stpm chemistry notes chapter 3

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    \SPA Ledaistry Lenptdr *.0 *. *. *.0 *.4 *.4 *.4 *.3 *. *. *.4 .% .' .4

    -jtd tent ted gjmbd hnsds lnggjt md nslrimdc ng dbdltrjgdhntivity sigld tedy cj gjt fjra

    mjgcs.

    Dbdltrjgdhntivity is n vdry usdfub ljgldpt fjr prdciltigh wedtedr ted mjgcigh mdtwddg

    twj ntjas wibb md ijgil, ljvnbdgt jr adtnbbil.

    Ljgsicdr n ljvnbdgt mjgc mdtwddg twj ntjas N ngc .

    N Mxj

    If mjte ntjas envd n siaibnr dbdltrjgdhntivity, mjte ntjas nttrnlt ted dbdltrjgs wite

    siaibnr pjwdr ngc ted dbdltrjgs wibb rdanig aicwny mdtwddg ted twj. Sed mjgc wibb teus

    md ljvnbdgt ; ted dbdltrjgs nrd senrdc mdtwddg ted twj ntjas.

    Dh ( 2.*) ngc ( 2.*)

    E Exj

    n ljvnbdgt mjgc

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    If jgd ntja is sihgifilngtby ajrd dbdltrjgdhntivd teng ted jtedr, it nttrnlts ted dbdltrjgs

    ajrd strjghby teng ted jtedr ngc ted dbdltrjgs nrd jg nvdrnhd lbjsdr tj jgd ntja teng ted

    jtedr. Sed dbdltrjgs nrd stibb senrdc, mut jgd ntja ens n sbihet cdfilit jf dbdltrjgs ngc teusn sbihet pjsitivd lenrhd ngc ted jtedr n sbihet surpbus jf dbdltrjgs ngc teus n sbihet

    gdhntivd lenrhd. =ule n mjgc is snic tj md pjbnr lj!nbdgt.

    Dh ( 2.*) ngc 2>.%)

    J Exj

    - +

    n pjbnr ljvnbdgt mjgc

    N sbihet pjsitivd lenrhd jr gdhntivd lenrhd jg ng ntja is rdprdsdgtdc my n +jr n

    syamjb rdspdltivdby.

    If ted ciffdrdgld mdtwddg ted twj ntjas is bnrhd, tedg ted senrigh jf dbdltrjgs is sjugdvdg tent ted ajrd dbdltrjgdhntivd ntja ens virtunbby sjbd pjssdssijg jf ted dbdltrjgs.

    Sed dbdltrjgs nrd, ig dffdlt, gjt senrdc nt nbb mut ng dbdltrjg ens dssdgtinbby mdtwddgtrngsfdrrdc frja jgd ntja tj ted jtedr. Sed ajrd dbdltrjpjsitivd ntja is pjsitivdbylenrhdc ngc ted ajrd dbdltrjgdhntivd ntja is gdhntivdby lenrhdc. Sed mjgcigh is teus

    ijgil.

    Dh -n 2%.3) ngc Lb 2>.%)

    Gn

    Lb

    xj

    -+

    ng ijgil mjgc

    If mjte ntjas nrd dbdltrjpjsitivd, gditedr ens n hrdnt nmibity tj nttrnlt dbdltrjgs ngc teddbdltrjgs cj gjt rdanig bjlnbisdc ig ted mjgc nt nbb. Sedy nrd frdd tj ajvd, mjte ntjas

    hnig n pjsitivd lenrhd ngc ted mjgcigh is adtnbbil.

    Dh "h 2*.) ngc "h 2*.)

    Ah

    Ah

    xj

    xj

    =+ =+

    n adtnbbil mjgc

    Ciffdrdglds ig dbdltrjgdhnti!ity lng md #sdc tj prdcilt ejw #le ijgil jr dtnbbil

    lenrnltdr n lj!nbdgt mjgc wibb en!d.

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    9ivdg suitnmbd dbdltrjgdhntivity cntn, it is teus pjssimbd tj prdcilt wedtedr n mjgc

    mdtwddg twj ntjas wibb md ijgil, pjbnr ljvnbdgt, ljvnbdgt jr adtnbbil.

    If mjte ntjas envd dbdltrjgdhntivitids bdss teng *. ; *.3 tedg ted mjgc is adtnbbil.

    If ditedr ntja ens ng dbdltrjgdhntivity hrdntdr teng *.3 ngc ted ciffdrdgld is bdss teng %.0

    tedg ted mjgc is ljvnbdgt.

    If ditedr ntja ens ng dbdltrjgdhntivity hrdntdr teng *.3 ngc ted ciffdrdgld is ajrd teng %.0

    mut bdss teng .* tedg ted mjgc is pjbnr ljvnbdgt.

    If ted ciffdrdgld is hrdntdr teng .* tedg ted mjgc is ijgil.

    Sedsd rubds nrd gjt pdrfdlt ngc tedrd nrd gjtnmbd dldptijgs! fjr dnapbd ted mjgc

    mdtwddg =i 2*.4) ngc =i 2*.4) is ljvnbdgt mut ted mjgc mdtwddg Lu 2*.3) ngc Lu 2*.3) isadtnbbil. Sed mjgc mdtwddg -n 2%.3) ngc ( 2.*) is ijgil mut ted mjgc mdtwddg =i 2*.4)

    ngc / 2'.%) is pjbnr ljvnbdgt. (jwdvdr ns mnsil hiucdbigds tedy nrd vdry usdfub prjvicdctent tedir biaitntijgs nrd npprdlintdc.

    Nbb mjgcs nrd nss#dc tj md lj!nbdgt ig priglipbd ciffdrdglds ig dbdltrjgdhnti!ity

    lng md #sdc tj prdcilt ejw #le ijgil jr dtnbbil lenrnltdr n lj!nbdgt mjgc wibb

    en!d.

