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"eiflsmjueirpmysl`s.lf" 9
@MAELPTR\
p-Bho`j Ahaeafts (Mihocafs ifd Fobha Cisas)
Lftrodu`tlof ;Croup 90 to 9= og tma parlodl` tibha og ahaeafts `ofstltuta tma pbho`j. Tma pbho`j `oftilfs eatihs,
eatihholds is wahh is fofeatihs.
Tma pbho`j ahaeafts miva cafarih vihaf`a smahh aha trofl `ofglcuritlof fs2 fp97.
Tma glrst eaebar og ai`m croup groe 9093 og tma pbho`j ahaeafts dlggar lf eify raspa`ts groe tma otmar
eaebars og tmalr raspa`tlva croups ba`iusa og seihh slza, mlcm aha`trofacitlvlty ifd ibsaf`a og dorbltihs.
Tma glrst eaebar og i croup ihso mis craitar iblhlty to gore pp euhtlpha bofds to ltsahg (a.c. @5@, @@, FF)ifd to ahaeaft og sa`ofd row (a.c @5O, @5F, @F, F5O) `oepirad to tma otmar eaebars og tma siea croup.Tma mlcmast oxlditlof og pbho`j ahaeaft ls aquih to tma croup fuebar 9>. Eovlfc dowf tma croup, tma
oxlditlof stita two hass tmif tma mlcmast croup oxlditlof stita ba`oeas eora stibha lf croups 90 to 97 dua
to lfart pilr agga`t (rahu`tif`a og s-subsmahh aha`trofs to pirtl lpita lf `mael`ih bofdlfc)
CROQ^ 93 AHAEAFTP ; TMA MIHOCAF GIELH\Ghuorlfa, `mhorlfa, broelfa, lodlfa ifd istitlfa ira eaebars og Croup 93. Tmasa ira `ohha tlvahy jfowf is
tma mihocafs (Craaj miho eaifs siht ifd cafas borf l.a., siht produ`ars). Tma mihocafs ira mlcmhy rai`tlva
fof-eatihhl` ahaeafts.
Aha`trofl` @ofglcuritlof
Ihh tmasa ahaeafts miva savaf aha`trofs lf tmalr outareost smahh (fs2 fp1) wml`m ls ofa aha`trof
smort og tma faxt fobha cis.
Itoel` ifd Lofl` Ridll
Tma mihocafs miva tma seihhast itoel` ridll lf tmalr raspa`tlva parlods dua to eixleue agga`tlva fu`hair
`mirca . Itoel` ifd lofl` ridll lf raisa groe ghuorlfa to lodlfa dua to lf raislfc fuebar og quiftue smahhs.
Loflsitlof Aftmihpy
Tmay miva hlttha tafdaf`y to hosa aha`trof. Tmus tmay miva vary mlcm loflsitlof aftmihpy. Dua to lf`raisa lf
itoel` slza, loflsitlof aftmihpy da`raisas dowf tma croup.
Aha`trof Cilf AftmihpyMihocaf miva eixleue facitlva aha`trof cilf aftmihpy lf tma `orraspofdlfc parlod. Tmls ls dua to tma gi`t
tmit tma itoes og tmasa ahaeafts miva ofhy ofa aha`trof hass tmif stibha fobha cis ofglcuritlofs. Aha`trof
cilf aftmihpy og tma ahaeafts og tma croup ba`oeas hass facitlva dowf tma croup. Mowavar, tma facitlva
aha`trof cilf aftmihpy og ghuorlfa ls hass tmif tmit og `mhorlfa. Lt ls dua to seihh slza og ghuorlfa itoe. Is i
rasuht, tmara ira strofc lftaraha`trofl` rapuhslofs lf tma rahitlvahy seihh 2p orbltihs og ghuorlfa ifd tmus, tma
axtri aha`trof (lf`oelfc) doas fot axparlaf`a eu`m ittri tlof.
Aha`trofacitlvlty
Tmay miva vary mlcm aha`trofacitlvlty. Tma aha`trofacitlvlty da`raisas dowf tma croup. Ghuorlfa ls tma eost
aha`trofacitlva ahaeaft lf tma parlodl` tibha
^mysl ih ^ropartlasGhuorlfa ifd `mhorlfa ira cisas, broelfa ls i hlquld wmarais lodlfa ls i sohld. Tmalr eahtlfc ifd bolhlfc
polfts staidlhy lf`raisa wltm itoel` fuebar. Ihh mihocafs ira `ohourad. Tmls ls dua to ibsorptlof og ridlitlofs
lf vlslbha raclof wml`m rasuhts lf tma ax ltitlof og outar aha`trofs to mlcmar afarcy havah. By ibsorblfc dlggaraft
quifti og ridlitlof, tmay dlsphiy dlggaraft `ohours. Gor axiepha, G2, mis yahhow, @h
2, craaflsm yahhow, Br
2, rad
ifd L2, vlohat `ohour. Ghuorlfa ifd `mhorlfa rai`t wltm witar. Broelfa ifd lodlfa ira ofhy spirlfchy sohubha lf
witar. But ira sohubha lf orcifl sohvafts su`m is `mhorogore, `irbof tatri`mhorlda, `irbof dlsuhpmlda ifd
mydro`irbofs to clva `ohourad sohutlofs. Ax`apt tma seihhar aftmihpy og dlsso litlof og G2
`oepirad to tmit
og @h2. Tma ]-] bofd dlsisso litlof aftmihplas groe mhorlfa ofwirds smow tma axpa`tad trafd ; @h @h 6 Br
Br 6 G G 6 L L. Tma raisof gor tma seihhar aftmihpy og dlsso`litlof og G2
ls tma rahitlvahy hircar aha`trofs-
aha`trofs rapuhslof ieofc tma hofa pilrs lf G2eoha`uha wmara tmay ira eu`m `hosar to ai`m otmar tmif lf
`isa og @h2
.
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"eiflsmjueirpmysl`s.lf" 2
@MAELPTR\
Tibha ; 9
Itoel` ifd pmysl`ih propart las
Ahaeaft G @h Br L
Itoel` Fuebar < 93 01 10
Itoel` Eiss 9< 01.41 3
4s2
4p1
ZJrU 4d9>
1s2
1p1
@ovihaft Ridlus / pe 74 9217 9942 9>>=
Aha`trof cilf aftmihpy /(jK eoh9
) 000 04< 021 2.14 WEora tma vihua og tma PR , eora powarguh ls tma oxldlslfc icaft. Maf`a tma ordar og oxldlslfc powar ls
G26 @h
26 Br
26
2
Plf`a PR^ ls tma mlcmast gor G2(ieofc ihh ahaeafts og parlodl` tibha), lt ls i strofcast oxldlslfc icaft.
Axiepha-9 @ovihaft ridlus og ghuorlfa ls 74 pe but tma bofd hafctm ls fot aquih to 92= pe ifd tmit ls 940 pe
ifd bofd afarcy ls goufd to ba `oepiribha to2
.
P o h u t l o f Tmls eiy ba ittrlbutad to.p .p rapuhslofs dua to seihh slza og G itoe.
Axiepha-2 Aha`trof igglflty og `mhorlfa ls eora tmif G. Lfsplta og tmls G2ls tma battar oxldlslfc icaft. Smy ?
P o h u t l o f PR^ og G2ls eu`m mlcmar tmif tmit og @h
2of i``ouft og seihhar bofd dlsso`litlof afarcy.
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"eiflsmjueirpmysl`s.lf" 0
@MAELPTR\
Mydritlof afarcy og ]
Peihhar tma lof, mlcmar ls tma mydritlof afarcy.
G @h Br
191 0=9 043 0>1 lf jK/eoh
Ifoeihous bamivlour og ghuorlfa
Tma ifoeihous bamivlour og ghuorlfa ls duato lts seihh slza, mlcmast aha`trofacitlvlty, how G- G bofd dlsso litlof
aftmihpy, ifd fof ivilhiblhlty og d orbltihs lf vihaf`a smahh. Eost og tma rai`tlofs og ghuorlfa ira axotmarel`
(dua to tma seihh ifd strofc bofd goread by lt wltm otmar ahaeafts). Lt gores ofhy ofa oxoi ld wmlha otmarmihocafs gore i fuebar og oxoi`lds. Mydrocaf ghuorlda ls hlquld (b.p. 2
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"eiflsmjueirpmysl`s.lf" 4
@MAELPTR\
Fota ; Lt ls fot posslbha to prapira ghuorlfa by aha`trohysls og iquaous sohutlof og FiG or JG. Lt ls ba`iusa wmaf
iquaous sohutlof og JG ls subka`tad to aha`trohysls, tmara wlhh ba gohhowlfc two oxlditlof lf `oepatltlof it
ifoda,
M2O 9/2O
2+ 2M+ + 2a PO^ 5 9.20 W
ifd
G 9/2G2+ a PO^ 5 2.=3 W
Is i eittar og ruha tmit substif`a wlhh ba oxldlsa wmosa PO^ ls mlcmar tmaragora witar cats oxldlsa it ifoda
ifd fot G
.(ll) @mael`ih eatmod ;Groe ^otisslue maxighuoroeifcifita (LW), J
2ZEfG
7U.
