,QLFLDFLyQDOD4XtPLFD 5(62/8&,Ï1'(&8(67,21(6 &XHVWLyQ &XHVWLyQ 'DGDVODVVLJXLHQWHVFRQILJXUDFLRQHVHOHFWUyQLFDV &VVS $VVSVS %VV ,QGLTXHUD]RQDGDPHQWH D(OJUXSR\SHUtRGRHQORVTXHVHKDOODQ$%\& E/RVLRQHVPiVHVWDEOHVTXHIRUPDUiQ$%\& Solución D$'DGRTXHODFRQILJXUDFLyQHOHFWUyQLFDGHODFDSDGHYDOHQFLDHVVSVH HVWiOOHQDQGRODFDSD0FRQQ~PHURFXiQWLFRSULQFLSDOSRUORTXHHOHOHPHQWR HVWDUiVLWXDGRHQHOWHUFHUSHUtRGR $O VHU V S TXLHUH GHFLU TXH VH HVWi OOHQDQGR OD VXEFDSD S \ TXH \D KDQ HQWUDGRFXDWURHOHFWURQHVSRUORTXHOHFRUUHVSRQGHHVWDUHQHOJUXSR %$OVHUODFRQILJXUDFLyQHOHFWUyQLFDGHODFDSDGHYDOHQFLDVFRUUHVSRQGHDO SHUtRGR\FRPRVHKDRFXSDGRHORUELWDOVFRQGRVHOHFWURQHVDOJUXSR & (Q HVWH FDVR OD FRQILJXUDFLyQ HOHFWUyQLFD HV V S OR FXDO LQGLFD TXH SHUWHQHFHDOVHJXQGRSHUtRGR\DOWHQHUOOHQRVORVWUHVRUELWDOHVSDOJUXSR E $ 'DGD OD FRQILJXUDFLyQ HOHFWUyQLFD D OD TXH OH IDOWDQ GRV HOHFWURQHV SDUD FRPSOHWDUODFRQILJXUDFLyQGHJDVQREOHVSHOLRQPiVHVWDEOHVHUi$ %(QHVWHFDVRODWHQGHQFLDHVDSHUGHUORVGRVHOHFWURQHVVGDQGR%FRQOR TXHDGTXLHUHODFRQILJXUDFLyQGH+HV &(QHVWHFDVRFRPRVXFRQILJXUDFLyQHVODGHO1HVSQRWLHQHWHQGHQFLDD IRUPDULRQHV &XHVWLyQ &XHVWLyQ D (VFULED OD HVWUXFWXUD HOHFWUyQLFD GH ORV iWRPRV GH ORV HOHPHQWRV FX\RV Q~PHURVDWyPLFRVVRQ\ E,QGLTXHMXVWLILFDQGRODUHVSXHVWDHOHOHPHQWRGHPD\RUHQHUJtDGHLRQL]DFLyQ \HOTXHWLHQHPD\RUFDUiFWHUPHWiOLFR F¢(QTXpJUXSR\SHUtRGRGHOVLVWHPDSHULyGLFRHVWiVLWXDGRFDGDHOHPHQWR" Solución D= VVSV = VVSVS (VWUXFWXUDGHODPDWHULD = VVSVS E (O HOHPHQWR GH = HV HO TXH WLHQH PD\RU HQHUJtD GH LRQL]DFLyQ DO WHQHU PD\RU Q~PHUR GH SURWRQHV \ PD\RU Q~PHUR GH HOHFWURQHV HQ OD FDSD GH YDOHQFLD (OTXHWLHQHPD\RUFDUiFWHUPHWiOLFRHVHOGH= \DTXHHVHOTXHFHGHPiV IiFLOPHQWH HO HOHFWUyQ GH OD FDSD GH YDOHQFLD \ WHQHU HO PD\RU UDGLR DO VHU HO SULPHUHOHPHQWRGHHVHSHUtRGR F'DGR TXH ORV WUHV HOHPHQWRV SUHVHQWDQ FRPR FDSD GH YDOHQFLD OD GH Q HVWiQHQHOWHUFHUSHUtRGR (OHOHPHQWRGH= GDGDVXFRQILJXUDFLyQHOHFWUyQLFDGHODFDSDGHYDOHQFLD HVWiVLWXDGRHQHOJUXSRSULPHUJUXSRGHOEORTXHV (O HOHPHQWR GH = DO WHQHU XQ VROR HOHFWUyQ S HVWi VLWXDGR HQ HO SULPHU JUXSRGHOEORTXHSHVGHFLUHQHOJUXSR (O HOHPHQWR GH = WLHQH FXDWUR HOHFWURQHV HQ HO RUELWDO S SRU OR TXH FRUUHVSRQGHDOFXDUWRJUXSRGHOEORTXHHVGHFLUDOJUXSR &XHVWLyQ &XHVWLyQ 3DUDFDGDXQDGHODVVLJXLHQWHVSDUHMDV D .= \&O= E )= \1D= F &O\. ,QGLTXHGHIRUPDUD]RQDGDTXpiWRPRRLRQWLHQHXQUDGLRPD\RU Solución D. VVSVSV &O VVSVS (OUDGLRGHO.HVPD\RUTXHHOGHO&O\DTXHHQpOVHLQLFLDXQDQXHYDFDSDFRQ UHVSHFWR DO FORUR \D TXH HO HOHFWUyQ GH YDOHQFLD HVWi HQ OD FDSD FXDUWD PLHQWUDVTXHORVGHOFORURVHTXHGDQHQODWHUFHUD E) VVS 1D VVSV (O UDGLR GHO 1D HV PD\RU TXH HO GHO ) SRU ODV PLVPDV UD]RQHV TXH HQ HO FDVR DQWHULRUSHURHVWDYH]FRQODVFDSDV\ F&O VVSVS . VVSVS ,QLFLDFLyQDOD4XtPLFD (O UDGLR GHO LRQ FORUXUR HV PD\RU TXH HO LRQ SRWDVLR DXQ FXDQGR DPERV LRQHV WLHQHQODPLVPDFRQILJXUDFLyQHOHFWUyQLFD$OVHUHO.XQFDWLyQHOQ~PHURGH SURWRQHV HQ HO Q~FOHR HV PD\RU TXH HO GH HOHFWURQHV HQ ODV FDSDV SRU OR TXH TXHGDQ PiV DWUDtGRV SRU HO Q~FOHR \ VH FLHUUDQ VREUH VX WDPDxR (Q HO &O HO UDGLR HV PD\RU SXHV WHQLHQGR OD PLVPD FRQILJXUDFLyQ HOHFWUyQLFD HO Q~PHUR GH SURWRQHVTXHDWUDHQDORVHOHFWURQHVHVPHQRUDOPLVPRWLHPSRTXHODUHSXOVLyQ GH ORV HOHFWURQHV HQWUH Vt HQ OD FDSD GH YDOHQFLD HV PD\RU TXH HQ HO iWRPR QHXWUR &XHVWLyQ &XHVWLyQ D,QGLTXHODFRQILJXUDFLyQHOHFWUyQLFDGHORViWRPRVGHORVHOHPHQWRV$%\& FX\RVQ~PHURVDWyPLFRVVRQUHVSHFWLYDPHQWH\ E(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHOLRQPiVHVWDEOHGHFDGDXQRGHHOORV F2UGHQHGLFKRVLRQHVSRURUGHQFUHFLHQWHGHVXVUDGLRV Solución D$= VVSVS %= VVSVS &= VVSVSV E$ VVS % VVSVS & VVSVS F$&% &XHVWLyQ &XHVWLyQ 2UGHQHORVHOHPHQWRVTXtPLFRV&D&O&V\)HQVHQWLGRFUHFLHQWHGHVX D&DUiFWHUPHWiOLFR E5DGLRDWyPLFR -XVWLILTXHODVUHVSXHVWDV Solución D)&O&D&V /RV QR PHWDOHV WHQGUiQ PHQRU FDUiFWHU PHWiOLFR TXH ORV PHWDOHV (QWUH ORV QR PHWDOHVHOGHPD\RUDILQLGDGHOHFWUyQLFDVHUiHOGHPD\RUFDUiFWHUQRPHWiOLFR TXH HQ HVWH FDVR HV HO ) SRU HVWDU SRU HQFLPD GHO &O HQ HO JUXSR \ VHU PiV HOHFWURQHJDWLYR(QWUH&D\&VDOHVWDUpVWHHQHOJUXSRFRQXQVRORHOHFWUyQ (VWUXFWXUDGHODPDWHULD HQ OD FDSD GH YDOHQFLD \ WHQHU PXFKR PD\RU WDPDxR TXH HO &D WHQGUi PiV WHQGHQFLDDFHGHUHOHOHFWUyQ\SRUWDQWRPD\RUFDUiFWHUPHWiOLFR E)&O&D&V (Q HVWH RUGHQ DXPHQWD HO SHUtRGR HQ HO TXH HVWiQ \ SRU WDQWR WLHQHQ PD\RU Q~PHURGHFDSDVGHHOHFWURQHV\SRUWDQWRPD\RUWDPDxR &XHVWLyQ &XHVWLyQ 'DGRVORVYDORUHVGHQ~PHURVFXiQWLFRVòòò \ò D,QGLTXHFXiOHVGHHOORVQRHVWiQSHUPLWLGRV E,QGLTXHHOQLYHO\HORUELWDOHQHOTXHVHHQFRQWUDUtDQORVHOHFWURQHVGHILQLGRV SRUORVYDORUHVGHORVQ~PHURVFXiQWLFRVSHUPLWLGRV Solución DòSXHVPO!O\HVWRQRHVSRVLEOH òSXHVSDUDO VyORSXHGHKDEHUPO EòFRUUHVSRQGHDOQLYHO\HVXQRUELWDOG òFRUUHVSRQGHDOQLYHO\HVHORUELWDOV &XHVWLyQ &XHVWLyQ &RQVLGHUHODVLJXLHQWHWDEODLQFRPSOHWD (OHPHQWRV 1D " $O " 6 " 5DGLRVDWyPLFRV " " " D 5HSURGX]FD OD WDEOD \ FRPSOpWHOD VLWXDQGR ORV YDORUHV QP QP \ QP\ORVHOHPHQWRV3&O\0JHQORVOXJDUHVRSRUWXQRV E,QGLTXH\H[SOLTXHTXpQRUPDKDVHJXLGR Solución D (OHPHQWRV 5DGLRVDWyPLFRV 1D 0J $O 3 6 &O ,QLFLDFLyQDOD4XtPLFD E 7RGRV VRQ HOHPHQWRV GHO WHUFHU SHUtRGR \ YD GLVPLQX\HQGR VX UDGLR DO GHVSOD]DUQRVKDFLDODGHUHFKD\D TXHDXPHQWD=\ HOHOHFWUyQTXHHQWUDHQOD PLVPDFDSDHVWDUiPiVDWUDtGR &XHVWLyQ &XHVWLyQ 'DGRVORVHOHPHQWRV$%\&GHQ~PHURVDWyPLFRV\UHVSHFWLYDPHQWH D (VFULEDODHVWUXFWXUDHOHFWUyQLFDGHHVRVHOHPHQWRV E 'HWHUPLQHHOJUXSR\SHUtRGRDORVTXHSHUWHQHFHQ F 2UGpQHORVHQRUGHQFUHFLHQWHGHVXHOHFWURQHJDWLYLGDG Solución D$ VVS % VVSVSV & VVSVSGVS E$SHUtRGRJUXSR %SHUtRGRJUXSR &SHUtRGRJUXSR F%&$ &XHVWLyQ &XHVWLyQ D (VFULED OD FRQILJXUDFLyQ HOHFWUyQLFD GH ORV iWRPRV GH ORV HOHPHQWRV FRQ Q~PHURVDWyPLFRV\ E ,QGLTXH UD]RQDGDPHQWH FXiO HV HO LRQ PiV HVWDEOH GH FDGD XQR GH HOORV \ HVFULEDVXFRQILJXUDFLyQHOHFWUyQLFD Solución D= VVSVSV = VVSVSGV = VVSVSGVS E=SXHVVLSLHUGHGRVHOHFWURQHVDOFDQ]DODFRQILJXUDFLyQGHJDVQREOH VVSVS = SXHV DO SHUGHU GRV HOHFWURQHV DOFDQ]D XQD FRQILJXUDFLyQ HVWDEOH FRQ XQDFDSDOOHQDVVSVSG (VWUXFWXUDGHODPDWHULD = SXHV DO JDQDU XQ HOHFWUyQ DOFDQ]D FRQILJXUDFLyQ GH JDV QREOH V V SVSGVS &XHVWLyQ &XHVWLyQ /D JUiILFD DGMXQWD UHODFLRQD YDORUHV GH HQHUJtD GH LRQL]DFLyQ (, FRQ ORV Q~PHURVDWyPLFRVGHORVHOHPHQWRV&RQODLQIRUPDFLyQTXHREWHQJDDSDUWLUGH HOOD D-XVWLILTXHODYDULDFLyQSHULyGLFDTXHVHSURGXFHHQORVYDORUHV(, E(QXPHUHORVIDFWRUHVTXHLQIOX\HQHQHVWDYDULDFLyQ\UD]RQHODLQIOXHQFLD GHOIDFWRUGHWHUPLQDQWH Solución D6LVHWLHQHHQFXHQWDHOSULPHUJUXSRGHODL]TXLHUGDGHODWDEODSHULyGLFDDO EDMDUHLQLFLDUFDGDSHUtRGRHPSLH]DDOOHQDUVHXQDQXHYDFDSDSRUORTXHORV HOHFWURQHV GLIHUHQFLDGRUHV GH HVH HOHPHQWR HVWiQ FDGD YH] PiV VHSDUDGRV GHO Q~FOHR\SRUWDQWRVXYDORUVHUiFDGDYH]PHQRUGDQGROXJDUDORVPtQLPRVGHOD JUiILFD$OLUGHVSOD]iQGRVHKDFLDODGHUHFKDHQFDGDSHUtRGRYDGLVPLQX\HQGR HOUDGLR\DXPHQWDQGRODFDUJDQXFOHDUHIHFWLYDSRUORTXHYDQDXPHQWDQGRORV YDORUHVGH(, /DVSHTXHxDVDOWHUDFLRQHVHQHORUGHQGHQWURGHXQPLVPRSHUtRGRVHGHEHQD TXH HO ~OWLPR HOHFWUyQ FRUUHVSRQGH D XQD FRQILJXUDFLyQ HOHFWUyQLFD GH Pi[LPD HVWDELOLGDGFRQXQVXEQLYHOYDFtROOHQRRVHPLOOHQR(MQVQVQS E/RVIDFWRUHVGHWHUPLQDQWHVVRQHOWDPDxRODFDUJDQXFOHDU\ODFRQILJXUDFLyQ HOHFWUyQLFD ,QLFLDFLyQDOD4XtPLFD &XHVWLyQ &XHVWLyQ (Q OD WDEOD VLJXLHQWH VH GDQ ODV HQHUJtDV GH LRQL]DFLyQ N-PRO GH ORV SULPHURV HOHPHQWRVDOFDOLQRV (, (, (, (, /L 1D . ([SOLTXH D¢3RUTXpGLVPLQX\HOD(,GHO/LDO." E¢3RUTXpQRKD\YDORUSDUDOD(,GHO/L" F¢3RUTXpDXPHQWDGHOD(,DOD(," Solución D3RUTXHFRQODPLVPDFRQILJXUDFLyQHOHFWUyQLFDQVYDDXPHQWDQGRHOUDGLR GHOHOHPHQWR E3RUTXHHO/LWLHQHVyORWUHVHOHFWURQHV F 3RU TXH D XQ LRQ FDGD YH] PiV SRVLWLYR FXHVWD PiV WUDEDMR DUUDQFDUOH XQ HOHFWUyQ &XHVWLyQ &XHVWLyQ 'DGRVORVHOHPHQWRV$\%FX\RVQ~PHURVDWyPLFRVVRQUHVSHFWLYDPHQWH= \= D(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHDPERV E&XiOWHQGUiPD\RUUDGLR"5D]RQHODUHVSXHVWD F¢&XiOWHQGUiPD\RUDILQLGDGHOHFWUyQLFD"5D]RQHODUHVSXHVWD Solución D$ VVSVSV % VVSVSGVS EU$!U%SXHVVRQGHOPLVPRSHUtRGR\ORVHOHFWURQHVYDQHQWUDQGRHQODPLVPD FDSDSHURFDGDYH]VRQDWUDtGRVSRUXQDPD\RUFDUJDQXFOHDU F % ! $ SXHV D % VyOR OH IDOWD XQ HOHFWUyQ SDUD REWHQHU FRQILJXUDFLyQ GH JDV QREOH\pVWHHVWDUiDWUDtGRSRUXQDPD\RUFDUJDQXFOHDU (VWUXFWXUDGHODPDWHULD &XHVWLyQ &XHVWLyQ ,QGLTXH SDUD ORV HOHPHQWRV $ % \ & FX\RV Q~PHURV DWyPLFRV VRQ UHVSHFWLYDPHQWH\ D&RQILJXUDFLyQHOHFWUyQLFD E-XVWLILTXHFXiOWHQGUiPD\RUHQHUJtDGHLRQL]DFLyQ F (O JUXSR \ HO SHUtRGR GHO VLVWHPD SHULyGLFR HQ TXH VH HQFXHQWUD FDGD HOHPHQWR Solución D$ VVSVS % VVSVS & VVSVSV E(OGHPD\RU(,HVHOHOHPHQWR%SXHVHOHOHFWUyQTXHKD\TXHDUUDQFDUHVWi HQ OD FDSD GH PHQRU UDGLR TXH OD GH & \ FRQ UHODFLyQ D $ DO HVWDU PiV D OD GHUHFKDGHOSHUtRGRHVWiPiVDWUDtGRSRUXQDPD\RUFDUJDQXFOHDU F$HVWiHQHOSHUtRGR\HQHOJUXSR %HVWiHQHOSHUtRGR\HQHOJUXSR &HVWiHQHOSHUtRGR\HQHOJUXSR &XHVWLyQ &XHVWLyQ 'DGDV ODV VLJXLHQWHV FRQILJXUDFLRQHV HOHFWUyQLFDV FRUUHVSRQGLHQWHV D iWRPRV QHXWURV &VVSVSGV $VVS%VVSVS 'V V S V S V ,QGLTXHUD]RQDGDPHQWH D *UXSR\SHUtRGRDTXHSHUWHQHFHFDGDHOHPHQWR E 4XpHOHPHQWRSRVHHPD\RUHQHUJtDGHLRQL]DFLyQ\FXiOPHQRU F 4XpHOHPHQWRWLHQHPD\RUUDGLRDWyPLFR Solución D$SRUHOPD\RUYDORUGHQHVWiHQHOSHUtRGR\GDGRTXHVHKDQOOHQDGR HOHFWURQHVHQHORUELWDOSHQHOJUXSR % SRU HO PD\RU YDORU GH Q HVWi HQ HO SHUtRGR \ GDGR TXH VH KDQ OOHQDGR HOHFWURQHVHQHORUELWDOSHQHOJUXSR & SRU HO PD\RU YDORU GH Q HVWi HQ HO SHUtRGR \ GDGR TXH VH KDQ OOHQDGR HOHFWURQHVHQHORUELWDOG\HQHOVHQHOJUXSR ,QLFLDFLyQDOD4XtPLFD ' SRU HO PD\RU YDORU GH Q HVWi HQ HO SHUtRGR \ GDGR TXH VH KDQ OOHQDGR HOHFWUyQHQHORUELWDOVHQHOJUXSR E(OGHPD\RU(,HVHO$\DTXHHVHOPiVSHTXHxR\WLHQHPD\RUQ~PHURGH HOHFWURQHVHQODFDSDGHYDOHQFLD (OGHPHQRU(,HVHO'\DTXHHVHOPiVYROXPLQRVR\VyORWLHQHXQHOHFWUyQHQ ODFDSDGHYDOHQFLD F (O GH PD\RU UDGLR HV HO ' \D TXH HV HO SULPHUR GHO SHUtRGR FXDUWR FRQ HO PD\RUQ~PHURGHFDSDV\PHQRUQ~PHURGHHOHFWURQHVHQODFDSDGHYDOHQFLD &XHVWLyQ &XHVWLyQ (VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHORVLRQHV&O= \.= D5D]RQHFXiOGHORVGRVLRQHVWHQGUiPD\RUUDGLR E5D]RQHFXiOGHORVGRVHOHPHQWRVQHXWURVWHQGUiPD\RUHQHUJtDGHLRQL]DFLyQ Solución &O VVSVS. VVSVS DU&O!U.\DTXHORVGRVWLHQHQODPLVPDFRQILJXUDFLyQHOHFWUyQLFDSHUR HQHO.KD\XQSURWyQPiVHQHOQ~FOHRSRUORTXHORVHOHFWURQHVHVWDUiQPiV DWUDtGRV\HOWDPDxRVHUiPHQRU E'HORVGRVHOHPHQWRVQHXWURVHOGHPD\RU(,VHUiHO&O\DTXHHOHOHFWUyQD DUUDQFDUHVWiHQODFDSD\HVHOSHQ~OWLPRHOHPHQWRGHOSHUtRGRPLHQWUDVTXH HO.HVHOSULPHURGHOSHUtRGRVLJXLHQWH\SRUWDQWRPiVYROXPLQRVR &XHVWLyQ &XHVWLyQ 7UHVHOHPHQWRVWLHQHQGHQ~PHURDWyPLFR\UHVSHFWLYDPHQWH D(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHORVPLVPRV E,QGLTXHUD]RQDGDPHQWHHOJUXSR\SHULRGRDTXHSHUWHQHFHFDGDXQRGHORV HOHPHQWRVDQWHULRUHV F,QGLTXHUD]RQDQGRODUHVSXHVWDHOFDUiFWHUPHWiOLFRRQRPHWiOLFRGHFDGD XQRGHORVHOHPHQWRVDQWHULRUHV Solución D= VVSVSGV = VVSVSGVS = VVSVSGVSV (VWUXFWXUDGHODPDWHULD E= 3RUHOYDORUGHQGHODFDSDPiVH[WHUQDHVWiHQHOSHUtRGR\GDGR TXHKD\HOHFWURQHVHQHORUELWDOGHQHOJUXSR = 3RUHOYDORUGHQGHODFDSDPiVH[WHUQDHVWiHQHOSHUtRGR\GDGR