Actividad 1. Soluciones

 

TBFN ]LCRMGLIB] ULX1 AJLIIW MN]TGCCN R]BMJB ]bcbmmglin cn rbspubstn mlrrbmtn1 >.

]b vgbrtbi bi bc bfhudl db dbmnitnmgýi 4 fc db Tlcubil, = fc db Olrfnfgdn, Olrfnfgdn, 8 fc db Dgmclrlfbtnil Dgmclrlfbtnil y > fc db Mclrlolrfl. Mclrlolrfl. Cns dbisgdndbs db bstls cæqugdls sb fubstrni bi cn sgkugbitb tnhcn1

Cæqugdl Mclrlolrfl Dgmclrlfbtnil Olrfnfgdn Tlcubil

Dbisgdnd k/fc >,4:? >,=82 >,>=4 5,:?;

]g cubkl db ui tgbfpl db rbplsl sb nhrb cn ccnvb dbc bfhudl sb lhtgbib prgfbrl1  N. tlcubil H. olrfnfgdn M. dgmclrlfbtnil D. mclrlolrfl 8.

]b tgbibi >555 fc db uin slcumgýi 5,2 F db @LJ mli pJ 6 >=, >=,;. ;. ]g n bstn slcumgýi sb cb ndgmglin > flc db @LJ bs fuy prlhnhcb prlhnhcb qub  N. pbrfnibzmn pbrfnibzmn mlistnitb cn mlimbitrnmgýi db cn slcumgýi H. nufbitb cn mlimbitrnmgýi db glibs PLJ \ V M. pbrfnibzmn pbrfnibzmn mlistnitb bc pJ db cn slcumgýi D. nufbitb cn mlimbitrnmgýi db glibs PJ+V XB]ULIDN UXBKRITN] N 2 DB NMRBXDL N CN ]GKRGBITB GIOLXFNMGÝI Bi cn tnhcn sbCN] dbsmrghbi nckuins =prlpgbdndbs db dls mlfpubstls quæfgmls n uin ntfýsobrn db prbsgýi

]ustnimgn îmgdl hutnilgml nkun

Oýrfucn Bstrumturnc MJ=-MJ8-MJ8-MLLJ -MLLJ   J8L 

Utl bhuccgmgýi ±M >?4 >55

Trbs fbzmcns prbpnrndns mli îmgdl hutnilæml y nkun, sb rbprbsbitni bi uin rbmtn dlidb cls puitls gitbrfbdgls gidgmni bc vnclr bi plrmbitnab pbsl n pbsl (% U/U) db mndn mlfplibitb bi cn fbzmcn.

=.

Unrn mnfhgnr cn mlimbitrnmgýi db cn slcumgýi db îmgdl hutnilæml gidgmndn bi bc bc puitl > , nc , 8 cl fîs ndbmundl ndbmundl bs

Bs CN D.

4. Nc mnfh mnfhgnr gnr cn mlimbitrnmgýi db cn slcumgýi db îmgdl hutnilæml dbc puitl > , nc , 8 bs vîcgdl nogrfnr qub  N. pbrfnibmb pbrfnibmb mlistnitb bc plrmbitnab db nkun bi cn slcumgýi H. dgsfgiuyb cn mlimbitrnmgýi db cn slcumgýi M. dgsfgiuyb cn fnsn db nkun bi cn slcumgýi D. pbrfnibmb mlistnitb cn mlimbitrnmgýi db cn slcumgýi 2.

N uin ntfýsobrn db prb prbsgýi, sgýi, pnrn mnfh mnfhgnr gnr cn cn mlimbitrnmgýi db cn slcumgýi db db îmgdl hutnilæml. N uin ntfýsobrn db prbsgýi, pnrn mnfhgnr cn mlimbitrnmgýi db cn slcumgýi db îmgdl hutnilæml gidgmndn bi bc puitl 8 nc = bc prlmbdgfgbitl fîs ndbmundl bs1

B] CN H.

?.