J2
ZEfG7U + 2 PbG
1 2J ZPbG
7U + EfG
0+
2
9G
2 :
204 G2
9EfG
vliEfG
Lf tmls rai`tlof, tma strofcar Hawls i`ld PbG1
dlsphi`as tma waijar ofa, EfG4
groe lts siht. EfG4
ls ufstibha
ifd raidlhy da`oeposas to clva EfG0
ifd ghuorlfa.
^RO^ARTLAP ;
(l) Dlitoel , ^iha craaf-yahhow cis wml m ippairs to ba iheost `ohourhass. Lt ls maivlar tmif ilr. Lt `ofdafsas
to yahhow hlquld it 9==>@ ifd yahhow sohld it 220>@. Lt mis pufcaft odour ifd ls mlcmhy polsofous.
(ll) Oxldlslfc `miri`tar ;Lt ls tma eost powarguh oxldlslfc icaft.G
2+ 2Fi] 2FiG + ]
2: wmara (] 5 @h, Br,)
(i) Lt `if oxldlsa ihh otmar mihlda lofs lfto mihocaf eoha`uhas
(b) Lt if oxldlsa @hO0 lfto @hO
4 ifd LO
0 to LO
4
G2+ @hO
0 + M
2O 2G + @hO
4 + 2M+
(`) Lt if oxldlsa MPO4 lfto P
2O
=2
2MPO4 + G
2 2G + P
2O
=2 + 2M+
(lll) Rai`tlof wltm FiOM sohutlof ; Sltm dlhuta ihjihl gores oxycaf dlghuorlda ifd wltm `of`aftritad ihjihl
hlbaritas O2.
2G2+ 2 FiOM (dlhuta) OG
2(c) + 2 FiG + M
2O
2G2+ 4 FiOM (`of`aftritad) O2(c) + 4 FiG + 2M2O(lv) Rai`tlof wltm FM
0;
2FM0+ 0G
2 F
2+ 7 MG
Lt ls tma dlstlf`tlof groe otmar mihocafs: otmar mihocafs gore axphoslva F]0
wltm `of`aftritad FM0
l.a. hlquor
ieeofli.
(v) Rai`tlof wltm M2P ;
M2P + G
2 PG
7+ 2 MG
(vl) Rai`tlof wltm PlO2; Lt itti`js chiss it ibout 9>>>@.
PlO2(s) + 2G
2(c) PlG
4(c) + O
2(c)
Tma rai`tlof ls show wltm dry G2.
(vll) Rai`tlof wltm PO0 ;
PO0+ G
2 IcG
@9=> GPO2OOPO
2G
(vlll) Rai`tlof wltm O2;
O2+ G
2 aircdls`maha`trl`slhaft
ogprasaf`alfofhy O2G
2
(lx) Rai`tlof wltm eatihs ifd fofeatihs ; Lt `oeblfas wltm eost og tma eatihs. Iheost ihh fof-eatihs
ax`apt O2& F
2lcflta spoftifaoushy lf prasaf`a og G
2.
2 Ic + G22 IcG : 2 Ih + 0 G
2 2 IhG
0
@ + 2 G2 @G
4 : Pl + 2 G
2 PlG
4
Ghuoro`irbofs ira axtraeahy lfart. @G4
`if ba maitad lf ilr wltmout burflfc. Ghuoro`irbofs ira lfart
to `of`aftritad MFO0
, M2PO
4ifd to strofc oxldlslfc icafts su`m is JEfO
4or O
0ifd to strofc
radu`lfc icafts su`m is HlIhM4or @ it 9>>@.
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"eiflsmjueirpmysl`s.lf" 1
@MAELPTR\
@MHORLFA (@h2) ;
^RA^IRITLOF ;(l) By maitlfc `mhorlda wltm `of`aftritad M
2PO
4lf prasaf`a og EfO
2.
4M+ + EfO2+ 2] ]
2+ Ef+2 + 2M
2O
Broeldas ifd lodldas ihso hlbarita Br2
ifd L2
raspa`tlvahy wltm `of`aftritad M2PO
4ifd EfO
2.
(ll) (i) Fi@h + MFO0
FiFO0+ M@h 0
MFO0+ 0M@h FO@h + @h2+ 2M2O
0Fi@h + 4 MFO0
0 FiFO0+ FO@h (fltrosyh `mhorlda) + @h
2+ 2M
2O
2FO@h + O2
2FO2+ @h
2: FO
2+ M
2O MFO
0(to ba ra`y had)
(b) Smaf @h2ls usad gor tma `mhorlfitlof og mydro`irbof tma by-produ`t ls M@h. Tma M@h ls `itihytl`ihhy
oxldlsad lfto M2O & @h
2uslfc oppar powdar elxad wltm rira airtm `mhorldas.
4 M@h + O2
`mhorldaairtmrirapowdar@u 2M2O + 2@h
2
(`) @iO h@
@h
+ 2M@h @i@h2+ @h
2+ M
2O
(d) 2JEfO4
+ 97 M@h2 J@h + 2 Ef@h2
+ 1 @h2
+ = M2
O
(a) ^bO2+ 4 M@h^b@h
2, + @h
2+ 2 M
2O
Tmasa eatmods ira ax huslvahy usad ofhy gor `mhorlfa.
(lll) Eifugi`tura og `mhorlfa ;
(i) Dai`ofs pro`ass ; By oxlditlof og mydrocaf `mhorlda cis by iteospmarl` oxycaf lf tma prasaf`a
og @u@h2(`itihyst) it 320 J.
4 M@h + O2
2@u@h 2 @h2+ 2 M
2O
(b) Aha trohytl` pro`ass ; @mhorlfa ls obtilfad by tma aha`trohysls og brlfa (`of`aftritad Fi@h sohutlof).
@mhorlfa ls hlbaritad it ifoda. Lt ls obtilfad is i byprodu t lf eify `mael`ih lfdustrlas a.c.: lf
eifugi`turlfc og sodlue mydroxlda.Fi] (iq) Fi+ (iq) + ] (iq)
Ifoda ; 2] ]2
+ 2a
^RO^ARTLAP ;(l) Lt ls i craaflsmyahhow cis wltm pufcaft ifd suggo`itlfc odour. Lt ls ibout 21 tleas maivlar tmif ilr. Lt `if
ba hlquaglad lfto craaflsmyahhow hlquld wml`m bolhs it 20 M@h
(b) @mhorlfa oxldlsas botm Br ifd h to Br2ifd L
2raspa`tlvahy.
] + @h2
]2+ 2@h
(`) Lt ls i powarguh bhai`mlfc icaft : bhai`mlfc i`tlof ls dua to oxlditlof.
@h2+ M
2O 2 M@h + O
@ohourad substif`a + O @ohourhass substif`aLt bhai`mas vacatibha or orcifl` eittar lf tma prasaf`a og eolstura. Bhai`mlfc agga`t og `mhorlfa ls pareifaft.
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"eiflsmjueirpmysl`s.lf" 7
@MAELPTR\
Fota ; Tma bhai`mlfc i`tlof og PO2ls taeporiry ba`iusa lt tijas phi`a tmroucm radu`tlof.
PO2+ 2 M
2O M
2PO
4 + 2 M
PO0
2 + @ohourad eitarlih PO4
2 + Radu`ad `ohourhass eitarlih.
Radu`ad @ohourhass eitarlih ilrogO2
@ohourad eitarlih.
(lv) Rai`tlof wltm FiOM ;
(i) 2 FiOM ( `ohd & dlhuta) + @h2 Fi@h + Fi@hO + M2O
(b) 7 FiOM (mot & `of`aftritad) + 0 @h2
1 Fi@h + Fi@hO0+ 0 M
2O
Tmasa rai`tlofs ira ihso clvaf by Br2
ifd L2.
(v) Rai`tlof wltm dry shijad hlea, @i(OM)2; To clva bhai`mlfc powdar.
2 @i(OM)2+ 2 @h
2 @i(O@h)
2+ @i@h
2+ 2 M
2O
QPAP ; @h2
ls usad
9. gor bhai`mlfc wood puhp (raqulrad gor tma eifugi`tura og pipar ifd riyof), bhai`mlfc `ottof ifd taxtlhas,
2. lf tma eifugi`tura og dyas, drucs ifd orcifl `oepoufds su`m is @@h4
, @M@h0
, DDT, ragrlcarifts, at`.
0. lf tma axtri`tlof og cohd ifd phitlfue.
4. lf starlhlslfc drlfjlfc witar ifd1. prapiritlof og polsofous cisas su`m is pmoscafa (@O@h2), tair cis (@@h
0FO
2), eustird cis
(@h@M2@M
2P@M
2@M
2@h).
BROELFA (Br2) ;
^RA^IRITLOF ;
(l) @oeeof eatmod ; 2 FiBr + 0M2PO
4(`of`aftritad) + EfO
2 Br
2+ EfPO
4+ 2FiMPO
4 + 2M
2O
(ll) Groe Pai-witar ;
Fi@h ls eilf `oepofaft but FiBr ls ihso prasaft lf soea quiftlty lf sai witar. @h2
cis ls pissad tmroucm
sai witar wmaf vipours og broelfa ira avohvad.
