Primer Informe de Electroquimica

 

VGJXF[]JCAC GAMJLGAB CFB MFGS[L CFB UF[ß

  HAMVBSAC CF JGDFGJF[ÉA QVÉIJMA F]MVFBA AMACÊIJMA U[LHF]JLGAB CF JGDFGJF[ÉA QVÉIJMA

BFZ CF LNI AUBJMAMJÝG A BA FBFMS[LBJ]J] MASFC[A

? FBFMS[LQVJIJMA JGCV]S[JAB Z ML[[L]JLG

CLMFGSF

? Cr. BVJ] HF[GAGCL [JMMJL ZAV[J

U[F]FGSACL UL[?  

MAIUL] MA[CFGA] OVBJL MF]A[

 

MVZVKAIKA SAUJA IA[JA

 

ILGSLZA ML[SJOL F]SFHNAGZ ^JLIA[A GAXA[[L AUVIAZSA H[AG@BJG [.

]FIF]S[F

? J^

NVAGMAZL ” ;51:

J.

JGS[LCVMMJLG

 

Cfgtrl Cfg trl

cfb

áikjtl áikjtl

prámtjm prámtjml l

cf

ba

jgdfgj jgdfgjfré fréa a

fs hugcai hugcaifgt fgtab ab fb

mlglmjijfgtl cf ba bfy cf Lni quf fxprfsa quf fb Xlbtaof fs prlplrmjlgab a ba mlrr mlrrjf jfgt gtf f qu quf f mjrm mjrmub uba a pl plrr ug mjrm mjrmuj ujtl tl,, fg cl clgc gcf f fsta fsta prlplrmjlgabj prlplrm jlgabjcac cac

fs

mlgs mlgsta tagt gtf f

cf

ba rfsjstfgmja rfsjstfgmja quf tfgda ug mjrmuj mjrmujtl tl pfrl fg fsta prámtj prámtjma ma

gls fghlmarfi fil ls fg ba cfilstramjýg cf ba bfy cf Lni apbjmaca a ba fbfmtrlquéijma quf sf muipbf fg bls mlgcumtlrfs cf sfdugca mbasf quf slg bas slbumjlgfs fbfmtrlbétjmas. Uara bl muab sf trakaoý mlg jghlriamjýg fspfméhjma quf pfrijtjý tfgfr ug mlglmjijfgtl quf akarquf plr mlipbftl tlcl slkrf ba bfy cf lni apbjmaca a ba fbfmtrlquéijma, cagcl a mlglmfr quf ba fbfmtrlquéijma fs ba raia cf ba quéijma quf fstucja bas rfammjlgfs quéijmas quf sf prlcumfg plr  ammjýg cf ba mlrrjfgtf fbêmtrjma (fbfmtrýbjsjs) cf jduab iagfra quf ba prlcummjýg cf uga mlrrjfgtf fbêmtrjma sf ca ifcjagtf rfammjlgfs quéijmas (pjbas, amuiubaclrfs), qujfrf cfmjr quf fs fb fstucjl cf bas rfammjlgfs quéijmas quf prlcumfg fhfmtls fbêmtrjmls y cf bls hfgýifgls quéijmls mausacls plr ba ammjýg cf bas mlrrjfgtfs l vlbt vlbtao aofs fs.. Sa Saik ikjê jêg g pl plcf cfil ilss if ifgm gmjl jlga garr quf quf bas bas rf rfam ammj mjlg lgfs fs qu quéi éijm jmas as qu quf f jgtfrvjfgfg fg fstls prlmfsls slg cf tjpl [fclx. Ulr fofipbl, bas katfréas slg ug mbarl fofipbl cf bas pjbas vlbtajmas cfkjcl a quf hugmjlgag ifcjagtf rfammjlgfs fbfmtrlquéijmas ([fclx), y sj ba mlgmfgtramjýg cf fbfmtrlgfs sf jduaba fg aikls pugtls, mfsa ba mlrrjfgtf fbêmtrjma. Saikjêg plcfils ifgmjlgar quf fb iatfrjab plr fb muab hbuyfg bls fbfmtrlgfs sf cfglijga mlgcumtlr. Bls mlgcumtlrfs pufcfg sfr cf cls cls tjtjpls pls?? ml mlgc gcumt umtlrf lrfss fb fbfm fmtr trýg ýgjm jmls ls l if iftá tábjbjmls mls,, y bls ml mlgc gcumt umtlrf lrfss fbfmtrlbétjmls. Ba mlgcummjýg tjfgf budar plr ba ijdramjýg cjrfmta cf bls fbfmtrlgfs a travês cfb mlgcumtlr kaol fb clijgjl cf ug pltfgmjab apbjmacl.

 

[F]VIFG Fsta prjif prjifra ra pramtjm pramtjma a cf baklratlr baklratlrjl jl tjfgf mlil mlil prlpýsjt prlpýsjtl l cfilstra cfilstrarr ba bfy cf Lni apbjmaca a ba fbfmtrlquéijma quf sf muipbf fg bls mlgcumtlrfs cf sfdugca mbas mbasf f qu quf f slg slg bas bas slbu slbumj mjlg lgfs fs fbfm fbfmtr trlb lbét étjm jmas as qu quf f vjfg vjfgf f a sfr sfr ba slbu slbumj mjýg ýg A (Mu]L3.6N;5) y slbumjýg K (Mu]L 3 .6N;5 + N;]L3), sjfgcl fsta partf cf ba fb fbfm fmtr trlqu lquéi éijm jma a qu quf f fst fstuc ucja ja ba bass rfa rfamm mmjl jlgf gfss qu quéi éijm jmas as quf quf prl prlcum cumfg fg fhfmt fhfmtls ls fbêmtrjmls y cf bls hfgýifgls quéijmls mausacls plr ba ammjýg cf mlrrjfgtfs l vlbtaofs. Sfgjfgcl fg mufgta ba partf tfýrjma cfb trakaol sf pasý a rfabjzar ba partf fxpfrjifgtab para ba muab agtfs cf rfabjzar ba iagjpubamjýg cfb fqujpl cf trakaol sf tuvl quf mlgtar mlg ug fsqufia cf ilgtaof, quf gls sjrvjý cf kasf para fb iagfol iagfo l cf bls jgstrui jgstruifgtls fgtls cf ifcjc ifcjca a mlil fb vlbtéiftrl y aipfré aipfréiftrl iftrl fstl fg mlgo mlgoug ugtl tl mlg mlg fb ág áglc lcl l y mátl mátlcl cl00 usai usails ls cl clss slbu slbumj mjlg lgfs, fs, uga uga slbu slbumj mjýg ýg A (Mu]L3.6N;5) y uga slbumjý slbumjýg g K (Mu]L3 .6N;5 + N;]L3) cf 655 iB maca ugl a 5.; I. Uara fb agábjsjs cf ba prámtjma trakaoails mlg ug aipfraof cf 5.;A mlgstagtf, y para ba fbaklramjýg cf bas prámtjmas sf tjfgfg quf rfabjzar iumnas ifcjcas cf vlbtaof cf amufrcl a maca slbumjýg, pfrl ba cjstagmja fgtrf fb mátlcl cf mlkrf y áglcl cf pblil sf maikja mlgstagtfifgtf fstas cjstagmjas slg? 5.;, 5.=, 5.3, 5.6, 5.8, 5.4, y 5.>0 cfb ijsil ilcl sf takubag tlcas bas ifcjcas rfabjzacas para cfspuês rfprfsfgtarbl dráhjmaifgtf mlg ba fmuamjýg mlrrfsplgcjfgtf.