]b tgbibi = rbmgpgbitbs n cn fgsfn tbfpbrnturn, bc prgfbrl mli nkun purn, bc sbkuidl mli uin slcumgýi nmulsn db InMc 5.52F y bc tbrmbrl mli uin slcumgýi nmulsn db InMc 5.5>F 5.5>F.. ]b dbtbrfgiý bc puitl db bhuccgmgýi db cls cæqugdls n dls prbsglibs dgobrbitbs, tnc mlfl sb lhsbrvn bi cn tnhcn.

CÆ^RGDL

Utl. Bhuccgmgýi ±M ;?5 ff Jk 2?5 ff Jk

 

 Nkun ]lcumgýi InMc 5.52 F ]lcumgýi InMc 5.5> F

>55 >52 >5>

7= >58 77

Db nmubrdl mli cl nitbrglr, bs mlrrbmtl m lrrbmtl nogrfnr qub bc puitl db bhuccgmgýi db uin slcumgýi  N. nufbitn, nufbitn, munidl cn prbsgýi nufbitn nufbitn y dgsfgiuyb cn mlimbitrnmgýi db cn slcumgýi H. dgsfgiuyb, munidl cn prbsgýi nufbitn y dgsfgiuyb cn mlimbitrnmgýi m limbitrnmgýi db cn slcumgýi slcumgýi M. nufbitn, nufbitn, munidl cn prbsgýi p rbsgýi nufbitn y nufbitn cn mlimbitrnmgýi db cn slcumgýi D. dgsfgiuyb, munidl m unidl cn prbsgýi dgsfgiuyb y nufbitn cn mlimbitrnmgýi db cn slcumgýi

 

;. Cn sgkugbitb tnhcn fubstrn giolrfnmgýi slhrb cns slcumglibs G y GG  ]lcumglibs

Fnsn flcnr dbc slcutl (k/flc)

Fnsn db slcutl (k)

_lcufbi db slcumgýi (mf=)

G GG

855 855

855 455

>555 255

F6

flcbs slcutl Cgtrls db slcumgýi

 N. cn slcumgýi G tgbib tgbib fnylr iñfbrl db flcbs db slcutl y su mlimbitrnmgýi mlimbitrnmgýi bs fnylr qub qub cn slcumgýi GG H. cn slcumgýi GG tgbib fbilr iñfbrl db flcbs db slcutl s lcutl y su mlimbitrnmgýi bs fnylr qub cn slcumgýi G M. cn slcumgýi G tgbib fbilr iñfbrl db flcbs db slcutl y su mmlimbitrnmgýi limbitrnmgýi bs fnylr qub cn slcumgýi GG D. cn slcumgýi GG tgbib fnylr iñfbrl db flcbs db d b slcutl y su mlimbitrnmgýi bs fnylr qub cn slcumgýi G

:.

N ui tuhl db b bisnyl isnyl qub mlitgbib nkun, sb cb nkrbkni 85k db InMc0 plstbrglrfbitb, sb nkgtn nkgtn cn fbzmcn y sb lhsbrvn qub uin pnrtb dbc InMc nkrbkndl il sb dgsubcvb pbrfnibmgbidl bi bc olidl dbc tuhl. Bs vîcgdl nogrfnr qub bi bc tuhl db bisnyl bc nkun y bc InMc mliolrfni  N. uin fbzmcn fbzmcn jbtbrlkçibn H. ui mlfpubstl M. uin fbzmcn jlflkçibn D. ui mlclgdb MLITB]TB CN] UXBKRITN] 7 W >5 DB NMRBXDL MLI CN ]GKRGBITB GIOLXFNMGÝI  N muntrl vnsls qub mlitgbibi mlitgbibi vlcñfbibs dgobrbitbs db nkun sb nkrbkn uin mnitgdnd dgstgitn db slcutl Z db nmubrdl mli cn sgkugbitb tnhcn.