    Dbdltrjgdhnti!ity ciffdrdglds sejw tent mjgcs mdtwddg gjg*icdgtilnb ntjs nrd nbb

    dssdgtinbby igtdrdcintd ig lenrnltdr mdtwddg ijgil ngc lj!nbdgt" Gj mjgc isljpbdtdby ijgil, ngc jgby mjgcs mdtwddg icdgtilnb ntjs nrd ljpbdtdby lj!nbdgt"

    Mjgcs mdtwddg icdgtilnb ntjs lnggjt md ijgil ns tedrd is gj ciffdrdgld ig

    dbdltrjgdhnti!ity" Sedy wibb tedrdfjrd md ditedr lj!nbdgt jr dtnbbil"

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    \SNSD\ JF -NSSD&

    "nttdr lng dist ig jgd jf terdd stntds! sjbic, bi1uic ngc hns. Sed stntd ig weile n ldrtnigsumstngld is ajst stnmbd nt n hivdg tdapdrnturd cdpdgcs jg ted mnbngld mdtwddg ted

    7igdtil dgdrhy jf ted pnrtilbds, weile cdpdgcs jg tdapdrnturd, ngc ted anhgitucd jf ted

    fjrld jf nttrnltijg mdtwddg teda.

    i) =jbics

    Ig n sjbic, ted pnrtilbds nrd tihetby pnl7dc tjhdtedr ig n bnttild. N bnttild is ng jrcdrdc ngc

    igfigitdby rdpdntigh nrrnghdadgt jf pnrtilbds. Sed prjpdrtids jf sjbics nrd cjaigntdc my

    ted fjrlds ig mdtwddg tedsd pnrtilbds weile lnusd teda tj nttrnlt dnle jtedr ngc prdsdrvd

    teis jrcdrdc nrrnghdadgt.

    N sjbic teus ens n fidc vjbuad ngc n fidc senpd.

    Nt nbb tdapdrnturds nmjvd nmsjbutd #drj, ted pnrtilbds envd 7igdtil dgdrhy. Ig n sjbic,ejwdvdr, teis 7igdtil dgdrhy is gjt dgjuhe tj lnusd ted pnrtilbds tj fby npnrt, ngc gjr is it

    dgjuhe tj lnusd sihgifilngt sdpnrntijg jf ted pnrtilbds. Sed pnrtilbds nrd teus rdstriltdc tjrjtntijgnb ngc vimrntijgnb ajtijg! gj trngsbntijgnb ajtijg jf ted pnrtilbds wite rdspdlt tj

    dnle jtedr is pjssimbd.

    Ig n sjbic, ted 7igdtil dgdrhy jf ted pnrtilbds is gjt gdnrby dgjuhe tj jvdrljad ted

    pjtdgtinb dgdrhy lnusdc my tedir autunb nttrnltijg.

    If n sjbic is edntdc, ted kigdtil dgdrhy jf ted pnrtilbds iglrdnsds, ngc tedy vimrntd ajrd.

    Ns tedy vimrntd ajrd, ted mjgcs mdtwddg ted pnrtilbds nrd wdnkdgdc, sjad nrd mrjkdg

    ngc spnlds nppdnr mdtwddg ted pnrtilbds. Nt teis pjigt ted sjbic ens adbtdc.

    =+I:=

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    $JG$% \S&.%S.&D\

    jgcigh ig ijgil ljapjugcs

    Ng ijgil mjgc is ng nttrnltijg mdtwddg jppjsitdby lenrhdc ijgs. Nftdr ted ijgs nrd fjradc

    tedy nbb ljad tjhdtedr tj fjra n bnttild. N bnttild is ng igfigitd ngc rdpdntigh nrrnghdadgtjf pnrtilbds. Nbb ted ngijgs nrd surrjugcdc my lntijgs ngc nbb ted lntijgs nrd surrjugcdc

    my ngijgs.

    Sed ljjrcigntijg guamdr jf ng ijg ig ng ijgil sjbic is ted guamdr jf jppjsitdby lenrhdc

    ijgs weile surrjugc it. Seis vnrids frja sumstngld tj sumstngld mut is usunbby ', jr 4.

    D/npbd 0 sjci# lebjricd

    Ig sjciua lebjricd, -nLb, dnle sjciua ijg is surrjugcdc my si lebjricd ijgs ngc vild

    vdrsn.

    Sed cinhrna mdbjw sejws ted strulturd jf sjciua lebjricd. Sed pnttdrg rdpdnts ig teis

    wny ngc ted strulturd dtdgcs 2rdpdnts itsdbf) ig nbb cirdltijgs jvdr ljugtbdss ijgs. Mjuaust rdadamdr tent teis cinhrna rdprdsdgts jgby n tigy pnrt jf ted wejbd sjciua lebjricd

    lrystnb.

    Dnle sjciua ijg nttrnlts sdvdrnb

    lebjricd ijgs ngc vild vdrsn sj ted

    ijgil mjgcigh is gjt oust mdtwddg jgd

    sjciua ngc jgd lebjricd ijg. Sedrd is

    n

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    *. "dbtigh ngc mjibigh pjigt

    Sed nttrnltijg mdtwddg jppjsitd ijgs is vdry strjgh. N bjt jf 7igdtil dgdrhy is teus

    rd1uirdc tj jvdrljad teda ngc ted adbtigh pjigt ngc mjibigh pjigt jf ijgil ljapjugcs is

    vdry eihe.

    Ig ted bi1uic stntd, ted ijgs stibb rdtnig tedir lenrhd ngc ted nttrnltijg mdtwddg ted ijgs is

    stibb strjgh. "ule ajrd dgdrhy is rd1uirdc tj sdpnrntd ted ijgs ljapbdtdby ngc tedciffdrdgld mdtwddg ted adbtigh ngc mjibigh pjigt is teus bnrhd.

    Ljapjugc -nLb "h

    "dbtigh pjigtjL 4%* 40

    jibigh pjigtjL *'03 >%%

    Sed eihedr ted lenrhd jg ted ijgs, ngc ted sanbbdr tedy nrd, ted strjghdr ted nttrnltijg

    mdtwddg teda wibb md ngc ted eihedr ted adbtigh ngc mjibigh pjigts. Ig "h, ted ijgsenvd n C ngc ; lenrhd ngc teus ted nttrnltijg mdtwddg teda is strjghdr teng ig -nLb, sjted adbtigh ngc mjibigh pjigts nrd eihedr.