 

JGCJMF J.

............................ .............................. ............................. ............................. .............................. ............................. ..............................; ................; JGS[LCVMMJLG.............

[F]VIFG.............. ............................ ............................. .............................. ............................. ............................. .............................. ............................. ............................. ....................= .....= LKOFSJXL]............... ............................. ............................. .............................. ............................. ............................. ............................. ............................................. ...............................6 6 JJ.

............................. .............................. ............................. ............................. .............................. ............................. ..........................8 ............8 IA[ML SFÝ[JML.............. ;.1 MFBCA FBFMS[LQVJIJMA............... .............................. ............................. ............................. ............................. .................................... ...................... 8 ............................ ............................. .............................. ............................. ............................. .............................................. ................................. ..4 4 ;.; BFZ CF LNI..............

;.;.1. BFZ CF LNI IJM[L]MÝUJMA? Mlgcumtjvjcac fbêmtrjma.....................................: ;.;.;. Bfy cf Lni iamrlsmýpjma............... ............................. ............................. ............................. ............................. .............................13 ...............13 JJJ.

UA[SF F^UF[JIFGSAB.............. ............................. ............................. ............................. ............................. .......................................14 .........................14

=.1.

............................ .............................. ............................. ............................. .............................. ................................................ .................................14 14 IÊSLCL.............

=.;. =. ;.

............................ ............................. ............................. .......................................... ........................... 14 IA IASF SF[J [JAB ABF] F] Z [F [FAM AMSJ SJXL XL] ].............

=.;.1.

IASF[JABF].............. ............................ ............................. .............................. ............................. ............................. ................................ ................. 14

=.;.;.

............................. ............................. .............................. ............................. ............................. ..................................14 ...................14 [FAMSJXL]...............



]ubhatl cf mlkrf pfgtanjcratacl.............. ............................. .............................. ............................. ............................. ........................14 .........14

=.;.=. =.=. =. =.

............................. .............................. ............................. ............................. .............................. ............................. ........................ ..........14 14 FQVJUL]..............

U[ U[LM LMFC FCJI JIJF JFGS GSL L F^ F^UF UF[J [JIF IFGS GSAB AB........................................................................1>

.............................. ............................. ............................. .............................. ............................. ............................... ................. 1: =.3 CASL] LKSFGJCL]...............

JX.

MÁBMVBL].............. ............................. ............................. ............................. .............................. ............................. ............................. ............................. .................. ....;1 ;1

a) Ur Urfp fpar aram amjý jýg g cf sl slbu bumj mjlg lgfs fs...........................................................................................;1 k) [FD [FD[F] [F]JÝG JÝG B BJGF JGFAB? AB? C CFIL FIL]S[ ]S[AM AMJÝG JÝG C CF F BA BF BFZ Z CF LN LNI I.............................;; m) CFS CFSF[I F[IJGA JGAMJÝ MJÝG G CF B BA A CF CFG]J G]JCAC CAC CF M ML[[ L[[JFG JFGSF SF...........................................;= X. [F]VBSACL]............. ............................ ............................. ............................. ............................. ............................. ............................................... ................................ ;4 XJ.

CJ]MV]JÝG CF CF [ [F F]VBSACL]............. ............................ ............................. ............................. .............................. ............................ .............=5 =5

XJJ.

............................ .............................. ............................. ............................. ............................. ............................. ........................ .........=1 =1 MLGMBV]JLGF].............

XJJJ.

KJKBJLD[ D[A AHÉA............. ............................ .............................. ............................. ............................. .............................. .......................................... ...........................== ==

............................. ............................. ............................. .............................. ............................. ............................. .............................. ...................................=3 ....................=3  AGF^L]..............

 

LKOFSJXL]

LKOFSJXL DFGF[AB Cfilstrar quf ba bfy cf lni sf muipbf fg mlgcumtlrfs cf sfdugca mbasf, uga slbumjýg A (Mu]L3.6N;5) y uga slbumjýg K (Mu]L 3 .6N;5 + N;]L3)

LKOFSJXL] F]UFMJHJML] 

Mabmubar bls drails cf subhatl cf mlkrf pfgtanjcratacl para ba prfparamjýg cf slbumjýg a 5.; Ilbar 



Mabmubar fb vlbuifg cf ámjcl subhÿrjml cf :4% fg pfsl para ba prfparamjýg cf ba slbumjýg a 5.; Ilbar



Nabbar ba fmuamjýg para cftfrijgar ba cfgsjcac cf mlrrjfgtf fg ba slbumjýg  A y K.



Drahjmar bls vablrfs fxpfrjifgtabfs cjstagmja vs vlbtaof cf ba slbumjýg A y K.

 

JJ.

IA[ML SFÝ[JML

;.1 MFBCA FBFMS[LQVJIJMA Ba mfbca fbfmtrlquéijma fs ug cjsplsjtjvl fxpfrjifgtab para dfgfrar fbfmtrjmjcac ifcjagtf uga rfammjýg rfclx fsplgtágfa fg clgcf ba sustagmja lxjcagtf fstá sfparaca cf ba rfcumtlra cf iagfra quf bls fbfmtrlgfs cfkfg atravfsar ug abaikrf cf ba sustagmja rfcumtlra namja ba lxjcagtf. Fg uga mfbca fb adfgtf rfcumtlr pjfrcf fbfmtrlgfs plr tagtl sf lxjca. Fb fbfmtrlcl fg clgcf sf vfrjhjma ba lxjcamjýg sf bbaia áglcl. Fg fb ltrl fbfmtrlcl ba sustagmja lxjcagtf lxjcag tf daga fbfmtrlgfs y plr tagtl sf rfcumf. Fb fbfmtrl fbfmtrlcl cl fg quf sf vfrjhj vfrjhjma ma ba rfcummjýg sf bbaia mátlcl. Ba mlrrjfgtf fbêmtrjma hbuyf cfb áglcl ab mátlcl plrquf nay uga cjhfrfgmja cf fgfrdéa pltfgmjab fgtrf bls fbfmtrlcls. Ba cjhfrfgmja cf pltfgmjab fbêmtrjml fgtrf fb áglcl y fb mátlcl sf ijcf fg hlria fxpfrjifgtab mlg ug vlbtéiftrl, clgcf ba bfmtura fs fb vlbtaof cf ba mfbca.

Hjdura 1? Mfbca fbfmtrlqujijma

Hufgtf? Iartjgfz (;516) Mfcas Fbfmtrlquéijmas, Vgjvfrsjcac Gamjlgab Autýglia

cf Iêxjml. 