2 Br (iq) + @h2
2@h (iq.) + Br2
Tma Br2 ls raeovad by i straie og ilr slf`a Br
2ls qulta vohitlha. Tma cis ls pissad tmroucm i sohutlof og
Fi2@O
0wmaf tma Br
2ls ibsorbad gorelfc i elxtura og FiBr ifd FiBrO
0. Tma sohutlof ls tmaf i ldlglad ifd
dlstlhhad to clva pura broelfa.
0Br2+ 0Fi
2@O
0 1FiBr + FiBrO
0+ 0@O
2
1FiBr + FiBrO0+ 0M
2PO
4 1MBr + MBrO
0+ 0Fi
2PO
4
1MBr + MBrO0
0Br2+ 0M
2O
^RO^ARTLAP ;
(l) Raddlsm browf hlquld, gilrhy sohubha lf witar. Lt ihso gores mydrita hlja @h2
(Br2 . =M2O) @hitmrita `oepoufd
(ll) Rast rai`tlofs ira siea is wltm @h2
LODLFA (L2) ;
^RA^IRITLOF ;
(l) @oeeof eatmod ; 2Fi+ 0M2PO
4(`of`aftritad) + EfO
2
2+ EfPO
4+ 2FiMPO
4+ 2M
2O
(ll) Groe @ihl`ma or @ruda `mlha siht patra ;
Tma eilf sour`a og lodlfa ls FiO0(sodlue lodita) wml`m ls goufd lf fitura wltm FiFO
0(`mlha sihtpatra).
FiO0
ls prasaft lf seihh ieouft. Igtar `rystihhlsitlof og FiFO0
, tma eotmar hlquor hagt `oftilfs FiO0
(sohubha). To tmls sohutlof FiMPO0ls iddad wmara upof
2ls pra`lpltitad.
2O0 + 7MPO0 2L + 7 PO42 + 7M+1 + LO
0 + 7M+ 0L
2+ 0 M
2O
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"eiflsmjueirpmysl`s.lf" 3
@MAELPTR\
(lll) Groe sai-waads ;
@artilf eirlfa phifts ibsorb ifd `of`aftrita L saha`tlvahy lf prasaf`a og @h ifd Br. Pai-waads ira drlad
ifd burft lf smihhow plts, ism hagt ls `ihhad jahp. Ism of axtri`tlof wltm mot witar dlssohvas out `mhorldas,
`irbofitas, suhpmitas ifd lodldas og sodlue ifd potisslue. Tma sohutlof of `of`aftritlof sapiritas out ihh
haivlfc bamlfd lodlda lf tma sohutlof. Pohutlof ls elxad wltm EfO2ifd `of`aftritad M
2PO
4 lf lrof ratorts.
Hlbaritad lodlfa ls `ofdafsad lf sarlas og airtmafwira jfowf is ihudahs.
2Fi + EfO2
+ 0M2PO
4 2FiMPO
4 + EfPO
4+
2+ 2M
2O
(lv) @uPO4 + 2J J2PO4+ @u2: 2@u2
@u22 +2
Tmls 2
cats dlssohvad lfto J gorelfc 0
, slf`a 0 lofs ira yahhow, tmaragora sohutlof davahops yahhow `ohour.
^RO^ARTLAP ;(l) Lt ls i dirj vlohat sohld, ufdarcoas subhleitlof, haist sohubha (ieofc mihocafs) lf witar but eu`m eora
sohubha lf J(iq.) dua to goreitlof og J0. Lt ls sohubha lf orcifl` sohvafts hlja @M@h
0, @@h
4at`. to cat vlohat
sohutlofs.
(ll) Rai`tlof wltm mypo ;
P2
O0
2 (tmlosuhpmita lofs) +2
P4O
72 (tatritmlofita lofs) + 2
Tmls rai tlof ls tma bisls og lodoeatrl tltritlof, wml`m ls irrlad out gor tma astleitlof og lodlfa uslfc stir`m
lfdl`itor.
(lll) Rai`tlof wltm FM0
;
FM0(c) +
2 Fo Rai`tlof
FM (iq) + (s) F . FM + 0M0 2 0 0
(Ieeofli hlquor)
I shurry ls goreadwml`m `if ba drlad
ifd of mieearlfc ltaxphodas `iuslfc
soufd (`rijars)
if axphoslva(Fltrocaftrllodldaieeoflitad)
=F0. FM
0 1F
2+ ,^t 2M
(ll) By maitlfc i mihlda wltm `of`aftritad i`ld ;
(i) Fi@h + M2PO
4 @91> FiMPO
4+ M@h
FiMPO4+ Fi@h
@11>Fi
2PO
4+ M@h
Tmls eatmod ls `ihhad is siht `ija eatmod is lt lfvohvas tma goreitlof og FiMPO4(siht `ija).
M@h `iffot ba drlad ovar ^2O
1(^
4O
9>) or qul`j hlea slf`a tmay rai`t wltm cis `mael`ihhy.
@iO + 2M@h @i@h2
+ M2O
^4O
9> + 0M@h ^O@h
0+ 0M^O
0
M@h ls, maf`a drlad by pisslfc tmroucm of`aftritad M2PO4.
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"eiflsmjueirpmysl`s.lf" =
@MAELPTR\
(b) MBr (or M) `iffot ba prapirad by maitlfc broelda (lodlda) wltm `of`aftritad M2PO
4ba`iusa MBr
ifd M ira strofc radu`lfc icafts ifd radu`a M2PO
4to PO
2ifd cat tmaesahvas oxldlsad to broelfa
ifd lodlfa raspa`tlvahy.
J] + M2PO
4 JMPO
4+ M]
M2PO
4+ 2M] PO
2+ ]
2+ 2M
2O (] 5 Br or)
Maf`a, MBr ifd M ira prapirad by maitlfc broeldas ifd lodldas raspa`tlvahy wltm `of`aftritad M0^O
4.
0JBr(J) + M0^O
4 J
0^O
4+ 0MBr (M)
(lll) By rai tlof og 4(Hiboritory Eatmod) ;^
4+ 7Br
2(7
2) 4^Br
0(4^
0) (produ`t lf sltu)
^Br0(^
0) + 0M
2O 0MBr (M) + M
0^O
0
(lv) By pisslfc M2P/PO
2lfto sohutlofs og mihocafs ;
M2P + ]
2 2M] + P
PO2+ 2M
2O + ]
2 2M] + M
2PO
4
^RO^ARTLAP ;
(l) Tmasa ira ohourhass, pufcaft seahhlfc cisas wltm i`ldl` tistas.
(ll) Tmasa ira faltmar `oebustlbha for supportar og `oebustlof.
(lll) Smaf parga`thy dry, tmay miva fo i tlof of hlteus, but lf prasaf`a og eolstura, tmay turf bhua hlteus rad,
smowlfc i`ldl` fitura. Ieofc M], Mls tma strofcast ifd MG ls tma waijast i`ld.
(lv) Tmasa ira qulta sohubha lf witar.
M@h loflsas is bahow ; M@h(c) + M2O () M
0O+ (iq) + @h (iq) : J
i5 9>3
Lt iquaous sohutlof ls `ihhad mydro`mhorl` i`ld. Mlcm vihua og dlsso`litlof `ofstift (Ji) lfdl`itas tmit lt ls i
strofc i`ld lf witar.
Smaf tmraa pirts og of`aftritad M@h ifd ofa pirt og of`aftritad MFO0
ira elxad, iqui racli ls goread
wml`m ls usad gor dlssohvlfc fobha eatihs, a.c., cohd, phitlfue.
Iu + 4 M+ + FO0 + 4 @h ZIu@h
4U + FO + 2 M
2O
0 ^t + 97 M+ + 4 FO0
+ 9= @h 0 Z^t@h7U2 + 4 FO + = M
2O
(v) Radu`lfc proparty ifd stiblhlty og mydri`lds ;M@h ; Lt ls qulta stibha ifd maf`a ls oxldlsad by strofc oxldlslfc icafts hlja EfO
2, JEfO
4, J
2@r
2O
3,
^bO2, ^b
0O
4.
(l) EfO2+ 4M@h Ef@h
2+ 2M
2O + @h
2
(ll) 2JEfO4+ 97M@h 2J@h + 2Ef@h
2+ =M
2O + 1@h
2
(lll) J2@r
2O
3+ 94M@h 2J@h + 2@r@h
0+ 3M
2O + 0@h
2
(lv) ^bO2+ 4M@h ^b@h
2+ 2M
2O + @h
2 : (v) b
0O
4+ =M@h 0^b@h
2+ 4M
2O + @h
2
Tmaragora, M@h ls i waij radu lfc icaft.
MBr ; Lt ls fot vary stibha ifd maf`a eora aislhy oxldlsad or i`ts is i strofc radu`lfc icafts. Lf iddltlof
to ibova radu`lfc propartlas og M@h, lt ihso radu`as M2PO
4to PO
2wml`m ls fot dofa by M@h.