    . Dbdltrilnb Ljgcultivity

    =igld ijgil sjbics ljgtnig ijgs, tedy nrd nttrnltdc my dbdltril fidbcs ngc wibb, if pjssimbd,

    ajvd tjwnrcs ted dbdltrjcds ngc teus ljgcult dbdltrility. Ig ted sjbic stntd, ejwdvdr, ted

    ijgs nrd gjt frdd tj ajvd sigld tedy nrd tihetby edbc ig pbnld my dnle jtedr. Seus ijgilljapjugcs cj gjt ljgcult dbdltrility ig ted sjbic stntd. Ijgil sjbics nrd teus hjjc

    igsubntjrs.

    Ig ted bi1uic stntd, ted ijgs nrd frdd tj ajvd ngc sj lng ajvd tjwnrcs tedir rdspdltivd

    dbdltrjcds. Seus ijgil ljapjugcs lng ljgcult dbdltrility ig ted bi1uic stntd.

    >. "dlengilnb prjpdrtids

    =igld ijgs nrd edbc strjghby ig pbnld my ted jtedr ijgs, tedy lnggjt ajvd jr sbip jvdr dnle

    jtedr dnsiby ngc nrd edgld enrc ngc mrittbd.

    jppjsitd ijgs nttrnlt bi7d ijgs rdpdb $ strulturd mrdn7s

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    -DSN(($% \S&.%S.&D\

    jgcigh ig adtnbs

    "dtnbbil mjgcigh is ted nttrnltijg mdtwddg lntijgs ngc n sdn jf cdbjlnbisdc dbdltrjgs. Sed

    lntijgs nrd nrrnghdc tj fjra n bnttild, wite ted dbdltrjgs frdd tj ajvd mdtwddg teda.

    Sed strulturd jf ted bnttild vnrids frja adtnb tj adtnb, ngc tedy cj gjt gddc tj md 7gjwg

    ig cdtnib. It is pjssimbd tj crnw n siapbifidc fjra jf ted bnttild?

    D/npbd * nhgdsi#

    Ah=+

    Ah=+

    Ah=+ Ah

    =+

    Ah=+ Ah

    =+

    Ah=+

    Ah=+

    Ah=+

    d dd d

    d

    dd

    dd

    d

    d d

    d

    Dbdltrilnb ljgc#lti!ity? sigld ted dbdltrjgs ig n adtnb nrd cdbjlnbisdc, tedy nrd frdd tj

    ajvd terjuhejut ted lrystnb ig n ldrtnig cirdltijg wedg n pjtdgtinb ciffdrdgld is nppbidcngc adtnbs lng teus ljgcult dbdltrility ig ted sjbic stntd. Sed cdbjlnbisdc dbdltrjg systda

    is stibb prdsdgt ig ted bi1uic stntd, sj adtnbs lng nbsj ljgcult dbdltrility wdbb ig ted bi1uic

    stntd.

    m> -dbtigh ngc mjibigh pjigt? nbtejuhe gjt hdgdrnbby ns strjgh ns ig ijgil ljapjugcs,

    ted mjgcigh ig adtnbs is rdbntivdby strjgh, ngc ns n rdsubt ted adbtigh ngc mjibigh pjigts jf

    adtnbs nrd rdbntivdby eihe.

    "dtnb -n 6 d "h

    "dbtigh pjigt jL 34 ' *&4 '3

    jibigh pjigt jL 44> &% 3&% **%&

    =anbbdr ijgs, ngc tejsd wite n eihe lenrhd, nttrnlt ted dbdltrjgs ajrd strjghby ngc sjenvd eihedr adbtigh pjigts teng bnrhdr ijgs wite n bjw lenrhd. -n ens sanbbdr lntijgs

    teng 6 sj ens n eihedr adbtigh ngc mjibigh pjigt. "h lntijgs envd n eihedr lenrhd teng-n sj ens n eihedr adbtigh ngc mjibigh pjigt.

    l> Jtedr peysilnb prjpdrtids? =igld ted mjgcigh ig adtnbs is gjg;cirdltijgnb, it cjds gjt

    rdnbby anttdr ejw ted lntijgs nrd jridgtdc rdbntivd tj dnle jtedr. Sed adtnb lntijgs lng mdajvdc nrjugc ngc tedrd wibb stibb md cdbjlnbi#dc dbdltrjgs nvnibnmbd tj ejbc ted lntijgs

    tjhdtedr. Sed adtnb lntijgs lng teus sbip jvdr dnle jtedr fnirby dnsiby. Ns n rdsubt, adtnbs

    tdgc tj md sjft, anbbdnmbd ngc cultibd.

    Seis is n

    siapbifidc :

    fjra jf ted

    adtnb bnttild

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    %J'N(DGS \S&.%S.&D\

    N ljvnbdgt mjgc is n senrdc pnir jf dbdltrjgs mdtwddg twj ntjas. edg n ljvnbdgt mjgcis fjradc, twj ntjail jrmitnbs jvdrbnp ngc n ajbdlubnr jrmitnb is fjradc. +i7d ntjail

    jrmitnbs, n ajbdlubnr jrmitnb lng jgby ljgtnig twj dbdltrjgs. vdrbnp jf ntjail jrmitnbs is

    teus jgby pjssimbd if mjte jrmitnbs ljgtnig jgby jgd dbdltrjg 2gjranb ljvnbdgt mjgc), jr ifjgd is fubb ngc ted jtedr dapty 2cntivd ljvnbdgt mjgc).

    Ljvnbdgt mjgcigh enppdgs mdlnusd ted dbdltrjgs nrd ajrd stnmbd wedg nttrnltdc tj twjgulbdi teng wedg nttrnltdc tj jgby jgd?