 

;.; BFZ CF LNI Ba bfy cf lni cjmf quf ba jgtfgsjcac quf mjrmuba plr ug mlgcumtlr cf fbfmtrjmjcac fs cjrfmtaifgtf suijgjstraca a ba varjamjýg cf vlbtaof y parabfba f jgvfrsaifgtf a ba rfsjstfgmja. ]u jiplrtagmja fs cfkjcl a quf ug mjrmujtl sf pufcf sakfr cfscf agtfs ba hlria fg quf va hugmjlgar agtfs cf mlgfmtar. Fb fstucjl cf ba fbfmtrlcjgáijma tjfgf mlil bfy hugcaifgtab, ba Bfy cf Lni, plstubaca plr fb hésjml y iatfiátjml abfiág Dflrd ]jiýg Lni, Lni, fstrfmnaifgtf vjgmubaca a bls vablrfs cf bas ugjcacfs kásjmas prfsfgtfs fg muabqujfr mjrmujtl fbêmtrjml mlil slg?  

Ultfgmjab fbêmtrjml l vlbtaof F, su ugjcac fs fb vlbtjl (X)

 

Jgtfgsjcac cf ba mlrrjfgtf J, muya ugjcac fs fb fg aipfrf (A)

 

[fsjstfgmja [ fg lni lni ( ) cf ba mmarda arda l ml mlgsui gsuijcl jclrr mlgfmt mlgfmtacl acl ab mmjrm jrmujt ujtl. l. Hjdura ;? Mjrmujtl fbêmtrjml

Hufgtf? ]frway, [ayilgc0 Kfjmngfr (;555). Hésjma para Mjfgmjas f

Jgdfgjfréa JJ (6ª fcjmjýg). ImDrawNjbb 

Mjrmujtl fbêmtrjml mfrracl mlipufstl plr uga pjba cf 1,6 vlbt, uga rfsjstfgmja l marda fbêmtrjma "[" y ba. Mjrmubamjýg cf uga jgtfgsjcac l hbuol cf mlrrjfgtf fbêmtrjma " J " suijgjstracl plr ba prlpja pjba.

 

Hýriuba Hýriub a iatfiátjma dfgfrab cf rfprfsfgtam rfprfsfgtamjýg jýg cf ba bfy cf lni. Cfscf fb pugtl cf vjsta iatfiátjml fb plstubacl agtfrjlr sf pufcf rfprfsfgtar plr ifcjl cf ba sjdujfgtf Hýriuba Dfgfrab cf ba Bfy cf Lni?  J 9

 F … … . (1 )  [

Hjdura =? Mliplrtaijfgtl cf ba mlrrjfgtf mlg fb vlbtaof.

Hufgtf? ]frway, [ayilgc0 Kfjmngfr (;555). Hésjma para Mjfgmjas f

Jgdfgjfréa JJ (6ª fcjmjýg). ImDrawNjbb 

;.;.1. BFZ CF LNI IJM[L]MÝUJMA? Mlgcumtjvjcac fbêmtrjma. Cfkfils sfñabar prjifraifgtf quf, fg bls mlgcumtlrfs, bls plrtaclrfs cf marda gl sf fgmufgtrag fg mlipbfta bjkfrtaca para ilvfrsf, fs cfmjr su ilvjijfgtl fs abfatlrjl tab mlil sf iufstra fg ba jbustramjýg ;a, fsta trayfmtlrja quf cfsmrjkf bls

 

plrtaclrfs sf cfkf a ba jgtframmjýg mlg bls cfiás fbfmtrlgfs y mlg bls jlgfs hjols cf ba rfc mrjstabjga vêasf ba jbustramjýg ;k. Curagtf fstas jgtframmjlgfs (mlbjsjlgfs) bls fbfmtrlgfs pjfrcfg drag magtjcac cf fgfrdéa mjgêtjma quf ba acqujrjý muagcl sf 9∛f F.  apbjmý fb maipl fbêmtrjml  F , maipl quf bf prlcumf uga hufrza fbêmtrjma  H 9∛

Hjdura 3? BFZ CF LNI IJM[L]MLUJMAIFGSF.

Hufgtf? nttp?//nypfrpnysjms.pny-astr.dsu.fcu/nkasffs/fbfmtrjm/lniijm.ntib Ba mlgvfrsjýg cf fgfrdéa fbêmtrjma fg fgfrdéa mjgêtjma cf bls fbfmtrlgfs y ba plstfrjlr mlgvfrsjýg fg fgfrdéa têrijma (mabfgtaijfgtl cfb mlgcumtlr) plcréag rfprfsfg rfpr fsfgtar tarsf sf mli mlil l pêr pêrcjc cjcas as cfk cfkjcas jcas a huf hufrzas rzas cf hrj hrjmmj mmjýg ýg slkrf slkrf bas mar mardas das iývjbfs. Fstas hufrzas cf hrjmmjýg pufcfg asfifoarsf a bas quf aparfmfg fg fb ilvj il vjij ijfg fgtl tl cf ug sý sýbjbjcl cl fg fb jg jgtf tfrjl rjlrr cf ug hbhbuj ujcl cl,, sjfg sjfgcl cl cjmna cjmnass hu hufr frza zass prlplrmjlgabfs a ba vfblmjcac cf cfrjva cf bls fbfmtrlgfs

vc

⃔

, fgtlgmfs sf tjfgf

 h r'  kvc 

(;)

 

Cfkjcl a quf ba hufrza fbêmtrjma y ba hufrza hrammjlgab tjfgfg sjdgls lpufstls, cfspu cf spuês ês cf mj mjfr frtl tl tjtjfi fipl pl fs fsta tass sf fq fquj ujbjbjkra krag g ca cagcl gcl bu buda darr a ug il ilvj vjij ijfg fgtl tl ugjhlrif mlg uga vfblmjcac tfrijgab l béijtf lktfgjca béijtf lktfgjca a partjr cf  Hf  h r'  5  fF  kvc  vc  

⃔

f

 ⃔

k

F 

(=)

Cýgcf? k? fs uga mlgstagtf cf prlplrmjlgabjcac y cfpfgcf cfb iatfrjab cfb muab fstá nfmnl fb mlgcumtlr. Ulr ltrl bacl, cfglijgails ilvjbjcac cf bls fbfmtrlgfs (  βf ) ab

mlmjfgtf f/k f/k,, fs cfmjr  βf 9 f / k, mlg bl muab fsmrjkjils ba fmuamjýg fg ba hlria vc



 f F 

(3)

Uufstl ba cfgsjcac cf mlrrjfgtf fs prlplrmjlgab a ba vfblmjcac cf cfrjva cf bls fbfmtrlgfs, ab rfipbazar ba fmuamjýg (3) fg (a), rfsubta  o  gq5v  c   o



gf f F 

(a) (6)

Ba fmuamjýg (6) jgcjma quf ba cfgsjcac cf mlrrjfgtf fs prlplrmjlgab ab maipl fgli lijjga fbêm fbêmtr trjm jml l sjfg sjfgcl cl ba mlgs mlgsta tagt gtf f cf pr prlp lplr lrmj mjlg lgab abjc jcac ac gf β f  y sf bf cfg mlgcumtjvjcac mlgcumtjvjca c fbêmtrjma fbêmtrjma  (ύ) y a su rf rfmmépr prl lml quf sf bf bbaia rfsjstjvjcac  fbêmtrjma cfb iatfrjab. Fs cfmjr 





