967V 93V 9V 87V 87V 956V 956V 93V 9V 96V 96V 76
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 Tabl 3 Taitio gy cofimd i th gy ag fom 5 to 553 Th maud valu i thi tabl almot match th thotical valu 5 55 56 57 58 5 = 353V 353V 55 = 3 V 3 V 56 = 38V 38V 57 = 36 V 36 V 58 = 33V 33V = 3V 3V 59 = 339V 339V 55 = 3378V 3378V 55 = 3366 V 3366 V 55 = 335 V 335 V 553 = 33V 7V 7V 53V 53V 378V 378V 5V 5V 5V 5V 66V 66V 79V 79V 87V 87V 99V 99V 5V 6V 6V 5V 5V 376V 376V 395V 395V 5V 5V 63V 63V 75V 75V 867V 867V 988V 5V 5V 5V 5V 69V 69V 37V 37V 97V 5V 69V 6V 7V 7V 86V 5V 5V 3V 3V 8V 8V 37V 37V 9V 9V 66V 66V 737V 89V 89V V V 7V 7V 37V 37V 9V 9V 63V 33 V V 99V 86V 7V 6V 59 55 55 55 553 59, = 5V 5V 55, = 8V 8V 55, = 35 V 35V 55, = 73V 7V 553, = 59 V 59V 3V 3V 6V 6V 368V 368V 89V 9V 3V 3V V V 366V 366V V V 3V 3V V V 6 Cocluio ) It ha b thought that Plack cotat h i a uival cotat blogig to th am catgoy a th pd of light i vacuum c ad th lctic chag Thu, it i valid to gad Plack cotat ot a a uival cotat but a a mico matial cotat o pa with th fi-tuctu cotat α o th Rydbg cotat R 77
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 ) Thi pap ha poitd out th xitc of a cotat Thi cotat i mall tha Plack cotat, ad i a phyical quatity with dimio of agula momtum That i, = (7) πε c I th mico wold, th a two cotat with th dimio of agula momtum What lat ad i th fi-tuctu cotat α S α = = (8) πε c Thi pap coclud that, jut lik ad α, i a cotat blogig to th mico matial cotat Th abov two itm a th mai cocluio of thi pap 3) Thi pap ha divd quatio (6) a a cadidat fo a ukow gy lvl i th hydog atom Howv, quatio (5) ca atly xplai th pctum of th hydog atom, but a pctum quiig quatio (6) ha ot b dicovd I additio, may data t ud to compa thotical ad xpimtal valu iclud gi mittd fom molcul oth tha hydog Thu th a alo poblm with quatio (6) Howv, thi pap pdict that th i a high pobability of a ukow gy lvl, which caot b xplaid by quatum haic, xitig i th hydog atom Ackowldgmt I would lik to xp my thak to th taff at ACN Talatio Svic fo thi talatio aitac Rfc Schiff, L I (968) Quatum Mchaic (p 7) Nw Yok: McGaw-Hill Suto, K () A gy-momtum latiohip fo a boud lcto iid a hydog atom Phyic ay, (), 3-37 http://dxdoiog/6/35838 Suto K () = gy lvl pt i th hydog atom Applid Phyic Rach, 6(5), 9-5 http://dxdoiog/5539/apv65p9 Appdix I thi pap, quatio (3) wa obtaid by tatig fom quatio (3) quatio (3) tat that a hydog atom ha a = gy lvl Howv, at pt, o xpimtal vidc ha b obtaid to uppot th xitc of uch a gy lvl Thfo, it will b cofimd h that quatio (3) ca b divd without lyig o quatio (3) Rfig to claical quatum thoy, th total haical gy of th lcto i a hydog atom ha a gativ valu Th total haical gy of a lcto i coidd to b zo wh th lcto i paatd fom th atomic uclu by a ditac of ifiity ad mai at t i that locatio Th total haical gy of quatio (5) i th valu obtaid fom thi ppctiv Howv, v if w plac a lcto at t a ifiit ditac fom it uclu, th lativitic gy of th lcto i fudamtally ot zo Accodig to iti, a lcto i thi tat hould hav t ma gy Accodig to quatum haic txtbook, th igvalu of th gy of a hydog atom a obtaid fom th Diac quatio, which i a lativitic wav quatio, i a follow (Schiff, 968) γ γ 3 = k If w igo fo th thid tm of thi quatio ad dfi it a a appoximatio, quatio (A) ca b witt a follow (A) m πε m c (A) = + (A) of quatio (A) dfi a abolut quatity, which iclud th lcto t ma gy 78
wwwcctog/ap Applid Phyic Rach Vol 7, No 5; 5 Th gy of a hydog atom quatio (5) copod to th ductio i th lcto t ma gy, whil covly, quatio (A) copod to th lcto maiig t ma gy v if th lcto which wa at t bgi movig i f pac, ad v if it i abobd ito a atom, th tatig poit of th lcto gy fo ith ca i it t ma gy Fom thi fact, th lativitic gy i abolut tm,, fo a hydog atom i dfid a blow:, = m c + (A3), Thi how that th followig iqualiti hold fo th lativitic gy ad total haical gy of th lcto i th hydog atom, < (A) < (A5) Thi do ot ma that th xitc of a = gy lvl ha b pov Howv, logically pakig, th low limit of th gy lvl of th hydog atom bcom = (i, = ) Thfo, quatio () ca b witt a follow: Solvig thi, th followig i obtaid = πε (A6) = = (A7) πε Fo th p copodig to thi, th followig valu i obtaid by ttig, = i quatio (3) p = m c (A7) Thi cofim that th xitc of i ot tial to ifig th valu of, which i a cadidat fo th miimum uit of phyical quatiti havig a dimio of agula momtum Copyight Copyight fo thi aticl i taid by th autho(), with fit publicatio ight gatd to th joual Thi i a op-acc aticl ditibutd ud th tm ad coditio of th Cativ Commo Attibutio lic (http://cativcommoog/lic/by/3/) 79