    *. -jranb ljvnbdgt mjgcs

    Ng jvdrbnp mdtwddg twj jrmitnbs, dnle ljgtnigigh jgd dbdltrjg, is n gjranb ljvnbdgtmjgc. Sed guamdr jf gjranb ljvnbdgt mjgcs weile ng ntja lng fjra cdpdgcs jg its

    guamdr jf ugpnirdc dbdltrjgs. =jad ntjas, bi7d lnrmjg, prjajtd dbdltrjgs frja s tj p

    jrmitnbs tj lrdntd ugpnirdc dbdltrjgs.

    *s s p

    / FH FH FH FH F

    / ens * ugpnirdc dbdltrjg ig n p jrmitnb $ fjras jgd ljvnbdgt mjgc

    Dh eycrjhdg fbujricd

    x x

    x x

    x

    x

    x

    jF E

    *s s p

    L FH FH F F

    Lnrmjg rdnrrnghds sbihetby tj an7d ajrd ugpnirdc dbdltrjgs $

    *s s p

    L FH F F F F

    L ens ' ugpnirdc dbdltrjgs $ fjras fjur ljvnbdgt mjgcs

    Dh adtengd

    j x

    xj

    xj

    xjLE

    E

    E

    E

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    *. :ntivd ljvnbdgt mjgcs

    Ngy ntja weile ens fibbdc vnbdgld sedbb jrmitnbs lng prjvicd mjte dbdltrjgs fjr n cntivdljvnbdgt mjgc. Seis iglbucds ngy dbdadgt ig hrjups 8, 8I, 8II jr % mut is ajst ljaajg

    ig -, ngc Lb.

    *s s p

    - FH FH F F F

    - ens terdd ugpnirdc dbdltrjgs ngc jgd dbdltrjg pnir

    Ngy ntja weile ens dapty vnbdgld sedbb jrmitnbs lng nlldpt n pnir jf dbdltrjgs fjr nljvnbdgt mjgc. Seis iglbucds ngy dbdadgt ig hrjups I, II ngc III mut is ajst ljaajg ig

    d, ngc Nb.

    *s s p

    FH FH F

    prjajtds ng dbdltrjg frja s tj p tj fjra > ugpnirdc dbdltrjgs?

    *s s p

    FH F F F

    ens > ugpnirdc dbdltrjgs ngc ng dapty jrmitnb

    Dh (>-(>

    j x

    x j

    xj ME

    E

    E

    j x

    x j

    xx

    xjG

    E

    E

    E

    . =ihan ngc pi mjgcs

    Ntjail jrmitnbs lng jvdrbnp ig jgd jf twj wnys?

    If tedy jvdrbnp cirdltby nbjgh ted igtdrgulbdnr nis, ns is ajst ljaajg, n ;mjgc is

    fjradc.

    + jr

    N *mjgc is n mjgc rds#btigh frj cirdlt j!drbnp jf twj jrmitnbs nbjgh ted

    igtdrg#lbdnr n/is.

    Nbb sighbd mjgcs mdtwddg twj ntjas nrd ;mjgcs.

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    It is jgby pjssimbd tj fjra jgd ;mjgc mdtwddg twj ntjas, sigld ngjtedr wjubc fjrld tjj

    angy dbdltrjgs igtj n sanbb spnld ngc hdgdrntd rdpubsijg. If cjumbd mjgcs nrd fjradc,

    tedrdfjrd, ted jrmitnbs aust jvdrbnp ig n ciffdrdgt wny.

    If twj jrmitnbs jvdrbnp nmjvd ngc mdbjw 2jr mdeigc ngc ig frjgt jf) ted igtdrgulbdnr nis,

    tedg n ;mjgc is fjradc.

    + jr

    N *mjgc is n mjgc rds#btigh frj j!drbnp jf ntjil jrmitnbs nmj!d ngc mdbjw ted

    igtdrg#lbdnr n/is.

    Nbb cjumbd mjgcs ljgsist jf n ;mjgc ngc n ;mjgc.

    Nbb tripbd mjgcs ljgsist jf n ;mjgc ngc twj ;mjgcs. If ted first ;mjgc rdsubts frja

    jvdrbnp nmjvd ngc mdbjw ted igtdrgulbdnr nis, ted sdljgc rdsubts frja jvdrbnp mdeigcngc ig frjgt jf ted igtdrgulbdnr nis.

    -jtd tent ;mjgcs lng jgby md fjradc my jvdrbnp jf p;jrmitnbs, sigld s;jrmitnbs cj gjt

    envd ted ljrrdlt hdjadtry.

    ;mjgcs lng nbsj md rdprdsdgtdc my jrmitnb cinhrnas.

    Dh dtedgd?

    >. =trdghte jf ljvnbdgt mjgcs

    Ljvnbdgt mjgcs nrd ig hdgdrnb strjgh. Sed sanbbdr ted ntjas, ted lbjsdr ted dbdltrjgs nrd

    tj ted twj gulbdi ngc ted strjghdr ted mjgc.

    jgc jgc cissjlintijg dgdrhy 7Eajb;*

    L;/ '&

    L;Lb >'

    L;r 3%

    L;I 4

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    '. "jbdlubnr, hingt ljvnbdgt ngc bnydrdc sumstnglds

    Ljvnbdgt mjgcigh lng rdsubt ig terdd vdry ciffdrdgt typds jf sumstngld?

    n) "jbdlubnr

    Ig angy lnsds, ted mjgcigh lnpnlity is rdnledc nftdr jgby n fdw ntjas envd ljamigdcwite dnle jtedr tj fjra n ajbdlubd. If gj ajrd ljvnbdgt mjgcs lng md fjradc nftdr teis,

    ted sumstngld wibb md ancd up jf n bnrhdr guamdr jf cislrddt ugits 2ajbdlubds) wite gj

    strjgh mjgcigh mdtwddg teda.