1   

 gf  f

(8)

Cfkf sfñabarsf acfiás quf tagtl ba mlgcumtjvjcac, asé mlil ba rfsjstjvjcac slg prlpjfcacfs quf cfpfgcfg cfb iatfrjab mlgcumtlr y gl cfpfgcfg cfb taiañl gj cf ba dfliftréa cfb mlgcumtlr.  Ab rfipbazar ba mlgcumtjvjcac fbêmtrjma fg ba fmuamjýg (6), lktfgfils

 

⃔

⃔

 o   F 

⃔1

F 

  

(4)

Fs a ba fmuamjýg (4) quf sf bf mlglmf mlil bfy cf Lni ijmrlsmýpjma. ijmrlsmýpjma. ]fdÿg fsta fmuamjýg ba rfsjstjvjcac fbêmtrjma pufcf fxprfsarsf mlil

     

 F   o

(>) Cf clgcf sf lktjfgf quf bas ugjcacfs cf ba cf ba rfsjstjvjcac   fs (X.i/A). X.i/A).   Fsta fmuamjýg acfiás jgcjma quf muagtl iaylr fs ba rfsjstjvjcac iás dragcf fs fb maipl fbêmtrjml gfmfsarjl para dfgfrar uga cfgsjcac cf mlrrjfgtf. Mlil vfrfils iás acfbagtf fb mlmjfgtf (X/A) sf bbaia lni (Ϊ), plr tagtl, bas ugjcacfs cf ba rfsj rf sjst stjv jvjc jcac ac fg fb ]J fs fb (Ϊ (Ϊ.i .i). ). Ba takb takba a 1 iu iufs fstr tra a abdu abdugl glss vabl vablrf rfss cf rfsjstjvjcacfs cf iatfrjabfs. Cf fbba sf lksfrva quf bls iftabfs y sus abfamjlgfs prfsfgtag rfsjstjvjcacfs iás pfqufñas, plr fbbl fs quf fstls iatfrjabfs slg ifolrfs mlgcumtlrfs cf ba fbfmtrjmjcac. Ulr ltrl bacl, bls ajsbaclrfs tjfgfg su rfsjstjvjcac rfsjst jvjcac iumnl iaylr quf bls mlgcumtlrfs, mlgcumtlrfs, sjfgcl fb hamtlr cfb lrcfg cf 15 ;;. Cfkf Cfk f sfñaba sfñabarsf rsf acfiás acfiás quf fb rfmé rfméprlm prlml l cf ba rfs rfsjst jstjvj jvjcac cac fs ba mlgcumtjvjcac  muyas ugjcacfs slg (Ϊ.i) -1sfdÿg fsta magtjcac, bls fbfifgtls muya mlgcumtjvjcac fs abta slg kufgls mlgcumtlrfs cf ba fbfmtrjmjcac. Cfkf Cf kf sfña sfñaba bars rsf f ac acfi fiás ás quf quf bls bls sfij sfijml mlgc gcum umtl tlrf rfss tjfg tjfgfg fg rf rfsj sjst stjv jvjc jcac acfs fs jgtfrifcjas fgtrf bls iftabfs y bls ajsbagtfs. Fstls iatfrjabfs tjfgfg uga drag jiplrtagmja fg fb cjsfñl cf cjsplsjtjvls fbfmtrýgjmls fg vjrtuc cf ba iagfra fg quf qu f ba tf tfip ipfr frat atura ura y fb añ añacj acjcl cl cf ji jipur purfz fzas as il ilcj cjhjhjma mag g su suss prl prlpj pjfc fcac acfs fs fbêmtrjmas. Vg ia iatf tfrj rjab ab qu quf f muip muipbf bf mlg mlg ba bfy bfy cf Lni Lni sf cf cfgl glij ijga ga ýnijml ýnijml.. Fg fstls iatfrjabfs, y a uga tfipfratura caca, ba rfsjstjvjcac pfriagfmf mlgstagtf, fs cfmjr, gl cfpfgcf cfb maipl fbêmtrjml. ]jg fikardl, fxjstfg ltrls iatfrjabfs mlil mli l bls sfi sfijml jmlgcum gcumtlr tlrfs fs muyl muyl mliplrt mliplrtaij aijfgt fgtl l fs gl bjgfab bjgfab cfglij cfglijgacl gaclss gl

 

ýnijmls,, fg fstl ýnijmls fstlss ia iatf tfrj rjab abfs fs,, ba cf cfgs gsjc jcac ac cf ml mlrrj rrjfg fgtf tf cf cfpfg pfgcf cf cf cfbb maipl maipl fbêmtrjml.

Sakba 1? [fsjstjvjcac, mlgcumtjvjcac y mlfhjmjfgtf cf tfipfratura cf abdugls

iatfrjabfs IASF[JAB Fbfifgtls Ubata Mlkrf Lrl Abuijgjl Sugdstfgl Njfrrl Ublil Ifrmurjl Abfamjlgfs Iagdagjga Mlgstagtág Gjmrlil Marklgl purl (drahjtl) Dfriagjl purl ]jbjmjl purl Ajsbaclrfs Xjcrjl Azuhrf Muarzl Ijma

[F]J]SJXJCAC ρ (Ϊ.i)

MLGCVMSJXJCAC ύ (Ϊ.i)-1

MLFHJMJFGSF CF SFIUF[A. α (µM)-1

1,34.15-> 1,4;.15-> ;,33.15-> ;,46.15-> =,;6.15-> 15,55.15-> ;;,55.15-> :6,55.15->

8,;:.154 6,>1.154 3,5:.154 =,66.154 1,>5.154 1,55.154 8,;:.154 5,1.154

5,55=> 5,55=:= 5,553 5.55=: 5,5536 5,5565 5,553= 5,555>>

33.15-> 3:.15-> 155.15->

5,;=.154 5,;=.154 5,1.154

1,55.15-6 5,55551 5,5553

-6

3

=,6.15 5,85 ;=55

;,:.15 ;,; 1,8.15-=

1515 ” 1513 1516 46.1518 1511 - 1516

15-15 ” 15-133 15-16 1,4=.15-1> 15.11 ” 15-16

-5,5556 -5,53> -5,546

Hufgtf? Mlrrjfgtf, rfsjstfgmja y hufrza fbfmtrliltrjz ” Xázqufz Darmja

;.;.;. Bfy cf Lni iamrlsmýpjma. Uara lktfgfr uga hlria iás usuab cf ba bfy cf Lni para apbjmamjlgfs prámtjmas mlgsjcfrfils ug sfdifgtl rfmtl cf abaikrf cf blgdjtuc B y sfmmjýg tragsvfrsab

 

 A, mlil sf iufstra fg ba jbustramjýg =, fgtrf muyls fxtrfils sf na apbjmacl uga cjhfrfgmja cf pltfgmjab ∈ X 9X k∛X a, ba ijsia quf prlcumf ug maipl fbêmtrjml  F  y uga mlrrjfgtf J. Hjdura 6? Mlgcumtlr cf blgdjtuc B y sfmmjýg A ugjhlrif ab quf sf bf apbjma uga

cjhfrfgmja cf pltfgmjab ΓX, ba ijsia quf prlcumf ug maipl F y mlil tab uga mlrrjfgtf J  ⃔    