vnsl > 8 = 4

_lcufbi db nkun (fc) 85 ?5 :5 45

Fnsn db Z ndgmglindn (k) 2 >2 85 >5

7. Db nmubrdl mli cn sgtunmgýi nitbrglr, bs vîcgdl nogrfnr nogrfnr qub cn mlimbitrnmgýi bs  N. fnylr bi bc vnsl = H. gkunc bi cls muntrl vnsls M. fbilr bi bc vnsl > D. fnylr bi bc vnsl 8 >5. ]g sb bvnplrn cn fgtnd dbc slcvbitb slcvbitb bi mndn uil db cls vnsls bs fuy prlhnhcb qub nc ooginc ginc db cn bvnplrnmgýi  N. cls muntrl vnsls mlitbikni mlitbikni gkunc fnsn db cn sustnimgn Z H. cn mlimbitrnmgýi db cns muntrl slcumglibs sbn gkunc M. dgsfgiuyn cn mlimbitrnmgýi db cn slcumgýi dbc vnsl dls D. nufbitb cn fnsn db cn sustnimgn Z bi cls muntrl vnsls >.

8.

=.

4.

Mli cls nmbgtbs bsbimgncbs bxtrnædls n pnrtgr db nckuins pcnitns, sb pubdbi prbpnrnr dgobrbitbs prldumtls nc fbzmcnrcls mli btnilc y nkun. Babfpcls db bstls prldumtls, mli su rbspbmtgvl plrmbitnab bi pbsl db nmbgtbs bsbimgncbs, sli1 cn mlclign (bitrb ui 8% y 4%), bc nkun db  pbroufb (:%) y bc pbroufb (85%). ]g sb vn n prbpnrnr cn fgsfn mnitgdnd bi pbsl db mndn uil db bstls prldumtls, bc ñigml biuimgndl vbrdndbrl bs1 n. Unrn bc pbroufb y bc nkun db pbroufb sb dbhb ndgmglinr cn fgsfn mnitgdnd bi fnsn db nmbgtbs bsbi bsbimgncbs. mgncbs. Cn mlclign bs bc prldumtl qub rbqugbrb uin fnylr f nylr mnitgdnd db nmbgtbs bsbimgncbs. h. Bi tldls cls prldumtls sb dbhb nkrbknr cn fgsfn mnitgdnd db nkun y btnilc. m. d. Bc pbroufb bs bc prldumtl qub rbqugbrb uin fbilr mnitgdnd db nkun y btnilc. ]g sb vni n prbpnrnr >5 k db nkun db pbroufb, sb rbqugbrbi1 : k db nmbgtb bsbimgnc y 8 k db nkun y btnilc. n. 5.: k db nmbgtb bsbimgnc y >5 k db nkun y btnilc. h. m. 5.: k db nmbgtb bsbimgnc y 7.8 k db nkun y btnilc. : k db nmbgtb bsbimgnc, > k db nkun y > k db btnilc. d.  Nckuins pgiturns vgiæcgmns mlitgbibi ml mlfpubstls fpubstls jnclk jnclkbindls bindls (X-Z (X-Z)) uin olrfn db munitgogmnr bstl bstlss mlfpubstl mlfpubstlss bs jnmgçidlcls rbnmmglinr mli nflignml, tnc mlfl sb prbsbitn bi cn sgkugbitb bmunmgýi X-Z + IJ= ↘ XIJ8 + JZ  JZ  ]g sb dbsbn trnisolrfnr bi su tltncgdnd >8 flcbs dbc mlfpubstl jnclkbindl, bc vlcufbi IJ = ?F rbqubrgdl bs  8.5 C 5.2 C m. n. 4.5 C >.5 C d. h. Cn prbsbimgn db fbtncbs dgsubctls bi mnitgdndbs supbrglrbs n 25 ppf sli plml rbmlfbidnhcb bi pgiturns db usl dlfçstgml. Cn fubstrn fu bstrn db pgiturn qub prbsbitn ui vnclr supbrglr n cn mlimbitrnmgýi rbmlfbidndn bs.

B] CN D.

 

2.

Ri cæqugdl jgbrvb munidl su prbsgýi db vnplr bs gkunc n cn prbsgýi bxtbrin qub nmtñn slhrb cn supbrogmgb dbc cæqugdl, nc nufbitnr cn mlimbitrnmgýi db ui slcutl bi ui slcvbitb sb dgsfgiuyb cn prbsgýi db vnplr y sb nufbitn su puitl db bhuccgmgýi, bi cn sgkugbitb tnhcn sb fub fubstrn strn bc puitl db bhuccgmgýi db 4 dgslcumglibs db nkun y cn fgsfn snc mli dgobrbitb mlimbitrnmgýi.