TXHKD\HOHFWURQHVHQHORUELWDOSHQHOJUXSR = 3RUHOYDORUGHQGHODFDSDPiVH[WHUQDHVWiHQHOSHUtRGR\GDGR TXHKD\HOHFWURQHVHQHORUELWDOVHQHOJUXSR F= 'DGRTXHHO~OWLPRRUELWDOHQHOTXHKDQHQWUDGRHOHFWURQHVHVHOG\ pVWHHVWiVHPLOOHQRFRUUHVSRQGHDXQPHWDOGHWUDQVLFLyQ = 'DGRTXHODFRQILJXUDFLyQHOHFWUyQLFDGHODFDSDGHYDOHQFLDHVVS VyOROHIDOWDXQHOHFWUyQSDUDDOFDQ]DUODFRQILJXUDFLyQGHJDVQREOH\SRUWDQWR HVXQQRPHWDO = &RPRODFDSDGHYDOHQFLDHVVVXWHQGHQFLDHVDSHUGHUGRVHOHFWURQHV\ SRUWDQWRXQPHWDODOFDOLQRWpUUHR &XHVWLyQ &XHVWLyQ /DVGRVWDEODVVLJXLHQWHVFRUUHVSRQGHQDUDGLRVDWyPLFRV (OHPHQWR /L %H % & 1 2 ) 5∆ (OHPHQWR /L 1D . 5E &V 5∆ D-XVWLILTXHODYDULDFLyQGHOUDGLRHQHOSHUtRGR E-XVWLILTXHODYDULDFLyQGHOUDGLRHQHOJUXSR Solución D &RUUHVSRQGHQ D ORV HOHPHQWRV GHO VHJXQGR SHUtRGR DO DYDQ]DU KDFLD OD GHUHFKD DXPHQWD HQ XQD XQLGDG OD FDUJD QXFOHDU \ VH DxDGH XQ HOHFWUyQ D OD FRUWH]D TXH HQWUDQ HQ OD PLVPD FDSD SHUR HVWRV HOHFWURQHV QR DSDQWDOODQ FRQ HIHFWLYLGDG GH XQD XQLGDG D ORV HOHFWURQHV GH OD PLVPD FDSD SRU OR TXH pVWRV HVWDUiQFDGDYH]PiVDWUDtGRVSRUODFDUJDSRVLWLYDGHOQ~FOHR E$OEDMDUHQHOJUXSRGHORVDOFDOLQRVHOQXHYRHOHFWUyQHQWUDHQHORUELWDOQV LQLFLiQGRVH XQD QXHYD FDSD \ SRU WDQWR DXPHQWDQGR HO UDGLR FRQ UHODFLyQ DO DQWHULRU &XHVWLyQ &XHVWLyQ /RVQ~PHURVDWyPLFRVGHORVHOHPHQWRV3\0QVRQ\UHVSHFWLYDPHQWH D(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHFDGDXQRGHHOORV ,QLFLDFLyQDOD4XtPLFD E,QGLTXHORVQ~PHURVFXiQWLFRVTXHFRUUHVSRQGDQDORVHOHFWURQHVVLWXDGRVHQ FDGDFDVRHQORVRUELWDOHVPiVH[WHUQRV Solución D3VVSVS 0QVVSVSGV E3ò 0Qò &XHVWLyQ &XHVWLyQ /RV HOHPHQWRV 1D $O \ &O WLHQHQ GH Q~PHURV DWyPLFRV \ UHVSHFWLYDPHQWH D(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHFDGDHOHPHQWR E(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHORVLRQHV1D$O\&O F2UGHQHGHIRUPDUD]RQDGDORVUDGLRVGHORVLRQHVDQWHULRUHV Solución D1DVVSV$OVVSVS &OVVSVS E1DVVS$OVVS&OVVSVS F$O1D&O (O FDWLyQ $O HV HO PiV SHTXHxR SXHV DXQTXH WLHQH OD PLVPD FRQILJXUDFLyQ HOHFWUyQLFD TXH 1D HQ DTXHO ORV HOHFWURQHV HVWiQ DWUDtGRV SRU SURWRQHV PLHQWUDV TXH HQ HO 1D VyOR HVWiQ DWUDtGRV SRU (O &O HV HO GH PD\RUUDGLR SXHVKDJDQDGRXQHOHFWUyQ\WLHQHXQDFDSDPiVTXHORVRWURVGRV &XHVWLyQ &XHVWLyQ /RVQ~PHURVDWyPLFRVGHORVHOHPHQWRV%U\5EVRQ\UHVSHFWLYDPHQWH D(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHDPERVHOHPHQWRV E,QGLTXHHOLRQPiVHVWDEOHGHFDGDHOHPHQWR\VXFRQILJXUDFLyQHOHFWUyQLFD F5D]RQHFXiOGHORVGRVLRQHVWHQGUiPD\RUUDGLR Solución D%UVVSVSGVS (VWUXFWXUDGHODPDWHULD 5EVVSVSGVSV E%UVVSVSGVS 5EVVSVSGVS F (O PD\RU UDGLR HV HO GHO %U SXHV DXQTXH ORV GRV LRQHV WLHQHQ OD PLVPD FRQILJXUDFLyQHOHFWUyQLFDHQpVWHORVHOHFWURQHVHVWiQDWUDtGRVSRUSURWRQHV \HQHO5ESRU &XHVWLyQ &XHVWLyQ /RV HOHPHQWRV $ \ % WLHQHQ HQ VXV ~OWLPRV QLYHOHV ODV FRQILJXUDFLRQHV $ VSV\% VSGVS-XVWLILTXH D6L$HVPHWDORQRPHWDO E4XpHOHPHQWRWHQGUiPD\RUDILQLGDGHOHFWUyQLFD F4XpHOHPHQWRWHQGUiPD\RUUDGLR Solución D$HVXQPHWDOSXHVDOWHQHUXQVRORHOHFWUyQHQODFDSDGHYDOHQFLDVX WHQGHQFLDHVDSHUGHUOR\IRUPDULRQHVSRVLWLYRV E%SXHVHOHOHFWUyQTXHHQWUDORKDFHHQXQRUELWDOFDVLOOHQR\HQXQDFDSD PiVFHUFDGHOQ~FOHRTXHHQ$SRUORTXHDOHVWDUPiVFHUFDVHGHVSUHQGHUiPiV HQHUJtD F$SXHVWLHQHXQDFDSDHOHFWUyQLFDPiVTXH% &XHVWLyQ &XHVWLyQ /RViWRPRVQHXWURV;<=WLHQHQODVVLJXLHQWHVFRQILJXUDFLRQHV ; VVS< VVS= VVSV D,QGLTXHHOJUXSR\HOSHUtRGRHQHOTXHVHHQFXHQWUDQ 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$OVVSVS1DVVS2VVS D1D\2 E$O (VWUXFWXUDGHODPDWHULD &XHVWLyQ &XHVWLyQ /RVHOHPHQWRV;<\=WLHQHQQ~PHURVDWyPLFRV\UHVSHFWLYDPHQWH D(VFULEDODFRQILJXUDFLyQHOHFWUyQLFDGHFDGDXQRGHHOORV E¢6HUtDQHVWDEOHVORVLRQHV;<\="-XVWLILTXHODVUHVSXHVWDV Solución D;VVSVS<VVSVSV =VVSVSGVS E ; QR SXHV TXHGDUtD V \ SRU WDQWR OD WHQGHQFLD VHUtD D DOFDQ]DU XQD FRQILJXUDFLyQGHJDVQREOH\SRUWDQWR; <VLSXHVWHQGUtDHQVX~OWLPDFDSDXQDFRQILJXUDFLyQGHJDVQREOH = QR SXHV OD WHQGHQFLD GH = VHUi D FDSWDU XQ HOHFWUyQ \ DOFDQ]DU DVt OD FRQILJXUDFLyQGHJDVQREOH &XHVWLyQ &XHVWLyQ 'DGRV ORV VLJXLHQWHV JUXSRV GH Q~PHURV FXiQWLFRV Q O P ,QGLTXH D&XiOHVQRVRQSHUPLWLGRV\SRUTXp E /RV RUELWDOHV DWyPLFRV TXH VH FRUUHVSRQGHQ FRQ ORV JUXSRV FX\RV Q~PHURV FXiQWLFRVVHDQSRVLEOHV Solución D\DTXHHOYDORUGHOVyORSXHGHOOHJDUKDVWDQ \DTXHHOYDORUGHOVyORSXHGHOOHJDUKDVWDQ <DTXHHOYDORUGHOQRSXHGHVHUQHJDWLYR EGVG &XHVWLyQ &XHVWLyQ 'DGDVODVVLJXLHQWHVFRQILJXUDFLRQHVHOHFWUyQLFDVSHUWHQHFLHQWHVDHOHPHQWRV QHXWURV $VVS%VVS&VVSVSV'VVS ,QGLTXHUD]RQDGDPHQWH D(OJUXSR\SHULRGRDOTXHSHUWHQHFHFDGDHOHPHQWR E(OHOHPHQWRGHPD\RU\HOGHPHQRUHQHUJtDGHLRQL]DFLyQ F(OHOHPHQWRGHPD\RU\HOGHPHQRUUDGLRDWyPLFR ,QLFLDFLyQDOD4XtPLFD Solución D$JUXSRSRUWHQHUGRVHOHFWURQHVHQHOVXEQLYHOSHQODFDSDGHYDOHQFLD\ SHUtRGRSRUVHUHOPD\RUYDORUGHQ % JUXSR SRU WHQHU FLQFR HOHFWURQHV HQ HO VXEQLYHO S HQ OD FDSD GH YDOHQFLD\SHUtRGRSRUVHUHOPD\RUYDORUGHQ &JUXSR SRUWHQHUXQ HOHFWUyQHQHOVXEQLYHOV HQODFDSD GHYDOHQFLD \ SHUtRGRSRUVHUHOPD\RUYDORUGHQ ' JUXSR SRU WHQHU FXDWUR HOHFWURQHV HQ HO VXEQLYHO S GH OD FDSD GH YDOHQFLD\SHUtRGRSRUVHUHOPD\RUYDORUGHQ E(OGHPD\RU(,HVHO%\DTXHGHQWURGHORVTXHHVWiQHQHOVHJXQGRSHUtRGR FRQ ORV HOHFWURQHV PiV FHUFD GHO Q~FOHR HV HO TXH WLHQH PD\RU Q~PHUR GH HOHFWURQHVHQODFDSDGHYDOHQFLDVHUiHQHOTXHHVWiQPiVDWUDtGRVSRUWHQHUOD PD\RUFDUJDSRVLWLYDHQHOQ~FOHR (O GH PHQRU ( , HV HO & \D TXH HO HOHFWUyQ D DUUDQFDU HVWi HQ OD FDSD PiV DOHMDGD GHO Q~FOHR GH WRGRV \ HO LRQ REWHQLGR SUHVHQWD FRQILJXUDFLyQ GH JDV QREOH F (O GH PD\RU UDGLR HV HO & \D TXH HV HO TXH WLHQH PD\RU Q~PHUR GH