Hufgtf? mlrrjfgtf, rfsjstfgmja y hufrza fbfmtrliltrjz ” Xázqufz Darméa

 Asuijfgcl quf fb maipl  F  fg fb jgtfrjlr fs cjhfrfg cjhfrfgtf tf cf mfrl y a ba vfz ugjhl ugjhlrif, rif, fgtlgmfs ba cjhfrfgmja cf pltfgmjab fgtrf bls fxtrfils k y a sfrá a

 ⃔

X    F.cs  F FB B k

(:)

Cfspfoagcl fb maipl fbêmtrjml sf tjfgf  F  

X 

(15)

 B

[fipbazagcl [fipb azagcl ba fmuamjýg (15) fg ba fmuamjýg (4), ba cfgsjcac cfgsjcac cf mlrrjf mlrrjfgtf gtf pufcf fsmrjkjrsf fg ba hlria  o    (

X   B

)

(11)

Sfgjfgcl fg mufgta quf ba cfgsjcac cf mlrrjfgtf fs ba jgtfgsjcac cf mlrrjfgtf plr  ugjcac cf árfa pfrpfgcjmubar, fstl fs  o 9 J / A , ba fmuamjýg (11) sf tragshlria fg

 

 J  A



 (X )

B

X    

 B  A



X    b 

J 

(1;)

Fs a ba mag magtjtjcac cac  ρ ( b / A ), quf sf bf ml mlgl glmf mf mli mlil l [fsj [fsjstfg stfgmja mja ([), cfb iatfrjab, fgtlgmfs  [    

 B  A

(1=)

 Ab rfipbazar ba fmuamjýg (1=) fg (1;), sf lktjfgf X  [J 

(13)

Ba fxpr fxprfs fsjý jýg g ca caca ca pl plrr ba fmua fmuamj mjýg ýg (1 (13) 3),, sf bf mlgl mlglmf mf mlil mlil bfy bfy cf Ln Lni i iamrlsmýpjma, pfrl fs jiplrtagtf mliprfgcfr quf fb vfrcacfrl mlgtfgjcl cf ba bfy cf Lni fs ba prlplrmjlg prlplrmjlgabjca abjcac c cjrfmta (fg fb masl cf mjfrtls iatfrjab iatfrjabfs) fs) fgtrf ba cjhfrfgmja ∈ X  mlg rfspfmtl a ba jgtfgsjcac cf mlrrjfgtf J l cf ba cfgsjcac cf mlrrjfgtf o o mlg rfspfmtl ab maipl fbêmtrjml F  mlrrjfgtf fbêmtrjml  F . Ba fmuamjýg (13) cfhjgf ba rfsjstfgmja [ cf muabqujfr mlgcumtlr, ya sfa quf lkfcfzma ba bfy cf Lni l gl, pfrl muagcl [ fs mlgstagtf fb mlrrfmtl bbaiar bfy cf Lni a fsta rfbamjýg  Aug muagcl ba fmuamjýg (13) iufstra uga rfbamjýg fgtrf ba rfsjstfgmja, ba cj cjhf hfrfg rfgmj mja a cf plt pltfgm fgmja jabb y ba jg jgtf tfgsj gsjcac cac cf mlr mlrrj rjfg fgtf tf,, cf cfkf kf prf prfmj mjsa sarsf rsf qu quf f ba rfsjstfgmja [ cf muabqujfr iatfrjab mlgcumtlr fs tltabifgtf jgcfpfgcjfgtf cf ba cjhfrfgmja cf pltfgmjab apbjmaca y cf ba jgtfgsjcac cf mlrrjfgtf, sjfgcl iás kjfg cfpfgcjfgtf cf ba dfliftréa cfb mlgcumtlr y cf ba gaturabfza cfb iatfrjab, asé plr  fofipbl sj fb mlgcumtlr fs rfmtl cf blgdjtuc b  y   y sfmmjýg tragsvfrsab mlgstagtf ba rfsjstfgmja [ fs prlplrmjlgab a ba blgdjtuc b  f  f jgvfrsaifgtf prlplrmjlgab ab árfa cf ba sfmmjýg tragsvfrsab A, sjfgcl ba mlgstagtf cf prlplrmjlgabjcac ba rfsjstjvjcac ρ Fg dfgfrab, ba rfsjstfgmja [, cf muabqujfr iatfrjab cf hlria arkjtrarja sf cftfrijga usagcl ba rfbamjýg

 

 [ 

X   J 



 F.cs   F.ccss    o .gcA    F.gcA ⃔

  ⃔ ⃔

⃔  

 A

(16)

A

Cf amufrcl mlg ba fmuamjýg (16), ba ugjcac cf ba rfsjstfgmja [ fg fb sjstfia jgtfrgamjlgab cf ugjcacfs fs fb lnijl, rfprfsfgtaca plr ba bftra lifda cfb abhakftl drjfdl (Ϊ). Fgtlgmfs 1 

1X 

(18)

1 A

Uara fb masl cf bls rfsjstlrfs quf lkfcfmfg ba bfy cf Lni, su dráhjm dráhjma a jgtfgsjcac cf mlrrjfgtf fg hugmjýg cf ba cjhfrfgmja cf pltfgmjab fs uga bégfa rfmta mlil sf iufstra fg ba jbustramjýg 3. Fg fb masl cf cjsplsjtjvls quf gl muipbfg mlg ba bfy cf Lni, ba rfbamjýg jgtfgsjcac cf mlrrjfgtf y cjhfrfgmja cf pltfgmjab pufcf gl sfr  uga prlplrmjýg cjrfmta, y pufcf sfr cjhfrfgtf mlg rfspfmtl a bls sfgtjcls cf ba mlrrjfgtf. Hjdura 8? [fbamjýg jgtfgsjcac cf mlrrjfgtf? (a) [fsjstfgmja ýnijma, (k) Cjlcl cf

vamél y (m) Cjlcl sfijmlgcumtlr 

(a)

(k (k))

(m (m))

Hufgtf? Mlrrjfgtf, rfsjstfgmja y hufrza fbfmtrliltrjz ” Xázqufz Darméa

JJJ.

JJJ.1. IÊSLCL

UA[SF F^UF[JIFGSAB

 

Fxpfrji frjifgt fgtab? ab? fs ug prlm prlmfsl fsl sjs sjstfi tfiátj átjml ml y uga aprlxjiamjýg mjfgtéhjma  mjfgtéhjma a ba Fxp jgvfstjdamjýg, fg ba muab fb jgvfstjdaclr iagjpuba uga l iás varjakbfs y mlgtrlba y ijcf muabqujfr maikjl fg ltras varjakbfs.