M2PO4+ MBr PO2+ Br2+ 2M2OIquaous MBr of axposura to iteospmarl` oxycaf ls oxldlsad to broelfa (yahhow)
4MBr + O2
2 Br2+ 2M
2O
M ; Lt ls haist stibha mydrocaf mihlda. Lt ls raidlhy oxldlsad ifd tmus i`ts is i powarguh radu`lfc icaft.Lf iddltlof to rai`tlof smowf by M@h, lt smows gohhowlfc rai`tlofs ihso.
(i) M2PO
4+ 2M PO
2+
2+ M
2O : M
2PO
4+ 7M P + 0
2+ 4M
2O:
M2PO
4+ =M M
2P + 4
2+ 4M
2O :
(b) 2MFO0+ 2M 2FO
2+
2+ 2M
2O (`) 2MFO
2+ 2M 2FO +
2+ 2M
2O
(d) MO0
+ 1M 02+ 2M
2O (a) J
2P
2O
=+ 2M J
2PO
4+
2+ M
2PO
4
(g) 2Ga@h0+ 2M 2Ga@h
2+
2+ 2M@h
Iquaous sohutlof og i`ld, lg axposad to O2ls oxldlsad to lodlfa.
4M+ O2
22+ 2M
2O
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"eiflsmjueirpmysl`s.lf" % sohutlof.
^RO^ARTLAP ;
(l) Lt ls `ohourhass, orroslva hlquld wltm pufcaft seahh wltm mlcm bolhlfc polft dua to mydrocaf bofdlfc.
(ll) Dry MG doas fot itti`j eatihs ufdar ordlfiry `ofdltlofs (ax`apt J), but lf prasaf`a og witar lt
dlssohvas eatihs wltm hlbaritlof og mydrocaf cis.
(lll) Lt ls i waij dlbisl` i`ld (dua to strofc MG bofd) ifd gores two sarlas og siht.
FiOM + M2G
2 FiMG
2+ M
2O : FiMG
2+ FiOM 2FiG + M
2O
(lv) MG ihso rai`t rai`ts wltm @@h4to gore graofs.
@@h4+ MG @G@h0+ M@h : @G@h0+ MG @G2@h2 + M@h.
8/12/2019 17 to 18 Group Theory_E
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"eiflsmjueirpmysl`s.lf" 9>
@MAELPTR\
Axiepha-4 (i) Smaf M@h rai`ts wltm glfahypowdarad lrof, lt gores garrous `mhorlda ifd fot garrl `mhorlda.
wmy ?
(b) @mhorlfa witar turfs bhua hlteus rad but sohutlof ba`oeas ohourhass igtar soeatlea.
P o h u t l o f (i) Lt gores M2
cis.
Ga + 2 M@h Ga@h2+ M
2.
Hlbaritlof og mydrocaf pravafts tma goreitlof og garrl` `mhorlda.
(b) Bhuahlteus `mifca lfto rad dua toi`ldl fitura(@h2
+ M2O MO@h+ M@h) but lt ls bhai`mlfc
icaft ihso (oxldlslfc icaft),tmaragora, lt da`ohourlsas tma rad hlteus.
O]LDAP OG @MHORLFA ;
@MHORLFA DLO]LDA (@hO2) ;
^RA^IRITLOF ;
(l) 2 Fi@hO0+ PO
2+ M
2PO
4 Fi@hogtri`as 2@hO
2+ 2FiMPO
4
@mhoritas og sodlue ifd potisslue `if ba usad
(ll) 2J@hO0+ 2 M2@2O4 @ 2@hO2(c) + 2@O2(c) + J2@2O4+ 2M2O
(lll) 2Ic@hO0+ @h
2 @ 2Ic@h (wmlta) + 2@hO2+ O2
(lv) @h2O
7+ F
2O
4 @hO
2+ ZFO
2+U Z@hO
4U
(v) 2M@hO0
+ 2M@h 2@hO2+ @h
2+ 2M
2O
^RO^ARTLAP ;
(l) \ahhow cis it rooe taeparitura dlssohvas lf witar avohvlfc mait ifd clvlfc i dirj craaf sohutlof.
@hO2
hlcmt @hO + ZOU
Lt jlhh bi`tarli battar tmif @h2.
(ll) Rai`tlof wltm ozofa ;2@hO2+ 2O
0 M @h
2O
7(yahhow sohld) + 2O
2
dl`mhorlfa maxi oxlda
Lf tma rai`tlof O0ls bamivlfc is if oxldlslfc icaft.
@hO2
dlssohvas lf FiOM gorelfc `mhorlta ifd `mhorita.
@h2O
7(s) ls i elxad ifmydrlda og M@hO
0ifd M@hO
4ba`iusa of dlssohvlfc lf witar lt clvas i elxtura
og tmasa two i`lds.
2@h2O
7+ 4FiOM 2Fi@hO
0+ 2Fi@hO
4+ 2M
2O.
Lf sohld stita, @h2O7 axlsts is @hO2
+
ifd @hO4
.
(lll) Rai`tlof wltm ihjihlfa M2O
2;
Lf tmls rai`tlof M2
O2
i`ts is i radu`lfc icaft. Lt radu`as @hO2lfto @hO
2
M2O
2 2M+ + O
2+ 2a
a + @hO2
@hO2
U 2
M2
O2+ 2@hO
2 2@hO
2 + 2M+ + O
2
or M2O
2+ 2@hO
2+ 2OM 2@hO
2
+ 2M2O + O
2
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"eiflsmjueirpmysl`s.lf" 99
@MAELPTR\
(lv) Rai`tlof wltm M ;Lf tmls rai`tlof Mbamivas is i radu`lfc icaft wmara lt radu`as @hO
2lfto @h ifd ltsahg ls oxldlsad to
2.
Z1a + 4 M+ + @hO2
@h + 2M2OU 2
Z2 2
+ 2aU 1
2@hO2+ =M+ + 9> 1L
2+ 2@h + 4M
2O
Dl`mhorlfa Eofoxlda (@h2O) ;
^RA^IRITLOF ;
2@h2+ McO2 (Grasmhy prapirad pra`lpltita, browf) @0>> Mc@h
2. McO + @h
2O
^RO^ARTLAP ;
@h2O ls yahhow-browf cis vary sohubha lf witar.
0@h2O + 9>FM
0 7FM
4@ h + 2 F
2+ 0M
2O
@h2O + 2FiOM 2FiO@h + M
2O
BHAI@MLFC ^OSDAR (@[email protected]
2O)
Bhai`mlfc powdar ls ihso `ihhad `ih`lue `mhoromypo`mhorlta ba`iusa lt ls `ofsldarad is i elxad siht og
mydro`mhorl` i`ld ifd mypo`mhorous i`ld.
@i(O@h)@h
^RA^IRITLOF;
@i(OM)2
+ @h2
@>
4>@i(O@h)@h + M
2O
^ropartlas(l) Lt ls i piha yahhow powdar. Lt mis i strofc seahh og `mhorlfa. Lt ls sohubha lf witar but i `hair sohutlof
ls favar goread dua to tma prasaf`a og lepurltlas.
(ll) Of hofc stifdlfc, lt ufdarcoas iutooxlditlof lfto `ih lue `mhorita ifd `ih lue `mhorlda.7 @iO@h
2 @i(@LO
0)
2+ 1 @i@h
2
(lll) 2 @iO@h2
2@o@h 2 @i@h2+ O
2
(lv) Lf prasaf`a og i hlttha ieouft og i dlhuta i`ld, lt hosas oxycaf.
2 @iO@h2+ M
2PO
4 @i@h
2+ @iPO
4+ 2 M@hO
M@hO M@h + OOf i``ouft og tma hlbaritlof og fis`aft oxycaf, lt smows oxldlslfc ifd bhai`mlfc propartlas.
(i) Oxldlslfc propartlas
@iO@h2+ M
2P @i@h
2+ M
2O + P
@iO@h2+ 2 JL + 2 M@h @i@h
2+ 2 J@h + M
2O + L
2
0 @iO@h2+ 2 FM
0 0 @i@h2+ 0 M2O + F2 Lt oxldlsas FO
2 to FO
0 , IsO
00 to IsO
40 ifd Ga2+ to Ga0+ (lf i`ldl` eadlue)
(b) Bhai`mlfc i`tlof
@ohourad eittar + ZOU `ohourhass produ`t.(v) Smaf bhai`mlfc powdar rai`ts wltm dlhuta i`lds or @O
2lt hlbaritas `mhorlfa wml`m ls jfowf is ivilhibha
`mhorlfa.
@iO@h2
+ 2 M@h @i@h2+ M
2O + @h
2
@iO@h2+ M
2PO
4 @iPO
4+ M
2O + @h
2
@iO@h2
+ @O2
@i@O0
+ @h2
MFO0ls i strofc oxldlslfc i`ld to ba ivoldad, mara.
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"eiflsmjueirpmysl`s.lf" 92
@MAELPTR\
APTLEITLOF OG IWILHIBHA @MHORLFA ;
Hat tma walcmt og siepha og bhai`mlfc powdar ba S c.