FDSDV HOHFWUyQLFDV\HVHOSULPHURGHOSHUtRGR (O GH PHQRU UDGLR HV HO % \D TXH GHQWUR GH ORV GHO VHJXQGR SHUtRGR ORV PiV SHTXHxRV HV HO TXH WLHQH PD\RU Q~PHUR GH HOHFWURQHV \ SRU WDQWR PD\RU Q~PHURGHSURWRQHVTXHORVDWUDLJDQ &XHVWLyQ &XHVWLyQ D'HILQDDILQLGDGHOHFWUyQLFD E¢4XpFULWHULRVHVLJXHSDUDRUGHQDUORVHOHPHQWRVHQODWDEODSHULyGLFD" F¢-XVWLILTXHFyPRYDUtDODHQHUJtDGHLRQL]DFLyQDORODUJRGHXQSHULRGR" Solución D/DHQHUJtDGHVSUHQGLGDFXDQGRXQ PROGHiWRPRVGHXQHOHPHQWRHQHVWDGR IXQGDPHQWDO\JDVHRVRFDSWDQXQPROGHHOHFWURQHV E6HRUGHQDQSRURUGHQFUHFLHQWHGHVXQ~PHURDWyPLFR\VHFRORFDQXQRGHEDMR GHRWURFXDQGRWLHQHQODPLVPDFRQILJXUDFLyQHOHFWUyQLFDHQODFDSDGHYDOHQFLD F &XDQGR QRV GHVSOD]DPRV KDFLD OD GHUHFKD HQ FDGD SHUtRGR YD GLVPLQX\HQGR HO UDGLR GH ORV HOHPHQWRV \ DXPHQWDQGR VX FDUJD QXFOHDU HIHFWLYDSRUORTXHYDQDXPHQWDQGRORVYDORUHVGH(, (VWUXFWXUDGHODPDWHULD &XHVWLyQ &XHVWLyQ D (VFULED ODV FRQILJXUDFLRQHV HOHFWUyQLFDV GH ORV LRQHV VLJXLHQWHV 1D= \ )= E-XVWLILTXHTXHHOLRQ1DWLHQHPHQRUUDGLRTXHHOLRQ) F-XVWLILTXHTXHODHQHUJtDGHLRQL]DFLyQGHOVRGLRHVPHQRUTXHODGHOIO~RU Solución D1DVVS)VVS E /RV GRV LRQHV WLHQHQ OD PLVPD FRQILJXUDFLyQ HOHFWUyQLFD SHUR HQ HO 1D ORV HOHFWURQHVHVWiQDWUDtGRVSRUORVSURWRQHVGHOQ~FOHRPLHQWUDVTXHHQHO) VyORKD\ F 3RU TXH HQ HO VRGLR QHXWUR VX FDSD GH YDOHQFLD HV V TXH HVWi HQ XQD FDSD PiVTXHHQHOIO~RU\SRUWDQWRPiVOHMRVGHOQ~FOHR\PHQRVDWUDtGRTXHHQHO IO~RU &XHVWLyQ &XHVWLyQ 'DGRVORVHOHPHQWRV$= %= \&= D(VFULEDVXVFRQILJXUDFLRQHVHOHFWUyQLFDV E2UGpQHORVGHPHQRUDPD\RUHOHFWURQHJDWLYLGDG F5D]RQHFXiOWLHQHPD\RUYROXPHQ Solución D$VVSVS%VVS&VVSVSV E&$% F & SXHV HQ pO VH LQLFLD OD FXDUWD FDSD GH HOHFWURQHV PLHQWUDV TXH ORV RWURV VyORWLHQHQWUHV\GRVFDSDVUHVSHFWLYDPHQWH &XHVWLyQ &XHVWLyQ D ¢3RU TXp HO YROXPHQ DWyPLFR DXPHQWD DO EDMDU HQ XQ JUXSR GH OD WDEOD SHULyGLFD" E¢3RUTXpORVHVSHFWURVDWyPLFRVVRQGLVFRQWLQXRV" F'HILQDHOFRQFHSWRGHHOHFWURQHJDWLYLGDG ,QLFLDFLyQDOD4XtPLFD Solución D3RUTXHHQFDGDJUXSRVHPDQWLHQHODFRQILJXUDFLyQHOHFWUyQLFDGHODFDSDGH YDOHQFLD SHUR DO EDMDU GLFKD FRQILJXUDFLyQ HVWi HQ RUELWDOHV GH XQ YDORU GH Q PD\RUHVGHFLUFDGDHOHPHQWRWLHQHXQDFDSDHOHFWUyQLFDPiV E 3RUTXH ORV HOHFWURQHV VyOR SXHGHQ H[LVWLU HQ ORV iWRPRV HQ QLYHOHV GH XQD HQHUJtD FRQFUHWD \ ORV HVSHFWURV VH SURGXFHQ FXDQGR ORV HOHFWURQHV VDOWDQ GH XQRV QLYHOHV D RWURV SRU WDQWR OD HQHUJtD GHVSUHQGLGD HVSHFWURV GH HPLVLyQ VyORSRGUiWRPDUORVYDORUHVGHODGLIHUHQFLDGHHQHUJtDGHORVQLYHOHVHQWUHORV TXHVHSURGXFHQORVVDOWRV F(VODWHQGHQFLDTXHWLHQHXQiWRPRDDWUDHUVREUHVtDOSDUGHHOHFWURQHVTXH FRPSDUWHFRQRWURiWRPRFRQHOTXHIRUPDXQHQODFHFRYDOHQWH &XHVWLyQ &XHVWLyQ 5D]RQH VL ODV VLJXLHQWHV FRQILJXUDFLRQHV HOHFWUyQLFDV VRQ SRVLEOHV HQ XQ HVWDGR IXQGDPHQWDORHQXQHVWDGRH[FLWDGR