JJJ. JJ J.;. ;. IA IASF SF[J [JAB ABF] F] Z [F [FAM AMSJ SJXL XL] ] JJJ.;.1. IASF[JABF] 1 hjlba cf 655 ib 



; hjlbas cf ;65ib



Ujpfta cf 15 ib



Ujsfta



Kabagza Agabétjma



Mlmlcrjbls



Fbfmtrlcls (Uk y Ab)

JJJ.;.;. [FAMSJXL] 

]ubhatl cf mlkrf pfgtanjcratacl

 

 Ámjcl subhÿrjml

 

 Adua cfstjbaca

JJJ.;.=. FQVJUL] 

 Aipfréiftrl (5-;6 A)



Xlbtéiftrl (5-;5 X) [fýstatl



[fmtjhjmaclr 



CF]M[JUMJÝG CFB FQVJUL

 

[FMSJHJMACL[?  Fs ug jg jgst strui ruifg fgtý tý quf mlgvjfrtf ba mlrrjfgtf abtfrga fg mlrrjfgtf mlgtjgua.

[FL]SASL? rfduba ba jgtfg jgtfgsjcac sjcac cf ba mlrrjfgtf, mlgtrlbagcl ba fgfrdéa quf pasa a ba marda Cjsplsj plsjtjv tjvl l quf ijc ijcf f XLBS XL BSJI JIFS FS[L [L?? Cjs cjhfrfgmja cf pltfgmjab.

AIUF[JIFS[L?

Jgst strui ruifgt fgtl l Jg

para pa ra

ifcjr ifc jr ba jgt jgtfgsj fgsjcac cac cf uga mlrr mlrrjfg jfgtf tf fbêmtrjma.

MFBCA?  Fq Fquj ujpl pl qu quf f ml mlgt gtjjfgf fgf a ba slbu slbumj mjýg ýg cf cfgt gtrl rl cf fbbl fbbl ab mátl mátlcl cl y áglcl.

JJ JJJ. J.=. =. U[ U[LM LMFC FCJI JIJF JFGS GSL L F^UF[J F^UF[JIF IFGS GSAB AB a) ]f prfpar prfparý ý ba slbumj slbumjýg ýg A, para para fbbl fbbl sf pfsý pfsý ;6 d cf Mu]L3.6N;L 5.;I, fg uga hjlba cf 655 ib sf bf añacjý fb subhatl y sf ahlrl mlg adua cfstjbaca. k) Ua Uara ra ba slb slbum umjý jýg g K, sf pfsý pfsý 1;.6 1;.6 d cf Mu]L3.6N;L 5.; I, fg uga hjlba cf ;65 ib sf añacjý fb subhatl y sf ahlrl, adjtagcl kjfg ba slbumjýg, bufd bu fdl l fg ltra ltra hjhjlb lba a cf ;65 ib sf bf añacjý añacjý ;.46 ib cf N;]L3  5.; I, ahlrágclbl mlg adua cfstjbaca, aikas slbumjlgfs sf ifzmbarlg. m) Fg uga mf mfbc bca a fb fbfm fmtr trlb lbét étjm jma a sf adrfd adrfdý ý =6 =65 5 ib cf ba slbum slbumjý jýg g A, sf mlblmarlg bls fbfmtrlcls, a ug fbfmtrlcl cf mlkrf (mátlcl) sf mlgfmtý fb mlml ml mlcrj crjbl bl rl rlol ol y ab fb fbfm fmtr trlcl lcl cf pb pbli lil l (á (ágl glcl cl)) fb ml mlml mlcr crjbjbl l gf gfdrl drl,, prjifraifgtf, sfparacls a uga cjstagmja cf ;mi, tjfgfg quf fstar  ukjmacls parabfbaifgtf, para uga ifolr bfmtura, fstls sf mlgfmtarlg ab rfmtjhjmaclr. c) Fb aipfré aipfréif iftr trl l sf hjoý hjoý a ug vablr vablr cf 5.; aipfrj aipfrjls, ls, varja varjagc gcl l as aséé ba cjstagmja fgtrf bls fbfmtrlcls sjfgcl fstls cf ;, =, 3, 6, 8, 4 y > mi, agltagcl asé ba bfmtura cf bls vlbtaofs mlrrfsplgcjfgtfs.

 

f) ]fd ]fdujc ujcaif aifgtf gtf sf rftjrag rftjrag bls fbfmtrl fbfmtrlcls cls para mabmuba mabmubarr fb árfa iloaca, iloaca, tagtl ba abtura y fb agmnl. h) ]f rfabj rfabjzag zag bls bls ijsils ijsils pas pasls ls para para ba slb slbumj umjýg ýg K.

=.3 CASL] LKSFGJCL] ]LBVMJÝG A? SAKBA Gµ; CASL] LKSFGJCL] CF BA] XA[JAMJLGF] CF XLBSAOF [F]UFMSL A BA CJ]SAGMJA UA[A BA ]LBVMJÝG A Blgd Bl gdjt jtuc uc(m (mi i) F ( Xlbt lbtjl) jl) ; ;.6 = =.5 3 =.3 6 =.: 8 3.1 4 3.6 > 6.1 Hufgtf? Fbaklramjýg Urlpja 

 Árfa? Fbfmtrlcl cf Mlkrf? N  ?   N   ? Abtura cfb fbfmtrlcl suifrdjcl =.8 mi  A  ?

Agmnl cfb fbfmtrlcl suifrdjcl 3.3 mi

Fbfmtrlcl cf Ublil?  N  ?  ?

Abtura cfb fbfmtrlcl suifrdjcl =.3 mi

 A  ?

Agmnl cfb fbfmtrlcl suifrdjcl 3.1 mi

]LBVMJÝG K?

 

SAKBA Gµ= CASL] LKSFGJCL] CF BA] XA[JAMJLGF] CF MAJCA CF  SFG]JLG [F]UFMSL A BA BLGDJSVC UA[A BA ]LBVMJÝG K

Blgd Bl gdjt jtuc uc(m (mi i) F ( Xlbt lbtjl) jl) ; 1.> = ;.1 3 ;.= 6 ;.6 8 ;.8 4 ;.: > =.5 Hufgtf? Fbaklramjýg Urlpja



 Árfa? Fbfmtrlcl cf Mlkrf? N  ?   N   ? Abtura cfb fbfmtrlcl suifrdjcl =.4 mi  A  ?

Agmnl cfb fbfmtrlcl suifrdjcl 3.3 mi

Fbfmtrlcl cf Ublil?  N  ?

Abtura cfb fbfmtrlcl suifrdjcl =.8 mi

 A  ?