]bkñi cls dntls prbsbitndls bi cn tnhcn, pubdb mlimcugrsb qub cn mlimbitrnmgýi db cn snc db cn slcumgýi. m. F bs fnylr qub cn mlimbitrnmgýi db cns C bs fbilr qub cn mlimbitrnmgýi db cns dgslcumglibs I y C. dgslcumglibs I y F. I bs fbilr qub cn mlimbitrnmgýi db cns L bs fnylr qub cn mlimbitrnmgýi db cns d. h. dgslcumglibs C y F. dgslcumglibs C y I. n.

?.

Cn rbcnmgýi bitrb cls mlfplibitbs db uin slcumgýi sb dn mlfl mlimbitrnmgýi, uin bxprbsgýi db cn mlimbitrnmgýi db uin slcumgýi bs bc plrmbitnab pbsl n pbsl l plrmbitnab fnsn n fnsn %p/p l % f/f

]b prbpnrni 4 slcumglibs db mclrurl db sldgl y cn mlimbitrnmgýi db mndn slcumgýi sb prbsbitn bi cn sgkugbitb tnhcn.

Cn slcumgýi qub tgbib fnylr mnitgdnd db slcutl dgsubctl plr mndn >55k db slcumgýi bs cn = m. >  d. 4  h. 8  n.

;.

Bi cn btgqubtn db ui ornsml db îmgdl mclrjædrgml npnrbmb cn sgkugbitb giolrfnmgýi1 ]lcumgýi db îmgdl mclrjædrgml nc 4% bi pbs l l,, ¼bc 4% bi pbsl gidgmn qub bc ornsml mlitgbib< n. 4 k db îmgdl mclrjædrgml plr mndn 7?% db slcumgýi. h. 4 k db îmgdl mclrjædrgml plr mndn >55% db slcutl 4 k db îmgdl mclrjædrgml plr mndn >55% db dgslcvbitb. m. d. 4 k db îmgdl mclrjædrgml plr mndn >55% db slcumgýi.

:.

Munidl bxgstb ui bqugcghrgl bitrb bc slcutl dgsubctl y bc dgslcvbitb, sb dgmb qub cn slcumgýi bs snturndn. Cns zlins plr dbhnal db cns murvns rbprbsbitni cns slcumglibs il snturndns y cns zlins plr bimgfn, cns slcumglibs slhrbsnturndns. N pnrtgr db cn giolrfnmgýi nitbrglr, bs mlrrbmtl nogrfnr qub bi uin slcumgýi il snturndn cn mnitgdnd db slcutl dgsubctl bs1 n. suogmgbitb pnrn cn mnitgdnd db dgslcvbitb. gisuogmgbitb pnrn cn mnitgdnd db dgslcvbitb. h. m. dbfnsgndn pnrn cn mnitgdnd db dgslcvbitb. d. bxnmtnfbitb gkunc n cn mnitgdnd db dgslcvbitb.

7.

Ri bstudgnitb rbncgzn ui bxpbrgfbitl bi bc qub tlfn trbs vnsls db prbmgpgtndls mli >55 k db nkun n 85µM y sgkub bc prlmbdgfgbitl qub sb dbsmrghb n mlitgiunmgýi1 Nc vnsl > cb nkrbkn >2 k db @Mc y nkgtn. Cubkl, nkrbkn ui mrgstnc ndgmglinc db @Mc qub sb dgsubcvb. Nc vnsl 8 cb nkrbkn =2 k db @Mc y nkgtn. Nc mnhl db ui tgbfpl, nkrbkn ui mrgstnc ndgmglinc db @Mc qub mnb nc olidl. Nc vnsl = cb nkrbkn 25 k db @Mc, mncgbitn jnstn ;5µM y cl dban rbplsnr pnrn dgsfgiugr cn tbfpbrnturn cbitnfbitb. Dbspuçs db ui tgbfpl, nkrbkn ui mrgstnc ndgmglinc db @Mc, bc munc bfpgbzn n mrbmbr nkclfbrnidl cn mnitgdnd db slcutl qub bstî bi bxmbsl. Cn tnhcn qub fbalr rbprbsbitn cn mlimcusgýi dbc bstudgnitb slhrb bc tgpl db slcumgýi qub sb lhtgbib bi mndn uil db cls vnsls bs1

B] CN M

>5.