DVVSV EVVSVS FVVSGV Solución D 6HUi XQ HVWDGR H[FLWDGR GH V V S SXHV HQ ORV RUELWDOHV S VH SXHGHQ DOEHUJDUKDVWDVHLVHOHFWURQHV E (VWD VHUi OD FRQILJXUDFLyQ HOHFWUyQLFD HQ HVWDGR IXQGDPHQWDO GHO HOHPHQWR FRQ = SXHV WRGRV ORV HOHFWURQHV HVWiQ RUGHQDGRV HQ RUELWDOHV GH HQHUJtD FUHFLHQWH F1RHVSRVLEOHHVWDFRQILJXUDFLyQHOHFWUyQLFDSXHVQRH[LVWHHORUELWDOG 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Solución D&OVVSVS.VVSVSV E&O\. 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VVSVSGVS\FRUUHVSRQGHDO*D VVSVSGVS\FRUUHVSRQGHDO.U (VWUXFWXUDGHODPDWHULD &XHVWLyQ &XHVWLyQ a) Escriba la configuración electrónica de los elementos A, B y C, cuyos números atómicos son 33, 35 y 37,UHVSHFWLYDPHQWH E,QGLTXHHOJUXSR\HOSHULRGRDOTXHSHUWHQHFHQ F5D]RQHTXpHOHPHQWRWHQGUiPD\RUFDUiFWHUPHWiOLFR Solución D $ V V S V S G V S % V V S V S G V S &VVSVSGVSV E$JUXSR\SHULRGR%JUXSR\SHULRGR &JUXSR\SHULRGR F & SXHV WLHQH XQ VROR HOHFWUyQ HQ OD FDSD GH YDOHQFLD \ VX WHQGHQFLD HV D FHGHUORGDQGR& &XHVWLyQ &XHVWLyQ ,QGLTXH D /RV VXEQLYHOHV GH HQHUJtD GDGRV SRU HO Q~PHUR FXiQWLFR VHFXQGDULR O TXH FRUUHVSRQGHQDOQLYHOFXiQWLFRQ E$TXpWLSRGHRUELWDOHVFRUUHVSRQGHQORVVXEQLYHOHVDQWHULRUHV F 6L H[LVWH DOJ~Q VXEQLYHO GH Q FRQ HQHUJtD PHQRU TXH DOJ~Q VXEQLYHO GH Q GLJDFXiO Solución D3DUDQ OSXHGHYDOHU\ EVSG\I F(OVWLHQHPHQRVHQHUJtDTXHHOG\HOSPHQRVTXHHOI &XHVWLyQ &XHVWLyQ a) Indique el número de electrones desapareados que hay en los siguientes átomos: $V= &O= $U= b) Indique los grupos de números cuánticos que corresponderán a esos electrones desapareados. ,QLFLDFLyQDOD4XtPLFD Solución D$VVVSVSGVSWLHQHHQORVWUHVRUELWDOHVS &OVVSVSWLHQHHQXQRGHORVRUELWDOHVS $UVVSVSQRWLHQHQLQJXQR E$Vòòò &O ò HO YDORU GH PO SXHGH VHU \ ² SXHV ORV WUHV RUELWDOHV HVWiQ GHJHQHUDGRV 6H KDHOHJLGR SRUTXH VH VXSRQH TXH FRPLHQ]D D OOHQDUVH SRUHOYDORUVHJXLGRGHO\ILQDOPHQWH² &XHVWLyQ &XHVWLyQ D 5D]RQH VL SDUD XQ HOHFWUyQ VRQ SRVLEOHV ODV VLJXLHQWHV VHULHV GH Q~PHURV FXiQWLFRVòòòò E ,QGLTXH D TXp WLSR GH RUELWDO FRUUHVSRQGHQ ORV HVWDGRV DQWHULRUHV TXH VHDQ SRVLEOHV F,QGLTXHHQFXiOGHHOORVODHQHUJtDHVPD\RU Solución DQRSXHGHVHUSXHVHOYDORUGHQVLHPSUHHVGLVWLQWRGHFHUR QRSXHGHVHUSXHVHOYDORUGHOSDUDXQGHWHUPLQDGRYDORUGH QSXHGHOOHJDUDQFRPRPi[LPR ES\G FGTXHHVHOGHPD\RUYDORUGHQ\SRUWDQWRGHPD\RUHQHUJtD &XHVWLyQ &XHVWLyQ 'DGDVODVVLJXLHQWHVHVSHFLHV$U&D\&O D(VFULEDVXVFRQILJXUDFLRQHVHOHFWUyQLFDV E2UGpQHODVUD]RQDQGRODUHVSXHVWDHQRUGHQFUHFLHQWHGHVXVUDGLRV 1~PHURVDWyPLFRV$U &D &O Solución D$UVVSVS&DVVSVS &OVVSVS (VWUXFWXUDGHODPDWHULD E &D $U &O ORV WUHV WLHQHQ OD PLVPD FRQILJXUDFLyQ HOHFWUyQLFD SHUR FXDQWRVPHQRVSURWRQHVORVDWUDLJDQGHVGHHOQ~FOHRPiVJUDQGHVHUiHOiWRPR RLRQ