Idd lfto i baijar `oftilflfc i`atl` i`ld sohutlof ifd ax`ass J. I yahhow browf sohutlof ls goread (0)
2
+ 0
Fow gaw drops og stir`m sohutlof ls iddad lfto lt. If lftafslva bhua `ohor ls obsarvad. Fow mypo ls usad is
tma tltrift. Fota tma vohuea wmara tma bhua `ohour dlsippair.
Rai`tlof lfvohvad ;
@iO@h2
+ 2@M0@OOM (@M
0@OO)
2@ i + M
2O + @ h
2
@h2+ 2J 2J@h + 2
2+ 2P
2O
02 P
4O
72 + 2
@ih`uhitlof ; %@h 5 9>>S
392
9UWEZ mypomypo
(vl) Bhai`mlfc powdar `ofvarts i`atofa or atmyh ih`omoh lfto @M@h0
@iO@h2
+ M2O @i(OM)
2+ @h
2
@M0@O@M
0+ 0 @ h
2 @@h
0@O@M
0+ 0 M @ h
2 @@h0@O@M
0+ @i(OM)
2
(@M0@OO)
2@i + 2 @M@h
0
O]\-I@LDP OG Mihocafs ;
MO] PARLAP ;
M\^O-GHOROQP I@LD ZMOGU ;
MOG mis baaf prapirad by tripplfc G2
ifdM2O lf ufrai`tlva eitrlx og sohld F
2it vary how taeparitura ifd
pmotohyslfc tma cisas.
G2+ M
2O mv MOG + MG
Ra`aft eatmod ls by pisslfc, G2ovar l`a it >@ ifd raeovlfc tma produ`t lfto i `ohd trip.
M2O + G
2
4>@ MOG + MG
MO@h, MOBr ifd MOh ira fot vary stibha ifd ira jfowf ofhy lf iquaous sohutlof.
M\^O-@MHOROQP I@LD ZM@hOU ;
^RA^IRITLOF ;
(l) Tma i`ld ls jfowf ofhy lf sohutlof, Lt ls obtilfad by smijlfc pra`lpltita og McO wltm mhorlfa witar.
2McO + 2@h2
+ M2O Mc
2O@h
2(Oxy mhorlda og ear`ury) + 2M@hO
(ll) @oeear`lihhy, lt ls obtilfad by pisslfc @O2tmroucm suspafslof og bhai`mlfc powdar ifd tmaf dlstlhhlfc.
2@iO@h2+ M
2O + @O
2 @i@h
2+ @i@O
0+ 2M@hO
Eixleue `of`aftritlof obtilfad ls 21% is lf tma pro`ass og dlstlhhitlof, tma i`ld da`oeposas lfto lts
ifmydrldas, @h2O.
2MO@h M2O + @h2O
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"eiflsmjueirpmysl`s.lf" 90
@MAELPTR\
^RO^ARTLAP ;(l) Lt ls i waij i ld. Lts `of`aftritad sohutlof ls yahhow lf `ohour wmlha dlhuta sohutlof ls `ohourhass. Lt ls ufstibha
ifd da`oeposas.
2M@hO 2M@h + O2
(ll) Lt dlssohvas eicfaslue wltm avohutlof og mydrocaf.
Ec + 0M@hO Ec(@hO)2+ M
2
(lll) Sltm ihjihlas, lt gores sihts `ihhad mypo`mhorltas.
(lv) Lt i ts is i powarguh oxldlslfc ifd bhai`mlfc icaft. Tmls ls dua to rahaisa og fis`aft oxycaf aislhy.
M@hO M@h + O
M]O2
PARLAP ;
@MHOROQP I@LD ZM@hO2U ;
^RA^IRITLOF ;Lt ls obtilfad lf iquaous sohutlof wmaf birlue `mhorlta suspafslof lf witar ls traitad wltm M
2PO
4. Tma
lfsohubha birlue suhpmita ls glhtarad ogg.
Bi(@hO2)
2+ M
2PO
4 BiPO
4+ 2M@hO
2
^RO^ARTLAP;
(l) Tma grasmhy prapirad sohutlof ls `ohourhass but lt soof da`oeposas to @hO2 wml m eijas tma sohutlof yahhow.
1 M@hO2
4 @hO2+ M@h + 2M
2O
(ll) Pihts og M@hO2
ira `ihhad `mhorlta ifd prapirad by ofa og tma gohhowlfc eatmods.
2@hO2+ 2FiOM Fi@hO
2+ Fi@hO
0+ M
2O
2@hO2+ Fi
2O
2 2Fi@hO
2+ O
2
@mhorltas ira usad is bhai`mas. Tmay ira stibha lf ihjihlfa sohutlof avaf wmaf bolhad, but lf i`ld sohutlof
tmay dlsproportlofita, pirtl uhirhy wmaf maitad.
1M@hO2
4@hO2+ M@h + 2M
2O ifd 4M@hO
2 2@hO
2+ M@hO
0+ M@h + M
2O
(lll) Tma i ld hlbaritas lodlfa groe J
4J+ M@hO2+ 2M
2O 4JOM + M@h + 2
2
M]O0PARLAP@MHORL@ I@LD ZM@hO
0U ;
^RA^IRITLOF ;Tmls i ld ls ofhyjfowf lf sohutlof. Tma i ld ls prapirad bytma i tlof og tma dlhuta M
2PO
4of birlue `mhorita.
Bi (@hO0)
2+ M
2PO
4 BiPO
4 + 2M@hO
0.
Igtar rai`tlof, BiPO4
ls raeovad by glhtritlof, ifd tma glhtrita ls aviporitad lf vi`uue tlhh 4> par`aft sohutlof
ls obtilfad. Mowavar, gurtmar `of`aftritlof by aviporitlof haids to da`oeposltlof.
0M@hO0
M@hO4+ @h
2+ 2O
2+ M
2O
MBrO0
`if ba prapirad by slelhir eatmod uslfc Bi(BrO0)
2.
^RO^ARTLAP ;@of`aftritad i`ld ls `ohourhass ifd pufcaft seahhlfc hlquld. Lt da`oeposas lf hlcmt. Mowavar, lt ls stibha lf
dirj. Lt i`ts is i strofc oxldlslfc ifd bhai`mlfc icaft lf hlcmt. Orcifl substif`as hlja pipar, `ottof, wooh,
at`., `it`m glra lf `ofti`t wltm tma i`ld.
M@hO0oxldlsas PO
2to PO
0; M@hO
0+ 0PO
2 M@h + 0PO
0
M@hO0
wmaf aviporitas to dryfass da`oeposas clvlfc @hO2.
4M@hO0
4@hO2(c) + 2M
2O(c) + O
2(c)
MBrO0 ls fot vary stibha, but ls jfowf lf sohutlof, ifd is sihts.
MhO0
ls goread by oxlditlof og L2
wltm of`aftritad MFO0
or O0.
=M+ + 9>FO0 + L
2 2LO
0 + 9>FO
2+ 4M
2O
hO0 oxldlsas L to L
2; hO
0 + 1L + 7M+ 0h
2+ 0M
2O
Lodl` i`ld ls raisofibhy stibha ifd axlsts is i wmlta sohld.
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"eiflsmjueirpmysl`s.lf" 94
@MAELPTR\
2J@hO0 2EfO
@91> 2J@h + 0O2
4J@hO0
ataepariturhow 0J@hO4+ J@h (lf ibsaf`a og `itihyst)
2[f(@hO0)
2 2[fO + 2@h
2+ 1O
2
@mhoritas ira usad lf glra worj.
^AR@MHORL@ I@LD ZM@LO4U ;
^RA^IRITLOF;(l) Lt ls tma eost stibha oxy-i`ld og `mhorlfa. Ifmydrous M@hO
4ls obtilfad by dolfc dlstlhhitlof og J@LO
4
(potisslue par`mhorita), wltm
(B) PO0
(@) @h2O
7 (D) PO
2
P o h u t l o f (@) @h2O7 wmaf dlssohvas lf witar produ`as M@hO0 ifd M@hO4, tmaragora, lt ls elxad ifmydrlda.
8/12/2019 17 to 18 Group Theory_E
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"eiflsmjueirpmysl`s.lf" 91
@MAELPTR\
Axiepha-= Clva ipproprlita raisofs gor ai`m og tma gohhowlfc ;
(i) Iddltlof og @h2to JL sohutlof clvas lt i browf `ohour but ax`ass og @h
2turfs lt `ohourhass.
(b) ^ar mhorl i`ld ls i strofcar i`ld tmif suhpmurl` i`ld.
(`) ML `if fot baprapirad bymaitlfcFiL wltm`of`aftritad M2PO
4.
P o h u t l o f (i) @h2
balfc i strofcar oxldlslfc icaft tmif L2, glrst oxldlsas JL toL
2wml`m lepirts browf `ohour
to tma sohutlof. But wmaf @h2ls pissad lf ax`ass, tma L
2so goread cats gurtmar oxldlsad to
MLO0
(`ohourhass)
2JL (iq) + @h2(c) 2J@h (iq) + L2(s) : 1@h2+ L2 + 7M2O 9>M@h + 2MLO0(b) Oxlditlof stita og @h lf M@hO
4ls + 3 ifd tmit og P lf M
2PO
4ls + 7. (@h ls eora aha`trofacitlva
tmif P). Is i rasuht, @hO0pirt og M@hO
4`if braij tma OM bofd eora aislhy to hlbarita i
protof tmif PO2pirt lf M
2PO
4. Tmus M@hO
4ls i strofcar i`ld tmaf M
2PO
4.