    =ule sumstnglds nrd lnbbdc jbdl#bnr s#mstnglds, ngc tedrd nrd angy dnapbds jf teda?L(', Lb, (d, =4,

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    tedr peysilnb prjpdrtids? Sed igtdrajbdlubnr fjrlds nrd wdn7 ngc hdgdrnbby gjg;

    cirdltijgnb, sj ajst ajbdlubnr ljvnbdgt sumstnglds nrd sjft, lruamby ngc gjt vdry strjgh.

    m) 9ingt ljvnbdgt

    Ig sjad lnsds, it is gjt pjssimbd tj sntisfy ted mjgcigh lnpnlity jf n sumstngld ig ted fjrajf n ajbdlubd! ted mjgcs mdtwddg ntjas ljgtigud igcdfigitdby, ngc n bnrhd bnttild is

    fjradc. Sedrd nrd gj cislrdtd ajbdlubds ngc ljvnbdgt mjgcigh dists mdtwddg nbb ncnldgt

    ntjas.=ule sumstnglds nrd lnbbdc hingt ljvnbdgt sumstnglds, ngc ted ajst iapjrtngt dnapbds

    nrd L, , =i ngc =i.

    D/npbd 0 cinjgc2cinajgc is ng nbbjtrjpd jf lnrmjg)

    Cjg't fjrhdt tent teis is oust n tigy

    pnrt jf n hingt strulturd dxtdgcigh jg

    nbb < ciadgsijgs.

    Ig hingt ljvnbdgt ljapjugcs, ljvnbdgt mjgcs aust md mrj7dg mdfjrd n sumstngld lng adbtjr mjib.

    9ingt ljvnbdgt ljapjugcs envd ldrtnig lenrnltdristil prjpdrtids?

    "dbtigh ngc mjibigh pjigt? tedsd nrd hdgdrnbby vdry eihe, sigld strjgh ljvnbdgt mjgcs

    aust md mrj7dg mdfjrd ngy ntjas lng md sdpnrntdc. Sed adbtigh ngc mjibigh pjigts

    cdpdgc jg ted guamdr jf mjgcs fjradc my dnle ntja ngc ted mjgc strdghte. Sedciffdrdgld mdtwddg adbtigh ngc mjibigh pjigts is gjt usunbby vdry bnrhd, sigld ljvnbdgt

    mjgcs nrd vdry cirdltijgnb ngc jgld mrj7dg, nrd mrj7dg ljapbdtdby.

    =umstngld L =i =i"dbtigh pjigt jL >00% *'*% >%% *0*%

    jibigh pjigt jL '4& >00 00% >%

    Dbdltrilnb ljgcultivity? tedrd nrd gj ijgs jr cdbjlnbisdc dbdltrjgs, sj tedrd is bittbd

    dbdltrilnb ljgcultivity ig ditedr sjbic jr bi1uic stntd.

    tedr peysilnb prjpdrtids? sigld ted ljvnbdgt mjgcs nrd strjgh ngc cirdltijgnb, hingt

    ljvnbdgt sumstnglds nrd enrc, strjgh ngc mrittbd.:inajgc is ig fnlt ted enrcdst sumstngld 7gjwg tj ang. /jr teis rdnsjg it is usdc ig cribbs,

    hbnss;luttigh ngc stybusds fjr turgtnmbds.

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    l) hingt ljvnbdgt bnydrdc

    =jad sumstnglds ljgtnig ng igfigitd bnttild jf ljvnbdgtby mjgcdc ntjas ig twj ciadgsijgs

    jgby tj fjra bnydrs. Sed ciffdrdgt bnydrs nrd edbc tjhdtedr my igtdrajbdlubnr fjrlds, ngc

    tedrd nrd jftdg cdbjlnbi#dc dbdltrjgs ig mdtwddg ted bnydrs. Dnapbds jf tedsd strulturdsnrd hrnpeitd ngc mbnl7 pejspejrus.

    D/npbd * hrnpeitd

    jr

    Ig hrnpeitd, dnle lnrmjg ntja is mjgcdc tj terdd jtedrs. Sed spnrd dbdltrjg is cdbjlnbi#dc

    ngc jllupids ted spnld ig mdtwddg ted bnydrs. Nbb ntjas ig ted snad bnydr nrd edbctjhdtedr my strjgh ljvnbdgt mjgcs, ngc ted ciffdrdgt bnydrs nrd edbc tjhdtedr my

    igtdrajbdlubnr fjrlds.

    N guamdr jf lenrnltdristil prjpdrtids jf hrnpeitd rdsubt frja teis strulturd?

    Dbdltrilnb ljgcultivity? cud tj ted cdbjlnbisdc dbdltrjgs ig dnle pbngd, hrnpeitd is n vdryhjjc ljgcultjr jf dbdltrility ig ted ngc y cirdltijgs, dvdg ig ted sjbic stntd 2ugusunbby

    fjr n gjg;adtnb). (jwdvdr, sigld ted cdbjlnbisntijg is jgby ig twj ciadgsijgs, tedrd is

    bittbd dbdltrilnb ljgcultivity ig ted # cirdltijg 2i.d. pdrpdgcilubnr tj ted pbngds).

    :dgsity? hrnpeitd ens n aule bjwdr cdgsity teng cinajgc 2.0 hla;>) cud tj ted

    rdbntivdby bnrhd cistnglds ig mdtwddg ted pbngds.

    (nrcgdss? hrnpeitd is aule sjftdr teng cinajgc sigld ted ciffdrdgt pbngds lng sbip jvdrdnle jtedr fnirby dnsiby. Seis rdsubts ig ted wicdsprdnc usd jf hrnpeitd ig pdglibs ngc ns ng

    igcustrinb bumrilngt.

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    \.--N&Y JF C$FFD&DGS SYPD\ JF %J-PJ.GC NGC S=D$&

    P&JPD&S$D\

    \.M\SNG%D -nturd jf mjgcigh

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    -J(D%.(N& \=NPD\

    edg ng ntja fjras n ljvnbdgt mjgc wite ngjtedr ntja, ted dbdltrjgs ig ted ciffdrdgtmjgcs ngc ted gjg;mjgcigh dbdltrjgs ig ted jutdr sedbb nbb mdenvd ns gdhntivdby lenrhdc

    lbjucs ngc rdpdb dnle jtedr. Ig jrcdr tj aigiaisd teis rdpubsijg, nbb ted jutdr sedbb

    dbdltrjgs sprdnc jut ns fnr npnrt ig spnld ns pjssimbd.