Cn sgkugbitb tnhcn fubstrn giolrfnmgýi slhrb cns slcumglibs G y GG

 

  Tbigbidl bi mubitn cn giolrfnmgýi sb pldræn giobrgr qub1 cn slcumgýi G tgbib fnylr iñfbrl db flcbs db slcutl y su mlimbitrnmgýi bs fnylr qub cn slcumgýi GG h. cn slcumgýi GG tgbib fbilr iñfbrl db flcbs db slcutl y su mlimbitrnmgýi bs fnylr qub cn slcumgýi G

m.

n.

>>.

d.

cn slcumgýi G tgbib fbilr iñfbrl db flcbs db slcutl y su mlimbitrnmgýi bs fnylr qub cn slcumgýi GG cn slcumgýi GG tgbib fnylr iñfbrl db flcbs db slcutl y su mlimbitrnmgýi bs fnylr qub cn slcumgýi G

Cn mlimbitrnmgýi bs uin fbdgdn db cn mnitgdnd rbcntgvn db ui slcutl qub sb dgsubcvb bi ui slcvbitb. N uin slcumgýi db snc bi nkun sb ndgmglin krnduncfbitb snc y plstbrglrfbitb sb ndgmglin nkun y sb fgdb su mlimbitrnmgýi. Cn krîogmn qub rbprbsbitn cn mlimbitrnmgýi durnitb bc trnismursl dbc bisnyl bs1

B] CN H

>8.

 N >C db nkun sb ndgmglin ml mlitgiunfbitb itgiunfbitb uin snc lhtbigbid lhtbigbidl l cn krnogmn qub sb prbsbitn n mlitgiunmgýi1

Db nmubrdl mli cn krîogmn bs mlrrbmtl nogrfnr qub hnal bstns mlidgmglibs bi >C db nkun cn mnitgdnd db snc dgsubctn bi bc puit l1 W bs fbilr db 85k W bs fnylr db 85k m. d. Z bs fbilr db 85k h. Z bs gkunc n 85k n.

>=.

 N muntrl vnsls qub ml mlitgbibi itgbibi vlcñfbibs dg dgobrbitbs obrbitbs db nkun sb nkrbkn uin mn mnitgdnd itgdnd dgstgitn db slcutl Z db nmubrd nmubrdl l mli cn sgkugbitb tnhcn.

Bi mndn vnsl sb olrfni fbzmcns jlflkçibns. Db nmubrdl mli cn sgtunmgýi nitbrglr, bs vîcgdl nogrfnr qub cn mlimbitrnmgýi bs1 fbilr bi bc vnsl > fnylr bi bc vnsl = m. n. fnylr bi bc vnsl 8 gkunc bi cls muntrl vnsls d. h.

h.

]g sb bvnplrn cn fgtnd f gtnd dbc slcvbitb bi mndn uil db cls vnsls bs fuy prlhnhcb qub nc oginc db ccn n bvnplrn bvnplrnmgýi1 mgýi1 cls muntrl vnsls mlitbikni gkunc fnsn db cn sustnimgn Z m. dgsfgiuyn cn mlimbitrnmgýi db cn slcumgýi dbc vnsl dls cn mlimbitrnmgýi db cns muntrl slcumglibs sbn gkunc d. nufbitb cn fnsn db cn sustnimgn Z bi cls muntrl vnsls

>2.

Bi cn btgqubtn db ui ornsml db vginkrb npnrbmb cn giolrfnmgýi1 ‒slcumgýi db îmgdl nmçtgml nc 4% bi fnsn l 4% bi pbsl. Bc 4% bi fnsn l bi

n.

pbsl gidgmn qub bc ornsml mlitgbib1 4 k db îmgdl nmçtgml bi 7? k db slc slcvbitb. vbitb. >55 k db slcutl y 4 k db îmgdl nmçtgml.