( ) ML ls i strofcar radu`lfc icaft. Lt, tmaragora, radu`as M2PO
4to PO
2ifd ltsahg cats oxldlsad
to L2.
FiL + M2PO
4 FiMPO
4+ MLU 2
M2PO
4+ 2ML PO
2+ L
2+ 2M
2O
2FiL + 0M2PO
4 2FiMPO
4+ L
2+ 2M
2O + PO
2
Poea leportift ordar(i) I`ld strafctm
(l) M6 MBr 6 M@h 6 MG (ll) MO@h 6 MOBr 6 MO (lll) M@hO4
6 M@hO0
6M@hO2
6 M@hO
(b) Oxldlslfcpowdar
(l) G26 @h
26 Br
26
2
(ll) BrO4 6 LO
4 6 @hO
4 (I``ordlfc to aha troda potaftlih)
( ) Ordar og dlsproportlofitlofs
0 ]O 2] + ]O0
(mypomihlta lof) : O 6 BrO 6 @hO
^saudo mihocafs ifd psaudo mihldas ;Poea lforcifl `oepoufds `ofslstlfc og two or eora itoes og wml m it haist ofa ls F miva baaf goufd to
bamiva hlja mihocafs & tmay ira jfowf is psaudo mihocaf sohlds, a.c. (@F)2
`yifocaf, (P@F)2
tmlo`yifocaf,
(Pa@F)2 sahafo`yifocaf, (P@PF0)2 izldo`irbofdlsuhpmlda. Plelhirhy gaw lofs ira jfowf tmit miva propartlasslelhir to tmosa og tma mihlda lofs. Tmay ira tmaragora `ihhad psaudomihlda lofs, a.c. (@F) `yiflda lof,
(P@F) tmlo`yifita lof, (Pa@F) sahafo`yifita lof, (O@F) `yifita lof, (F@F)2 `yifielda lof,
(F0) izlda lof at`.
LFTARMIHOCAF @OE^OQFDP ;Sa jfow tmit mihocaf itoes miva dlggaraft aha`trofacitlvlty. Dua to tmls dlggaraf`a lf aha`trofacitlvlty tma
mihocaf itoes `oeblfa wltm ai`m otmar ifd clva rlsa to tma goreitlof og blfiry `ovihaft `oepoufds, wml`m
ira `ihhad lftarmihocaf `oepoufds. Tmasa ira og gour typas.
IB IB0
IB1
IB3
@hG @hG0
@hG1
hG3
BrG BrG0
BrG1
L@h L@h0 LG1LG LG0
^RA^IRITLOF ;
(l) By tma dlra`t `oeblfitlof og mihocafs ;
@h2
+ G2
(aquih vohueas) J430 2@hG : @h2+ 0G2(ax`ass) J130 2@hG0 :
L2+ @h
2 2L@h :
(aquleohir)
Dlhutad wltm witar ; Br2(c) + 0G
2 2BrG
0
G2ls dlhutad wltm F
2; L
2+ 0G
2 @3= 2LG
0
G2ls tijaf lf graof ; Br2+ 1G2(ax`ass) 2BrG1
LG3`if fot ba prapirad by dlra`t `oeblfitlof og L
2& G
2.
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@MAELPTR\
(ll) Groe howar lftarmihocafs ;
@hG + G2
@hG0
: @hG0+ G
2(ax`ass)
@01>@hG
1
BrG0+ G
2(ax`ass)
@2>>BrG
1: LG
1+ G
2 @23> LG
3
Tmls eatmod ls cafarihhyipphlad gor tma prapiritlof og mihocaf ghuorldas.
(lll) Otmar eatmods;
7M@h + JLO0+ 2JL 2J@h + 0M
2O + 0L@h
@h2+ @hG
0 @01>21> 0@LG : J@h + 0G
2 @2>> JG + @hG
1
0h2
+ 1IcG 1Ich + hG1
: =G2+ ^bL
2 ^bG
2+ 2hG
3
^RO^ARTLAP ;
(l) Tmasa oepoufds eiy ba cisas, hlqulds or sohlds.
Cisas ; @hG, BrG, @hG0, LG
3: Hlqulds ; BrG
0, BrG
1: Pohlds ; L@h, LBr, LG
0, L@h
0.
(ll) Lftarmihocafs `oftilflfc ghuorlfa ira `ohourhass but lftar mihocafs `ofslstlfc og maivlar mihocafs
ira `ohourad. Tma lftafslty og `ohour lf`raisas wltm lf`raisalf tma eoha`uhir walcmt og tma`oepoufds.
(lll) Ihh lftarmihocafs ira `ovihaft eoha`uhas ifd ira dlieicfatl` lf fitura slf`a ihh tma vihaf`a aha trofs
prasaft is bofdlfc or fof-bofdlfc aha`trofs ira pilrad.
(lv) Tma bolhlfc polfts lf`raisas wltm tma lf`raisa lf tma aha`trofacitlvlty dlggaraf`a batwaaf I ifd Bitoes.
(v) Tmareih stiblhlty ogIB typa lftarmihocaf `oepoufds da raisas wltm tma da raisa lf aha`trofacitlvlty
dlggaraf`a batwaaf I ifd B itoes. LG 6 BrG 6 @hG 6 L@h 6 LBr 6 Br@h.
Eora pohir ls tma I B bofd eora ls tma stiblhlty og lftarmihocaf.
(vl) Lftarmihocaf `oepoufds ira eora rai tlva tmif tma piraft mihocafs but hass rai`tlva tmif G2.
L@h + 2Fi FiL + Fi@hTma ordar og rai`tlvlty og soea lftarmihocafs ls is gohhows ;
@hG06 BrG
06 LG
36 BrG
16 BrG.
(vll) Mydrohysls ; Ihh tmasa ufdarco mydrohysls clvlfc mihlda lof darlvad groe tma seihhar mihocaf ifd i
mypomihlta (wmaf IB), mihlta (wmaf IB0), mihita (wmafIB
1), ifd parmihita (wmafIB
3) iflof darlvad
groe tma hircar mihocaf.IB + M
2O MB + MOI
Br@h + M2O M@h + MOBr : L@h + M
2O M@h + MLO
L@h0+ 2M
2O 0M@h + MLO
2: LG
1+ 0M
2O 1MG + MLO
0
LG3+ 7M
2O 3MG + M
1LO
7 : BrG
1+ 0M
2O 1MG + MBrO
0
Oxlditlof stita og I itoe doas fot `mifca durlfc mydrohysls.
(vlll) Rai`tlof wltm fof-eatihhl ifd eatihhl` oxldas ;
4BrG0+ 0PlO
2 0PlG
4+ 2Br
2 + 0O
2 : 4BrG
0+ 2SO
0 2SG
7+ 2Br
2 + 0O
2
(x) Rai`tlof wltm ihjihl eatih mihldas ;
LBr + FiBr FiLBr2
: L@h0+ J@h JL@h
4
QPAP ;Tmasa `oepoufds `if ba usad is fof iquaous sohvafts. Lftarmihocaf `oepoufds ira vary usaguh
ghuorlfitlfc icafts. @hG0
ifd BrG0
ira usad gor tma produ`tlof og QG7
lf tma afrl meaft og2 01Q .
Q(s) + 0 @hG0(h) QG
7(c) + 0 @hG (c)
Axiepha-
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"eiflsmjueirpmysl`s.lf" 93
@MAELPTR\
CROQ^ 9= AHAEAFTP ; (TMA [ARO CROQ^ GIELH\)
Croup 9= `ofslsts og slx ahaeafts; mahlue, faof, ircof, jryptof , xafof ifd ridof . Ihh tmasa ira cisas ifd
`mael`ihhy ufrai tlva. Tmay gore vary gaw `oepoufds . Ba`iusa og tmls tmay ira taread fobha cisas.
O``urraf`a
Ihh tma fobha cisas ax`apt ridof o``ur lf tma iteospmara. Tmalr iteospmarl` ibufdif`a lf dry ilr ls ~ 9%
by vohuea og wml`m ircof ls tma eikor `ofstltuaft. Mahlue ifd soeatleas faof ira goufd lf elfarihs og
ridloi`tlva orlclf a.c., plt mbhafda, eofizlta, `havalta. Tma eilf `oeear`lih sour a og mahlue ls fiturih cis.
]afof ifd ridof ira tma rirast ahaeafts og tma croup. Ridof ls obtilfad is i da`iy produ`t og 227
Ri.
Ri227== Rf222=7 + Ma
42
Eost ibufdift ahaeaft lf ilr ls Ir. Ordar og ibufdif`a lf tma ilr ls Ir 6 Fa 6 Jr 6 Ma 6 ]a.