    "jbdlubnr senpds ngc ted nghbds mdtwddg mjgcs lng md prdciltdc my ted 8=D, L>;,->

    ;

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    If jgd jf tedsd dbdltrjg pnirs is n bjgd pnir, ted mjgc nghbd is sbihetby bdss teng *% jcud tj

    ted strjghdr rdpubsijg frja bjgd pnirs, fjrligh teda lbjsdr tjhdtedr.

    mjgc nghbd 1 >>5j

    "jbdlubds weile ncjpt teis senpd nrd snic tj md D-S.

    D.h. =, -;

    l> Fj#r dbdltrjg pnirs

    If tedrd nrd fjur mjgcdc pnirs jg ted ldgtrnb ntja, ted nghbd mdtwddg ted mjgcs is npprj

    *%3j.

    "jbdlubds weile ncjpt teis senpd nrd snic tj md SDSKN(D:KN+.

    D.h. L(', =iLb',-('C

    , =';

    If jgd jf ted dbdltrjg pnirs is n bjgd pnir, ted mjgc nghbd is sbihetby bdss teng *%3j, cud tjted dtrn bjgd pnir rdpubsijg weile puseds ted mjgcs lbjsdr tjhdtedr 2npprj *%&j).

    "jbdlubds weile ncjpt teis senpd nrd snic tj md SKI9-N+

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    If twj jf ted dbdltrjg pnirs nrd bjgd pnirs, ted mjgc nghbd is nbsj sbihetby bdss teng *%3j,

    cud tj ted dtrn bjgd pnir rdpubsijg 2npprj *%'j).

    "jbdlubds weile ncjpt teis senpd nrd snic tj md D-S.

    D.h. (, /

    c> Fi!d dbdltrjg pnirs

    If tedrd nrd fivd mjgcdc pnirs jg ted ldgtrnb ntja, ted terdd mjgcs nrd ig n pbngd nt *%jtj

    dnle jtedr, ted jtedr nrd nt 3%jtj ted pbngd.

    "jbdlubds weile ncjpt teis senpd nrd snic tj md SKI9-N+ M \i/ dbdltrjg pnirs

    If tedrd nrd si dbdltrjg pnirs jg ted ldgtrnb ntja, ted nghbd mdtwddg ted mjgcs is 3% j.

    "jbdlubds weile ncjpt teis senpd nrd snic tj md LSN(D:KN+.

    D.h. =/

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    If tedrd nrd ' mjgcigh pnirs ngc bjgd pnirs, ted mjgcdc pnirs nrd nt 3%jig ted pbngd ngc

    ted bjgd pnirs nt *4%j. Sed nghbds nrd stibb dnltby 3%jmdlnusd ted bjgd pnirs nrd jppjsitd

    dnle jtedr sj tedir rdpubsijg lngldbs jut.

    "jbdlubds weile ncjpt teis senpd nrd snic tj md =@NKD > % SKI9-N+ * D-S

    N

    M

    M

    **0 ; **4

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    ' ' % SDSKN(D:KN+

    N

    M

    MM

    M

    *%3.0

    ' > * SKI9-N+

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    $GSD&-J(D%.(N& FJ&%D\

    Sedrd nrd gj ljvnbdgt mjgcs mdtwddg ajbdlubds ig ajbdlubnr ljvnbdgt ljapjugcs. Sedrdnrd, ejwdvdr, fjrlds jf nttrnltijg mdtwddg tedsd ajbdlubds, ngc it is tedsd weile aust md

    jvdrljad wedg ted sumstngld is adbtdc ngc mjibdc. Sedsd fjrlds nrd 7gjwg ns

    igtdrajbdlubnr fjrlds. Sedrd nrd terdd anig typds jf igtdrajbdlubnr fjrld?

    *. 8ng cdr nnbGs fjrlds

    Ljgsicdr n ajbdlubd jf jyhdg, .

    J Jd d d

    dd d

    d

    ddd

    d

    Sed dbdltrjgs ig teis ajbdlubd nrd gjt stntil! tedy nrd ig n stntd jf ljgstngt ajtijg. It is

    tedrdfjrd bi7dby tent nt ngy hivdg tiad ted cistrimutijg jf dbdltrjgs wibb gjt md dnltby

    syaadtrilnb ; tedrd is bi7dby tj md n sbihet surpbus jf dbdltrjgs jg jgd jf ted ntjas.-

    J Jdd

    dd

    d dd

    dd

    dd

    +

    Seis is 7gjwg ns n tdpjrnry cipjbd. It bnsts fjr n vdry sejrt tiad ns ted dbdltrjgs nrd

    ljgstngtby ajvigh. Sdapjrnry cipjbds nrd ljgstngtby nppdnrigh ngc cisnppdnrigh.

    Ljgsicdr gjw ng ncnldgt ajbdlubd. Sed dbdltrjgs jg teis ajbdlubd nrd rdpdbbdc my ted

    gdhntivd pnrt jf ted cipjbd ngc nttrnltdc tj ted pjsitivd pnrt, ngc ajvd nlljrcighby.

    J Jdd

    dd

    d dd

    dd

    dd

    + -

    J Jdd

    dd

    d dd

    dd

    dd

    + -

    Seis is 7gjwg ns ng igc#ldc cipjbd. Sedrd is n rdsubtigh nttrnltijg mdtwddg ted twj

    ajbdlubds, ngc teis 7gjwg ns n 'ng cdr 4nnb6s fjrld.

    8ng cdr nnbGs fjrlds nrd prdsdgt mdtwddg nbb ajbdlubds, nbtejuhe tedy lng md vdry wdn7.