Agmnl cfb fbfmtrlcl suifrdjcl 3.1 mi

JX. a) Ur Urfp fpar aram amjý jýg gc cff sslb lbum umjl jlgf gfss ]LBVMJÝG A? 655 ib cf MV]L3 5.; I

MÁBMVBL]

 

Drails cf MV]L3  xdMV]L ;3:.8>

 ilb 5.;  9  B

3

dMV] MV] L

3

ilbMV]L

3

∛=

655 Ô 15  B

 xdMV] L 9 5.; Ô 5.6 Ô ;3:.8> 3

 xdMV] L 9 ;3.:8> 3

]LBVMJÝG K? ;65 ib cf MV]L3 5.; I+ ;65 ib cf N ;]L3 5.; I Drails cf MV]L3  xdMV]L

3

dMV] MV] L 5.;

 ilb  9  B

;3:.8>

3

ilbMV]L

3

∛=

;65 Ô 15  B

 xdMV] L 9 5.; Ô 5.;6 Ô ;3:.8> 3

 xdMV MV] ] L 9 1;.3>3 3

Ijbjbjtrls cf N;]L3 Catls cf N;]L3  ρ N  ] L 91.>3 ;

3

 d ib

Uurfza9:4% Ilbarjcac cfb ámjcl quf sf va a cjbujr?  I 9

15 Ô % Ô ρ ]

 UI 

15 Ô :4 Ô 1.>3

 I 9

:>

 

 I 91>.;1 I 

;65 ib cf N;]L3 M 1 X 19M ; X ; 1>.;1 I ÔX 1 95.; I Ô ;65 ib

X 19;.46 ib

k) [FD[F]JÝG BJGFAB? CFIL]S[AMJÝG CF BA BFZ CF L LNI NI ]lbumjýg A D[ÁHJMA Gµ 1 Cjstagmja vs X Xlbtaof lbtaof cf bba a slbumjýg A

b vs X 8 6

h(x) 9 5.31 x + 1.4= [» 9 5.::

3     )    X     (    f    o    a    t     b    l    X

= ; 1 5

1

;

=

3

6

8

4

Cjstagmja fgtrf pbamas (mi)

Hufgtf? Fbaklramjýg prlpja ]lbumjýg K D[ÁHJMA Gµ; Cjstagmja vs X Xlbtaof lbtaof cf bba a slbumjýg A

>

:

 

b vs X =.6 =

h(x) 9 5.; x + 1.3> [» 9 5.:>

;.6     )    X     (    f    o    a    t     b    l    X

; 1.6 1 5.6 5

1

;

=

3

6

8

4

>

:

Cjstagmja fgtrf pbamas (mi)

Hufgtf? fbaklramjýg prlpja

m) CFS CFSF[I F[IJGA JGAMJÝ MJÝG G CF B BA A CF CFG]J G]JCAC CAC CF ML[[J ML[[JFGS FGSF F Uara ba slbumjýg A? Cf ba fmuamjýg?  F 9 ρ

  J  b  ]

(1)

 

BG(cjstagmja ) 5.8:=1341> 1.5:>81;;: 1.=>8;:3=8 1.85:3=4:1 1.4:146:34 1.:36:1516 ;.54:33163

BG(Xlbtaof) 5.:18;:54= 1.5:>81;;: 1.;;=4463= 1.=85:4866 1.315:>8:4 1.6535443 1.8;:;3563

Bjgfabjzails tliagcl bldarjtils?   J  ]

Bg(F)9Bg( ρ )+Bg(b) Fgtlgmfs?

y9 a+kx

Z ba dráhjma rfsubta? Dráhjma Gµ=. Bjgfabjzamjýg

BG(Cjstagmja) vs BG(Xlbtaof)

    )    f    o    a    t     b    l    v     (    G    B

1.> 1.8 1.3 1.; 1 5.> 5.8 5.3 5.; 5 5.8

h(x) 9 5.3: x + 5.68 [» 9 5.::

5.>

1

1.;

1.3 BG(cjstagmja)

Hufgtf? Fbaklramjýg prlpja

1.8

1.>

;

;.;

 

Lktfgjfgcl ba fmuamjýg? y95.3:3=x+5.6646 Fgtlgmfs? Bg( ρ  J )9 5.6646 ]

 ρ

  J  9 fxp ( 5.6646 ) ]

Cf clgcf? J9 5.; A ]913.>: mi;  ρ 9

fxp  ( 5.6646 ) Ô 13.>: 5.;

mi  ρ 91=5  A

;

Cf ilcl quf ba cfgsjcac cf mlrrjfgtf, mlrrfsplgcf a?  ρj9

  1  A 1=5 mi;

=  ρ A 94.4 Ô 15∛   A ; mi

Uara ba slbumjýg K

BG(cjstagmj a) 5.8:=1341> 1.5:>81;;: 1.=>8;:3=8 1.85:3=4:1 1.4:146:34 1.:36:1516

BG(Xlbtaof) -5.=8861;:; 5.5:3534>= 5.=;88=3;8 5.346>>6 5.6>=1:>5> 5.8864;:>1

 

;.54:33163

5.4=;5::=4

Cfb muab fbjijgails fb prjifr pugtl, plr abfoarsf cf bls cfiás y lktfgfils ba dráhjma.

BG(Cjstagmja) vs BG(Xlbtaof) 5.> h(x) 9 5.1; x ∛ 5.5> [» 9 5.:6

5.4 5.8     )    f    o    a    t     b    l    v     (    G    B

5.6 5.3 5.= 5.; 5.1 5

5

1

;

=

3

6

BG(cjstagmja)

D[ÁHJMA Gµ 3 . Bjgfabjzamjýg

Hufgtf? Fbaklramjýg prlpja Lktfgjfgcl ba fmuamjýg? y95.838=x-5.6>>1 Fgtlgmfs?  J  ]

Bg( ρ )9 -5.6>>1   J   ρ ] 9 fxp (∛5.6>>1 )

8

4

>

 

Cf clgcf? J9 5.; A ]9Urlifcjl cfb árfa iloaca ]9 1=.:3 + 16.>3 ;

]913.>: mi;  ρ 9

fxp  (∛5.6>>1 ) Ô 13.>: 5.; ;

 mi  ρ 9 31.=6  A

Cf ilcl quf ba cfgsjcac cf mlrrjfgtf, mlrrfsplgcf a?  ρj9

  1  A 31.=6 mi; ∛;

 ρ K9;.3 Ô 15

X.

 A ;

mi

[F]VBSACL]

U[FUA[AMJÝG CF BA ]LBVMJÝG A?  xdMV] L 9 ;3.:8> 3

U[FUA[AMJÝG CF BA ]LBVMJÝG K  xdMV MV] ] L 9 1;.3>3 3

X  N  ] L 9 ;.46 ib ;

3

 

CFIL]S[AMJÝG CF BA BFZ CF LNI ]lbumjýg A Dráhjma Gµ 6 Cjstagmja vs Xlbtaof cf ba slbumjýg A

b vs X 8 6

h(x) 9 5.31 x + 1.4= [» 9 5.::

3     )    X     (    f    o    a    t     b    l    X

= ; 1 5

1

;

=

3

6

8

4

Cjstagmja fgtrf pbamas (mi)

]lbumjýg K D[ÁHJMA Gµ 8 Cjstagmja vs Xlbtaof cf ba slbumjýg K

CFSF[IJGAMJÝG CF BA CFG]JCAC CF ML[[JFGSF

>

:

 

MLIUA[AMJÝG FGS[F BA] ; ]LBVMJLGF] D[ÁHJMA G 4 . Mliparamjýg fgtrf bas cls slbumjlgfs

cjstagmja vs vlbtaof ]LBBVMJÝG A ]L

]lbu ]l bummjý jýg gK

8 6     )    X     (    f    o    a    t     b    l    X

3 = ; 1 5

1

;

=

3

6

8

Cjstagmja (mi)

Hufgtf? Fbaklramjýg prlpja Mábmubl cf cfgsjcac cf mlrrjfgtf Uara ba slbumjýg A ∛=

 ρ A 94.4 Ô 15

Uara ba slbumjýg K ∛;

 ρ K9;.3 Ô 15

 A mi

;

 A mi

;

4

>

:

 

XJ.