Aha`trofl` @ofglcuritlof
Ihh fobha cisas miva cafarih aha`trofl` `ofglcuritlof fs2fp7 ax`apt mahlue wml`m mis 9s2 . Eify og tma
propartlas og fobha cisas lf`hudlfc tmalr lfi`tlva fitura ira is`rlbad to tmalr `hosad smahh stru`turas.
Loflsitlof Aftmihpy
Dua to stibha aha`trofl` `ofglcuritlof tmasa cisas axmlblt vary mlcm loflsitlof aftmihpy . Mowavar, lt da-
`raisas dowf tma croup wltm lf`raisas lf itoel` slza.
Itoel` Ridll
Itoel` ridll lf`raisa dowf tma croup wltm lf`raisa lf itoel` fuebar.
Aha`trof Cilf Aftmihpy
Plf`a fobha cisas miva stibha aha`trofl ofglcuritlofs, tmay miva fo tafdaf`y to i``apt tma aha`trof ifd
tmaragora, miva hircar posltlva vihuas og aha trof cilf aftmihpy.
^mysl ih propartlas
Ihh tma fobha cisas ira eofo-itoel`. Tmay ira `ohourhass, ifd tistahass. Tmay ira spirlfchy sohubha lf
witar. Tmay miva vary how eahtlfc ifd bolhlfc polfts ba`iusa tma ofhy typa og lftaritoel` lftari`tlof lf
tmasa ahaeafts ls waij dlsparslof gor`as,. Mahlue mis tma howast bolhlfc polft (4.2J) og ify jfowf sub-
stif`a. Lt mis i ufusuih proparty og dlgguslfc tmroucm eost `oeeofhy usad hiboritory eitarlihs su`m is
rubbar, chiss or phistl`s.
Tibha ; 2
I t o e l ` i f d p m y s l ` i h p r o p a r tl a s
Ahaeaft Ma Fa Ir Jr ]a
Itoel` Fuebar 2 9> 9= 07 14
Itoel` Eiss 4 2>.9= 0 =0.=> 909.0>
Aha`trofl` `ofglcuritlof 9s2 ZMaU 2s
22p
7ZFaU 0s
20p
7ZIrU 0d
9>4s
24p
7ZJrU 4d
9>1s
21p
7
Itoel` Ridlus (pe) 92> 97> 9 2>> 22>
Loflzitlof aftmihpy / (jK eoh9
) 2032 2>=> 912> 9019 993>
Dafslty (it PT )/c `e0
9.= 9>4
9>4
9.= 9>0
0.3 9>0
1.< 9>0
Eahtlfc polft / J 24.7 =0.= 991.< 979.0
Bolhlfc polft / J 4.2 23.9 =3.2 99
@mael`ih ^ropartlas ; Lf cafarih, fobha cisas ira haist rai`tlva. Tmalr lfartfass to `mael`ih rai tlvlty ls ittrlbutad
to tma gohhowlfc raisofs;
(l) Tma fobha cisas ax apt mahlue (9s2) miva `oephatahy glhhad fs2 fp7 aha`trofl` `ofglcuritlof lf tmalr vihaf`asmahh.
(ll) Tmay miva mlcm loflsitlof aftmihpy ifd eora posltlva aha trof cilf aftmihpy.
Tma rai`tlvlty og fobha cisas mis baaf lfvastlcitad o``islofihhy avar slf`a tmalr dls`ovary, but ihh ittaept
to gor`a tmae to rai`t to gore tma `oepoufds wara ufsu``assguh gor qulta i gaw yairs. Lf Eir`m 9 jK eoh 9). Ma eida aggorts to
prapira siea typa og `oepoufd wltm ]a+ ^tG7 byelxlfc ^t G7 ifd ]afof.Igtar tmls dls`ovary, i fuebar ogxafof `oepoufds eilfhy wltm eost aha trofacitlva ahaeafts hlja ghuorlfa ifdoxycaf,miva baafsyftmaslsad.
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"eiflsmjueirpmysl`s.lf" 9=
@MAELPTR\
Tma `oepoufds og jryptof ira gawar. Ofhy tma dlghuorlda (JrG2) mis baaf studlad lf datilh. @oepoufds og
ridof miva fot baaf lsohitad but ofhy ldaftlglad (a.c., RfG2) by ridlotri`ar ta`mflqua. Fo trua `oepoufds og
Ir, Fa or Ma ira yat jfowf .
Lg Mahlue ls `oeprassad ifd hlqulglad lt gores Ma() hlquld it 4.2 J. Tmls hlquld ls i foreih hlquld hlja ify otmarhlquld. But lg lt ls gurtmar `oohad tmaf Ma() ls obtilfad it 2.2 J, wml`m ls jfowf is supar ghuld, ba`iusa lt lsi hlquld wltm propartlas og cisas. Lt `hlebs tmroucm tma wihhs og tma `oftilfar & `oeas out. Lt mis vary mlcm
tmareih ofdu tlvlty & vary how vls`oslty.
@hitmarita `oepoufds ;Lfart cis eoha`uhas cat trippad lf tma `icas goread by tma `rystih stru`tura og witar.
Durlfc tma goreitlof og l`a ]a itoes wlhh ba trippad lf tma `ivltlas (or `icas) goread bytma witar eoha`uhas
lf tma `rystih stru`tura og l`a. @oepoufds tmus obtilfad ira `ihhad `hitmarita `oepoufds.
Tmara ira fo `mael`ih bofds. Tmay do fot possass if axi`t `mael`ih goreuhi but ipprox lt ls 7 witar
eoha`uhas ; 9 lfart cis eoha`uha. Tma `ivlty slza ls kust seihhar tmif tma itoe og tma fobha cis. Pu`m
`oepoufds ira ihso goread by tma otmar orcifl` hlqulds hlja dlmydroxybafzafa (gor axiepha qulfoh). Tma
seihhar fobha cisas Ma ifd Fa do fot gore hitmrita `oepoufds ba`iusa tma cis itoes ira seihh afoucm
to as`ipa groe tma `ivltlas. @hitmrita provldas i `ofvaflaft eaifs og storlfc ridloi`tlva lsotopas og Jr ifd
]a produ`ad lf fu hair rai`tors.
Axiepha-9> Fiea tma fobha cis wml`m
(I) ls eost ibufdift lf iteospmara. (B) mis haist bolhlfc polft.P o h u t l o f (I)Ircof.
(B) Mahlue : Axlsts is eofo-itoel` eoha`uhas ifd ira mahd tocatmar by waij vif dar Siihs
gor`as. Tmasa vif dar Siihs gor`as lf`raisa wltm tma lf`raisa lf itoel` slza og tma itoe, ifd
tmaragora, tma bolhlfc polfts lf`raisas groe Ma to Rf. Maf`a Ma mis haist bolhlfc polft.
Axiepha-99 Smit ls tma utlhlty og tma `hitmarita `oepoufds?
P o h u t l o f Lt `if ba usad to sapirita elxtura og lfart cisas `oftilflfc siy Ma ifd ]a. ^ro`ass ls eu`m
`maipar tmif siy dlstlhhitlof is i eaifs og sapiritlof.
@OE^OQFDP OG ]AFOF ;
]AFOF DLGHQORLDA (]aG2);
^RA^IRITLOF;
(l) ]a + G2 )Flogihhoy(eatiheofahorTubaFl
bir9,J=30
]aG
2
Wohuea ritlo smouhd ba 2 ; 9 otmarwlsa otmar mlcmar ghuorldas tafd to gore.
(ll) ]a + O2
G2
@99= ]aG2
+ O2
(lll) ]a + G2
)ir`(Mc ]aG2
(lv) Ra`afthydls`ovarad eatmod ;
J+ ZIcG4U Zpotisslue tatrighuoroircaftita ()U ls glrst prapirad ifd tmls ls rai`tad wltm BG
0.
J+ ZIcG4U 0BG IcG0(rad sohld) + JBG4
2 IcG0+ ]a
2IcG2(Browf sohld) + ]aG2
^RO^ARTLAP ;(l) @ohorhass `rystihhlfa sohld ifd subhleas it 2>>@
]aG2
+ M2
]a + 2MG
(v) Mydrohysls ;
(i) 2]aG2
+ 2M2O 2]a+ 4MG + O
2(show)
Tma ibova ls faltmar i `itlofl` mydrohysls for if iflofl mydrohysls is saaf lf lofl` aqulhlbrlue. Lt ls
i `ovihaft `oepoufd ifd mydrohysls ls hlja tmit og ^@h1.
(b) Mydrohysls ls eora ripld wltm ihjihl.
]aG2+ 2 FiOM ]a + O
2+ 2FiG + M
2O (gist)
Tma rai`tlof (i) ls showar probibhy dua to dlssohutlof og ]aG2
lf MG.
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"eiflsmjueirpmysl`s.lf" 9
@MAELPTR\
]AFOF TATRIGHQORLDA (]aG4) ;
^RA^IRITLOF ;
]a + 2G2
tubaFl,bir
,J
3
=30]aG
4
9 ; 1
^RO^ARTLAP ;(l) Lt ls i `ohorhass rystihhlfa sohld ifd subhleas it 2;9
G0]a 2tubaFl
bir,J
3>7>130 ]aG
7 (ll) ]aG
4+ O
2G
2 ]aG
7+ O
2
^RO^ARTLAP;
(l) @ohourhass `rystihhlfa sohld ifd subhleas it 2
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"eiflsmjueirpmysl`s.lf" 29
@MAELPTR\
(v) Rai tlof wltm slhl i (PlO2) ;
2]aG7
+ PlO2
2]aOG4
+ PlG4
(vl) Tmareih da`oeposltlof (agga t og mait) ;
2]aG7
]aG2
+ ]aG4
+ 0 G2
]aG2
& ]aG4
do fot ufdarco da`oeposltlof
(vll) Goreitlof og iddltlof `oepoufds ;
]aG7+ PbG
1 Z]aG1U+ ZPbG
7U : ]aG
7+ BG
0 Z]aG1U+ ZBG
4U
(vlll) Rai tlof Sltm M2; ]aG
7+ 0M
2 7MG + ]a
(lx) Rai tlof og ]aG7
wltm ]aO0
; ]aO0
+2]aG7
0 ]aOG4
(x) G dofitlfc/ G i``aptlfc propartlas ; ]aG7
rai`ts wltm ghuorlda lof i``aptors to gore `itlofl spa`las ifd
ghuorlda lof dofors to gore ghuoroiflofs.
]aG7
+ EG E+ Z]aG3U (E 5 Fi, J, Rb or @s)
dofitlof { ]aG7
+ ^tG1
(]aG1
+) ( tG7
)
Axiepha-92 Doas tma mydrohysls og ]aG4it =>@ haid to i radox rai`tlof ?
P o h u t l o f ]aG4
+ M2O @=> ]aOG2 + 2MG..
Tma oxlditlof stitas og ihh tma ahaeafts lf tma produ`ts raeilf tma siea is lt wis lf tma rai`tlfc
stita. maf`a, lt ls i fot radox rai`tlof .
]AFOFO]\CAF @OE^OQFDP ;
Mydrohysls og ]aG4
ifd ]aG7
wltm witar clvas ]aO0.
7 ]aG4+ 92 M
2O 4 ]a + 2 ]aO
0+ 24 MG + 0 O
2
]aG7+ 0 M
2O ]aO
0+ 7 MG
^irtlih mydrohysls og ]aG7
clvas oxyghuorldas, ]aOG4
ifd ]aO2G
2.
]aG7
+ M2O ]aOG
4+ 2 M G
]aG7+ 2 M
2O ]aO
2G
2+ 4 MG
]aO0
ls i `ohourhass axphoslva sohld ifd mis i pyrieldih eoha`uhir stru`tura. ]aOG4
ls i `ohourhass vohitlha
hlquld ifd mis i squira pyrieldih eoha`uhir stru`tura.
QPAP ;
Mahlue ls i foflfghieeibha ifd hlcmt cis. Maf`a, lt ls usad lf glhhlfc bihhoofs gor eataorohocl`ih obsarvitlofs.
Lt ls ihso usad lf cis`oohad fu`hair rai`tors. Hlquld mahlue (b.p.4.2 J) glfds usa is `ryocafl` icaft gor
`irrylfc out virlous axparleafts it how taeparituras. Lt ls usad to produ`a ifd sustilf powarguh
supar`ofdu`tlfc eicfats wml`m gore if assaftlih pirt og eodarf FER spa`troeatars ifd Eicfatl`
Rasofif`a Leiclfc (ERL) systaes gor `hlfl`ih dlicfosls. Lt ls usad is i dlhuaft gor oxycaf lf eodarf dlvlfc
ippiritus ba`iusa og lts vary how sohublhlty lf bhood.
Faof ls usad lf dls`mirca tubas ifd ghuoras`aft buhbs gor idvartlsaeaft dlsphiy purposas. Faof buhbs ira
usad lf botifl ih cirdafs ifd lf craaf mousas.
Ircof ls usad eilfhy to provlda if lfart iteospmara lf mlcm taeparitura eatihhurcl`ih pro`ass (ir` wahdlfc
og eatihs or ihhoys) ifd gor glhhlfc aha`trl` buhbs. Lt ls ihso usad lf tma hiboritory gor mifdlfc substif`as tmit
ira ilrsafsltlva.
]afof ifd Jryptof ira usad lf hlcmt buhbs daslcfad gor spa lih purposas.
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"eiflsmjueirpmysl`s.lf" 22
@MAELPTR\
E L P @ A H H I F A O Q P P O H W A D A ] I E ^ H A P
9. Ldaftlgy ZIU ZBU ifd Z@U ifd clvas tma `oephata `mael`ih rai`tlofs lfvohvad.
Ifs. ZIU 5 Br : ZBU 5 BrO0
: Z@U 5 `of`aftritad M2PO
4
Poh. 0Br2+ 7OM 1Br + BrO
0 + 0M
2O
1Br + BrO0+ 7M+ 0Br
2+ 0M
2O
2. @oeeaft of tma gohhowlfc.
(i) Aha`trohysls og L@F lf pyrldlfa sohutlof.
(b) Lodlfa dlssohvas lf ohaue.
(`) Aha`trl`ih `ofdu`tlvlty og eohtaf lodlfa.
Poh. (i) Lodlfa ls hlbaritad it itmoda lfdl`itlfc tma loflsitlof og L@F lfto L+ ifd @F.
(b) Brlcmt bhua sohutlof ls goread wml m mis baaf smowf to miva L2+ ifd L0+.
2 L2+ 7M
2PO
4. PO
0 2L
2+ + 2MP
0O
9> + 1M
2PO
4+ PO
2
0 L2+ 7M
2PO
4. PO
0 2L
0+ + 2MP
0O
9> + 1M
2PO
4+ PO
2.
(`) Lt ls dua to tma prasaf`a og (L0
+ ifd L0) spa`las produ`ad by sahg loflsitlof og lodlfa 0L2
L0
+ + L0
0. Smy ifmydrous MG hlquld ls fot aha`trohysad ihofa to cat G2?
Poh. Ifmydrous MG ls ofhy shlcmthy loflzad ifd ls, tmaragora i poor `ofdu`tor og aha`trl`lty Tmus i elxtura og JG
ifd MG ls aha`trohysad to lf`raisa tma `ofdu`tlvlty.
4. Sml`m og tma gohhowlfc produ t(s) ls/ira obtilfad lf tma gohhowlfc rai`tlof
JBrO0+ G2+ JOM produ`t(s)(I) JBrO
4 (B) JG (@) MOG (D) Br
2
Poh. JBrO0+ G
2+ 2JOM JBrO
4+ 2JG + M
2O. Ifs (I,B)
1. Eit`m tma gohhowlfc .
@ohuef - L @ohuef - LL
(I) @LO2
@L2O
0 (p) Bolhlfc wltm FiOM sohutlof.
(B) ZIL (OM)4U IL(OM)
0 q Of pisslfc ozofa.
@ ^4
^M0+ M
2^O
2 (r) Rai`tlof wltm mydrocaf.
(D) ]aG2
]a (s) Of pisslfc @O2cis.
Poh. (Iq) : (Bs) : (@p) : (Dp,r)
(I) 2@LO2+ 2O
0 @L
2O
7+ 2O
2oxlditlof by ozofa.
(B) @O2+ M
2OM
2@O
0 @O
02 + 2M+ 2IL0+ + 0@O
02- + 0M
2O 2IL(OM)
0+ 0@O
2
Is i`ldl` proparty og IL(OM)0ls vary waij.
(@) ^4+ 0FiOM + 0M
2O wire/bolh ^M
0+ 0FiM
2^O
2.
ILjihlfa mydrohysls.
(D) 2]aG2+ 4OM- 2]a + 4G + 2M
2O + O
2
Ihjihlfa mydrohysls.
]aG2+ M2 2]a + 2MGRadu`tlof by mydrocaf.
8/12/2019 17 to 18 Group Theory_E
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@MAELPTR\
7. Fi2P
2O
0eiyrai t wltm tma `oepoufds clvaf lf `ohuef (L). Fi
2P
2O
0axmlblts tma propartlas og tma typa clvaf
lf tma `ohuef (LL)
@ohuef - L @ohuef - LL
(rai`tift) (typa og proparty smowf)
(I) @mhorlfa (@L2) (p) @oephaxlfc raicaft
(B) Plhvar broelda (q) Dlsproportlofitlof
(@) Mydro`mhorl` i`ld (r) Ofhy is radu`tift
(D) Lodlfa (L2) (s) If-iftl`mhor
Ifs. (I - r, s) : (B - p) : (@ - q) : (D - r)
Poh. (I) Fi2 0
2
2 OP
+ 4@L2+ 1M
2O 2FiM 4
7
OP
+ =M@L
Lt dastroys ify ax`ass og `mhorlfa of gibrl` lf bhai`mlfc lfdustry. Tmus lt i`ts is iftl`mhor.
(B) Ic+ + 2P2O
02 ZIc (P
2O
0)
2U0 (sohubha `oephax)
(@) Fi2 0
2
2 OP
+2M@L 2Fi@L + 24
OP
+O
P + M2O
(D) 2Fi2 0
2
2 OP
+ L2 Fi2P4O7+ 2FiL