    Sedy nrd ted rdnsjg nbb ljapjugcs lng md bi1udfidc ngc sjbicifidc. 8ng cdr nnbGs fjrldstdgc tj envd strdghtes mdtwddg * 7Eajb;*ngc 0% 7Eajb;*.

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    Sed strdghte jf ted 8ng cdr nnbGs fjrlds ig mdtwddg ajbdlubds cdpdgcs jg twj fnltjrs?

    n) ted guamdr jf dbdltrjgs ig ted ajbdlubd

    Sed hrdntdr ted guamdr jf dbdltrjgs ig n ajbdlubd, ted hrdntdr ted bi7dbiejjc jf ncistjrtijg ngc teus ted hrdntdr ted frd1udgly ngc anhgitucd jf ted tdapjrnry cipjbds.

    Seus ted 8ng cdr nnbGs fjrlds mdtwddg ted ajbdlubds nrd strjghdr ngc ted adbtigh ngc

    mjibigh pjigts nrd bnrhdr.

    Dh gjmbd hnsds?

    =umstngld (d -d Nr 6r

    -uamdr jf dbdltrjgs *% *4 >

    "dbtigh pjigtjL ;& ;0 ;*43 ;*0&

    jibigh pjigtjL ;3 ;0% ;*4 ;*0

    Dh nb7ngds?

    =umstngld L(' L( L>(4 L'(*%-uamdr jf dbdltrjgs *% *4 >'

    "dbtigh pjigtjL ;*4 ;*4> ;*3% ;*>4

    jibigh pjigtjL ;*' ;44 ;' %

    n) =urfnld nrdn jf ted ajbdlubds

    Sed bnrhdr ted surfnld nrdn jf n ajbdlubd, ted ajrd ljgtnlt it wibb envd wite ncnldgt

    ajbdlubds. Seus ted hrdntdr its nmibity tj igculd n cipjbd ig ng ncnldgt ajbdlubd ngc tedhrdntdr ted 8ng cdr nnbGs fjrlds ngc adbtigh ngc mjibigh pjigts.

    Seis pjigt lng md ibbustrntdc my ljapnrigh ciffdrdgt ajbdlubds ljgtnigigh n siaibnr

    guamdr jf dbdltrjgs?

    =umstngld 6r Lb L(>L(2L(>)L(> L(>L(L(L(>-uamdr jf dbdltrjgs > >' >' >'

    "dbtigh pjigtjL ;*0& ;*%* ;*03 ;*>4

    jibigh pjigtjL ;*0 ;>0 ;* %

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    L(>L(2L(>)L(> L(>L(L(L(>adteybprjpngd mutngd

    L LL

    E EE

    EE

    E E

    L

    E

    E

    E

    L LL L

    E EE E

    E

    EEEE

    E

    -jtd tent mutngd ens n bnrhdr surfnld nrdn teng ;adteybprjpngd, nbtejuhe tedy envd tedsnad ajbdlubnr fjraubn 2L'(*%). =trnihet;lenig ajbdlubds nbwnys envd eihedr mjibigh

    pjigts teng tedir isjadrs wite mrngledc lenigs.

    . :ipjbd;cipjbd mjgcigh

    Sdapjrnry cipjbds dist ig nbb ajbdlubds, mut ig sjad ajbdlubds tedrd is nbsj n

    pdrngdgt cipjbd.

    "jst ljvnbdgt mjgcs envd n cdhrdd jf ijgil lenrnltdr rdsubtigh frja n ciffdrdgld ig

    dbdltrjgdhntivity mdtwddg ted ntjas. Seis rdsubts ig n pjbnr mjgc ngc n cipjbd.

    E Lb

    -+

    LJ

    +-

    Ig angy lnsds, ejwdvdr, ted prdsdgld jf pjbnr mjgcs 2cipjbds) cjds gjt rdsubt ig n

    pdrangdgt cipjbd jg ted ajbdlubd, ns tedrd nrd jtedr pjbnr mjgcs 2cipjbds) ig ted snad

    ajbdlubd weile envd ted dffdlt jf lngldbbigh dnle jtedr jut. Seis dffdlt lng md sddg ig n

    guamdr jf bigdnr, trihjgnb pbngnr ngc tdtrnedcrnb sumstnglds?

    LJ J

    L

    Lb

    Lb Lb

    Lb

    M

    F

    F F

    L />LLb'

    Ig nbb ted nmjvd lnsds, tedrd nrd cipjbds rdsubtigh frja pjbnr mjgcs mut ted vdltjr sua jftedsd cipjbds is #drj! i.d. ted cipjbds lngldb dnle jtedr jut. Sed ajbdlubd teus ens gj

    jvdrnbb cipjbd ngc is snic tj md gjg*pjbnr.

    -jg;pjbnr ajbdlubds nrd tejsd ig weile tedrd nrd gj pjbnr mjgcs jr ig weile ted cipjbds

    rdsubtigh frja ted pjbnr mjgcs nbb lngldb dnle jtedr jut. Sed jgby igtdrajbdlubnr fjrlds

    tent dist mdtwddg gjg;pjbnr ajbdlubds nrd tdapjrnry;igculdc cipjbd nttrnltijgs, jr 8ngcdr nnbOs fjrlds.

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    Ig jtedr ajbdlubds, ejwdvdr, tedrd nrd cipjbds jg ted ajbdlubd weile cj gjt lngldb dnle

    jtedr jut?

    L

    Lb

    Lb Lb

    E

    -

    +

    !

    J

    J

    +

    -

    GE

    E

    E

    -

    +

    L(Lb> = -(>

    Ig nbb ted nmjvd lnsds, tedrd nrd cipjbds rdsubtigh frja pjbnr mjgcs wejsd vdltjr sua is

    gjt #drj! i.d. ted cipjbds cj gjt lngldb dnle jtedr jut. Sed ajbdlubd teus ens n pdrangdgt

    cipjbd ngc is snic tj md pjbnr.