CJ]MV]JÝG CF [F]VBSACL]

]f na tfgjcl mujcacl fg muagtl a ba prfparamjýg cf bas slbumjlgfs a 5.;I, plr fbbl sf kusmý cf rfhfrfgmjas fb pfsl ilbfmubar cfb subhatl cf mlkrf pfgtanjcratacl y fb ámjcl mblrnécrjml, y sf na tfgjcl iumna prfmaumjýg ab ilifgtl cf pfsar y cjbujr  bas sustagmjas. Fg bas dráhjmas lktfgjcas para ba cfilstramjýg cf ba bfy cf Lni, para ba slbumjýg  A y K, sf bbfda a ba mlgmbusjýg quf, para mlgcumtlrfs cf sfdugca mbasf, quf slg bas slbumjlgfs slbumjlgfs fbfmtrlbé fbfmtrlbétjmas tjmas sf muipbf ba bfy cf Lni fg aikls masls, ya quf sf pufcf lksfrvar quf fb vlbtaof fs cjrfmtaifgtf prlplrmjlgab a ba cjstagmja, plr fbbl sf mlgsjdujý uga rfmta mlg ug [; aprlxjiacaifgtf cf 1, fb muab rfhjfrf quf bls catls lktfgjcls nag sjcl mlrrfmtls. Ulr ltra partf, fg ba dráhjma Gµ sf mlipara bas rfmtas lktfgjcas cf bls catls a aipfraof mlgstagtf, fg ba muab ba slbumjýg A prfsfgta vablrfs iás abtls cf vlbtaof quf bls cf ba slbumjýg K, fstl cfkjcl a quf, ab adrfdarbf ámjcl subhÿrjml a ba slbumjýg cf mlkrf, sf jgnjkf êsta plr fb fqujbjkrjl cf ba rfammjýg quf havlrfmf ab ámjcl, cf ilcl quf sf gfmfsjta ifgls vlbtaof para mlgcumjr ba mlrrjfgtf. Fg muagtl a ba cfgsjcac cf mlrrjfgtf, l mliÿgifgtf, ltrls autlrfs bl bbaiag mlgcumtjvjcac, quf fstá cfhjgjca mlil ba ifcjca cf ba mapamjcac cf uga sustagmja para cfoar pasar ba mlrrjfgtf fbêmtrjma a travês cf êb, rfsubta quf lktfgfils ug vablr iás abtl para ba slbumjýg K, fstl cfkjcl a quf ba slbumjýg plsff iaylr  magtjcac magtjc ac cf jlgfs quf ba slbumjýg A, y plr fbbl uga ifolr mlgcummjýg cf mlrrjfgt mlrrjfgtf f fbêmtrjma. Fstf rfsubtacl fs býdjml ya quf, mlil ba rfsjstjvjcac fs jduab a ugl fgtrf ba cfgsjcac cf mlrrjfgtf, fb vlbtaof fs jgvfrsaifgtf prlplrmjlgab a fsta cfgsjcac, plr fbbl, fs quf taikjêg bls vablrfs cfb vlbtaof slg ifglrfs fg ba slbumjýg K.

 

XJJ. 

MLGMBV]JLGF]

]f cfilstrý a travês cfb iêtlcl fxpfrjifgtab quf ba bfy cf Lni sf muipbf muipb f para mlgcumt mlgcumtlrfs lrfs cf sfdugc sfdugca a mbasf quf fs ba slbumj slbumjýg ýg cf subhatl subhatl cf mlkrf pfgtanjcratacl y subhatl amjcjhjmacl a 5.; I fg bl muab trakails mlg uga jgtfgsjcac mlgstatf cf 5.; Aipfrjls.

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  Bls drails cf subhatl subhatl cf mlkrf pfgt pfgtanjcrat anjcratacl acl para ba prfpar prfparamjýg amjýg cf slbumjlgfs a 5.; Ilbar rfsubtl cf ;3.:8>d y 1;.3>3d

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Fb vlbuifg cf ámjcl subhÿrjml cf :4% fg pfsl para ba prfparamjýg cf ba slbumjýg a 5.; Ilbar fs ;.46 iB

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Ba fmuamjýg para cftfrijgar ba cfgsjcac cf mlrrjfgtf y su rfsubtacl fg ba slbumjýg A y K. slg bls sjdujfgtfs?

]lbumjýg A ∛=  y95.3:3=x+5.6646  ρ A 94.4 Ô 15

]lbumjýg K y95.838=x-5.6>>1 ∛;

 ρ K9;.3 Ô 15

 A ;

mi

 A mi

;

 

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Bas dráhjmas cf bls vablrfs fxpfrjifgtabfs cjstagmja vs vlbtaof cf ba slbumjýg A y K nfmnl mlg fb Fxmfb gls rfsubta cf ba sjdujfgtf iagfra. Cjstagmja vs Xlbtaof cf ba slbumjýg A

 J vs X 8 6     )     (    X    f    o    a    t     b    l    X

h(x) 9 5.31 x + 1.4= [» 9 5.::

3 = ; 1 5

1

;

=

3

6

8

4

Cjstagmja fgtrf pbamas (mi)

]lbumjýg K Cjstagmja vs Xlbtaof cf ba slbumjýg K

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XJJJ.

KJKBJLD[AHÉA

Mrm Mrm Na Nagc gckll kll`` lh Mnfi Mnfijs jstr tryy agc agc Un Unys ysjm jmss >v >va a fc fcjm jmjý jýg g (;5 (;55;) 5;) M[M M[M Ur Urfs fsss Mlrplratf Uádjgas 6>5 – 6>6 ]frway, [ayilgc. Unysjms hlr ]mjfgtjsts agc Fgdjgffrs (=ª Fgdjgffrs (=ª fcjmjýg). ]augcfrs Mlbbfdf Uukbjsnfrs. ]frway,, [ayilgc0 Kfjmn ]frway Kfjmngfr gfr (;555). Hés Hésjma jma para Mjf Mjfgmj gmjas as f Jgd Jgdfgj fgjfré fréa a JJ (6ª fcjmjýg). ImDrawNjbb.

 

 AGF^L] ]LBVMJLG A

HJDV[A P4Y? U[FUA[AMJLG CF BA] ]LBVMJLGF] CF Mu]L3 . 6 N ; L a 5.;I

 

HVFGSF U[LUJA HJDV[A P>Y? IJCJFGC FGCL BA MAJCA CF XLBS XL BSAO AOF F UL[ UL[ MACA MACA MFGS MFGSJI JIFS FS[L [L QVF QVF  AXAG_A FB FBFMS[LCL FG BA MFBCA

HVFGSF

U[LUJA

 

]LBVMJLG K

HJDV[A P:Y? BBFGAGCL FB ]VBHASL CF MLK[F UFGSANJC[ASACL A BA MFBCA

HJDV[A P15Y? IJCJFGCL FB XLBSAOF CFB FBFMS[LCL FG BA MFBCA

 

HVFGSF U[LUJA