>4. n.

h. >?.

m. d.

>55 k db slcvbitb y 4 k db îmgdl nmçtgml. 4 k db îmgdl nmçtgml bi >55 k db slcvbitb

Cn prbsgýi db vnplr db uin sustnimgn sb dbogib mlfl cn prbsgýi qub babrmb bc kns db bsn sustnimgn munidl sb bimubitrn bi bqugcghrgl mli cn onsb cæqugdn l sýcgdn. Cn sgkugbitb krîogmn gcustrn cn prbsgýi db vnplr db 4 cæqugdls n dgobrbitbs tbfpbrnturns, cls muncbs sli utgcgzndls mlfl slcvbitbs pnrn cn lhtbimgýi y/l purgogmnmgýi db nckuils mlfpubstls lrkîigmls bfpcbndls bi cn prbpnrnmgýi db dbsgiobmtnitbs1

Dbc krîogml pubdb nogrfnrsb qub bc cæqugdl mli fnylr tbidbimgn n bvnplrnrsb bs bc1 n. çtbr dgbtæcgml. mclrlolrfl. h.

m. d.

tbtrnmclrurl db mnrhlil. nkun.

 

>;.

Tbigbidl bi mubitn qub bc puitl db bhuccgmgýi bs cn tbfpbrnturn n cn munc cn prbsgýi db vnplr db ui cæqugdl bs gkunc n cn prbsgýi bxtbrin, pubdb nogrfnrsb qub n uin prbsgýi ntflsoçrgmn db ?55 ff Jk, cn sustnimgn mli fnylr tbfpbrnturn db bhuccgmgýi bs bc1 tbtrnmclrurl db mnrhlil. çtbr dgbtæcgml. m. n. nkun. mclrlolrfl. d. h.

>:.

Cn slcuhgcgdnd bs cn fîxgfn mlimbitrnmgýi db slcutl qub ndfgtb uin dbtbrfgindn mnitgdnd db slcvbitb n mgbrtn tbfpbrnturn, tbfpbrnturn, Bi cn krîogmn sb fubstrn cn murvn db slcuhgcgdnd pnrn nckuins sncbs qub sb s b bimubitrni dgsubctns bi bc lrknigsfl bi ouimgýi db cn tbfpbrnturn.

Db nmubrdl mli cn giolrfnmgýi nitbrglr bs vîcgdl nogrfnr qub n ?5µM bc mlfpubstl fbils slcuhcb bs1 InMc @Mc m. n. @IL= @G d. h. >7.

85.

 N 25 µM, sb dgsubcvbi ?5 k db @IL= bi >55 k db nkun. Db nmubrdl mli cn krîogmn nitbr nitbrglr, glr, bs mlrrbm mlrrbmtl tl nogrfnr qub cn slcumgýi qub sb prbpnrn bs1 n. gisnturndn, plrqub n bsn tbfpbrnturn sb pubdbi m. snturndn, plrqub n bsn tbfpbrnturn sb pubdbi dgslcvbr jnstn >;5 k db snc dgslcvbr jnstn ?5 k db snc h. gisnturndn, plrqub n bsn tbfpbrnturn sb pubdbi d. snturndn, plrqub n bsn tbfpbrnturn sb pubdbi dgslcvbr jnstn 75 k db snc dgslcvbr fbils db ?5 k db snc Cn sgkugbitb krîogmn rbcnmglin bc iñfbrl db flcbs db slcutl dgsubctl bi dgstgitls vlcñfbibs db uin fgsfn slcumgýi. slcumgýi.

Db nmubrdl mli cn krîogmn, bs mlrrbmtl nogrfnr qub bi ;55 y >555 fc, cns flcbs db slcutl dgsubctl bi cn slcumgýi sli nprlxgfndnfbitb1 nprlxgfndnfbitb1 n. 8,2 y 4 h. 8,2 y = m. = y 2 d. >,2 y =