    L(2L(>)L(> L(>LL(>-uamdr jf

    dbdltrjgs

    >' > >' >

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    >. (ycrjhdg mjgcigh

    Ig ajst lnsds ns sddg nmjvd, ted prdsdgld jf pdrangdgt cipjbds jgby an7ds n sbihet

    ciffdrdgld tj ted anhgitucd jf ted igtdrajbdlubnr fjrlds. Sedrd is jgd dldptijgnb lnsd,

    ejwdvdr, wedrd ted pdrangdgt cipjbd an7ds n euhd ciffdrdgld tj ted strdghte jf tedmjgcigh mdtwddg ted ajbdlubds.

    Ljgsicdr n ajbdlubd jf eycrjhdg fbujricd, (/. Seis lbdnrby ens n pdrangdgt cipjbd nstedrd is n bnrhd ciffdrdgld ig dbdltrjgdhntivity mdtwddg ( 2.*) ngc / 2'.%). Sed dbdltrjgs

    ig teis mjgc nrd jg nvdrnhd aule lbjsdr tj ted / teng ted (?

    E F

    + -

    Sed rdsubt jf teis is tent ted ( ntja ens jg nbajst gj dbdltrjg cdgsity nrjugc its gulbdus

    nt nbb ngc is tedrdfjrd vdry sanbb. Sed ( ntja is tedrdfjrd nmbd tj npprjnledbdltrjgdhntivd ntjas jg ncnldgt ajbdlubds vdry lbjsdby ngc fjra n vdry strjgh

    igtdrajbdlubnr cipjbd;cipjbd mjgc.

    E F E F E F

    Seis is 7gjwg ns eycrjhdg mjgcigh. It is jgby pjssimbd if ted eycrjhdg ntja is mjgcdc

    tj n vdry dbdltrjgdhntivd dbdadgt! i.d. -, jr /. It is gjt fugcnadgtnbby ciffdrdgt frjacipjbd;cipjbd mjgcigh! it is ust n strjghdr fjra jf it.

    N eycrjhdg mjgc lng md cdfigdc ns ng nttrnltijg mdtwddg ng dbdltrjpjsitivd eycrjhdgntja 2id ljvnbdgtby mjgcdc tj -, jr /) ngc ng dbdltrjgdhntivd ntja jg ng ncnldgt

    ajbdlubd.

    Dnapbds jf sumstnglds ljgtnigigh eycrjhdg mjgcs nrd (/, (, -(>, nbljejbs,lnrmjybil nlics, naigds, nlic naicds ngc urdn.

    J

    E

    E

    J

    E

    E

    J

    E

    E

    GE

    E

    E

    G

    EE

    E

    GE

    E

    E

    "#crjhdgmjgcs

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    Ig dnle lnsd ted eycricd jf pdrijc sejws n mjibigh pjigt weile is nmgjranbby eihe

    2 (, -(>ngc (/).

    Sed hdgdrnb iglrdnsd ig mjibigh pjigt cjwg ted hrjups rdsubt frja ted iglrdnsd ig 8ng cdr

    nnbGs fjrlds weile rdsubts frja ng iglrdnsigh guamdr jf dbdltrjgs ig ted ajbdlubds.

    Sedrd nrd pdrangdgt cipjbds mut tedy nrd gjt vdry strjgh.

    Sed nmgjranbby eihe mjibigh pjigts jf (, -(>ngc (/ nrd n rdsubt jf eycrjhdg

    mjgcigh mdtwddg ted ajbdlubds. Seus rdsubts ig vdry strjgh igtdrajbdlubnr fjrldsmdtwddg ted ajbdlubds cdspitd ted fnlt tent ted 8ng cdr nnbGs fjrlds nrd wdn7dr teng ig

    ted jtedr eycricds.

    m) jtedr dffdlts jf eycrjhdg mjgcigh

    Sed dffdlts jf eycrjhdg mjgcigh jg ted peysilnb prjpdrtids jf n sumstngld nrd gjt

    rdstriltdc tj dbdvntdc adbtigh ngc mjibigh pjigts! it lng igfbudgld ted prjpdrtids jf

    sumstnglds ig jtedr wnys?

    Sed bjw cdgsity jf ild. Seis is cud tj eycrjhdg mjgcigh. Ig ild, ted wntdr ajbdlubdsnrrnghd tedasdbvds ig sule n wny ns tj aniaisd ted najugt jf eycrjhdg mjgcigh

    mdtwddg ted ajbdlubds. Seis rdsubts ig n vdry jpdg ednhjgnb strulturd wite bnrhd spnlds

    witeig ted lrystnb. Seis nlljugts fjr its bjw cdgsity.

    edg ted ild adbts, ted strulturd ljbbnpsds igtj ted jpdg spnlds ngc ted rdsubtigh bi1uic,

    cdspitd mdigh bdss jrcdrdc, jllupids bdss spnld ngc is teus ajrd cdgsd.

    Seus ild fbjnts jg wntdr.

    Sed edbilnb gnt#rd jf CGN. Seis is nbsj cud tj eycrjhdg mjgcigh. "jbdlubds jf :-Nljgtnig -;( mjgcs ngc sj eycrjhdg mjgcigh is pjssimbd. Sed bjgh lenigs nbsj ljgtnig

    LB mjgcs ngc ted ( ntjas lng fjra n eycrjhdg mjgc wite teis dbdltrjgdhntivd ntja.

    Seis rdsubts ig ted ajbdlubd spirnbbigh, ns ted LB mjgcs ngc ted -;( mjgcs npprjnlednle jtedr.

    Seis is ng dnapbd jf ng igtrnjbdl#bnreycrjhdg mjgc, wedrd ted nttrnltijg is mdtwddg

    n eycrjhdg ntja ngc ng dbdltrjgdhntivd ntja jg ted snad ajbdlubd. Seis aust mdcistighuisedc frja igtdrajbdlubnr eycrjhdg mjgcigh, ig weile ted nttrnltijg is mdtwddg n

    eycrjhdg ntja ngc ng dbdltrjgdhntivd ntja jg ng ncnldgt ajbdlubd.