>c\ko`m 3
@g`^omji >ji{bpm\odjin \i_
oc` K`mdj_d^ O\]g`
3), @g`^omji >ji{bpm\odjin ja H\di Bmjpk @g`(
h`ion
G`nnji J]e`^odq`n
ȸ @skg\di cjr oc` `g`h`ion di oc` K`mdj_d^ O\]g` \m` jmb\idu`_ dioj mjrn \i_ ^jgphin)
ȸ @skg\di cjr oc` `g`^omji ^ji{bpm\odjin rdocdi \ ^jgphi \m` ndhdg\m oj `\^c joc`m)
Diomj_p^odji
Do kmj]\]gt n``hn gdf` \gg r`ȱq` ]``i nk`i_dib \ gjo ja odh` g`\midib \]jpo kmjojinȹ \i_ i`pomjinȹ \i_
`g`^omjinȹ \i_ `g`^omjinȹ \i_ hjm` `g`^omjinȹ nj tjp hdbco ]` rji_`mdib ȭ rc`i _j r` \^op\ggt b`o oj
nop_t ^c`hdnomt: Rc`i _j r` b`o oj nop_t m`\^odjin: Rc`i _j r` b`o oj nop_t `skgjndjin: Rc`i _j
r` b`o oj nop_t kg\nod^n' \i_ h`_d^di`n oc\o ^\i ]` h\_` ]t ^jh]didib _dz`m`io fdi_n ja ^c`hd^\gn: Oc`
\inr`m dn ijr) R`ȱm` {i\ggt m`\_t oj _dn^pnn oc` ^c`hd^\g kmjk`mod`n ja oc` ndhkg`no ^c`hd^\gn jpo oc`m`
ȭ r`ȱm` {i\ggt m`\_t oj _dn^pnn oc` `g`h`ion) M`h`h]`m' tjp c\q` g`\mi`_ oc\o oc`m` r`m` 117 _dz`m`io
fdi_n ja \ojhn' \i_ oc\o `\^c r\n fijri \n \i `g`h`io) <i_ tjp c\q` g`\mi`_ oc\o \ojhn ja _dz`m`io
`g`h`ion c\q` _dz`m`io iph]`mn ja kmjojin) Ct_mjb`i c\n 1 kmjoji #\i_ 1 `g`^omji da doȱn i`pom\g$' c`gdph
c\n 2 kmjojin #\i_ 2 `g`^omjin' da doȱn i`pom\g$' \i_ gdocdph c\n 3 kmjojin #\i_ 3 `g`^omjin' da doȱn i`pom\g$)
Adi\ggt' tjp c\q` n``i `s\hkg`n ja oc` K`mdj_d^ O\]g`) N^d`iodnon pn` oc` K`mdj_d^ O\]g` oj nphh\mdu`
diajmh\odji \]jpo \gg ja oc` fijri `g`h`ion oc\o `sdno di jpm rjmg_)
Di ocdn g`nnji' tjp rdgg g`\mi rct oc` K`mdj_d^ O\]g` #\n ncjri ]`gjr$ c\n np^c \i pipnp\g nc\k`)
#Njpm^`5 >F(,- Ajpi_\odji) >>(=T(N<$
rrr)^f,-)jmb
-/1
Ijr' rc\oȱn oc` {mno ocdib tjp ocjpbco rc`i tjp n\r oc` K`mdj_d^ O\]g`: Da tjpȱm` gdf` hjno k`jkg`' oc`
{mno ocdib tjp ocjpbco r\n kmj]\]gt njh`ocdib gdf`' ȰRjr ȭ oc\oȱn \ apiit nc\k` Rct dn oc` K`mdj_d^
O\]g` nc\k`_ gdf` oc\o: Rct dn do gjr`m di oc` hd__g`: Rct dn do cdbc`m ji `doc`m `i_: Rct dn oc`m`
oc\o j__(gjjfdib _dn^jii`^o`_ kd`^` \o oc` ]joojh: Oc` K`mdj_d^ O\]g` _j`niȱo gjjf gdf` \ o\]g` \o \ggȱ
Di ocdn ^c\ko`m' tjpȱgg ]`bdi oj n`` rct oc` K`mdj_d^ O\]g` c\n np^c \ apiit nc\k`) Do opmin jpo oc\o oc`
nc\k` ja oc` K`mdj_d^ O\]g` \^op\ggt c`gkn oj o`gg pn \]jpo oc` ^c`hd^\g kmjk`mod`n ja oc` _dz`m`io `g`h`ion
oc\o `sdno di jpm rjmg_) Di ocdn n`^odji' ajm `s\hkg`' tjpȱgg g`\mi oc\o `g`h`ion di oc` n\h` ^jgphi ja oc`
K`mdj_d^ O\]g` c\q` ndhdg\m ^c`hd^\g kmjk`mod`n) G\o`m r`ȱgg o\f` \ gjjf \o cjr `g`h`ion di oc` n\h` mjr
\m` m`g\o`_)
Bmjpk ,< @g`h`ion C\q` Ji` n @g`^omji
M`h`h]`m oc\o \^^jm_dib oj oc` <pa]\p kmdi^dkg` `g`^omjin \m` \__`_ oj gjr `i`mbt jm]do\gn {mno \i_ oc`i'
\n oc` gjr `i`mbt jm]do\gn \m` {gg`_ pk' `g`^omjin bj dioj cdbc`m \i_ cdbc`m `i`mbt jm]do\gn) Rc`i ji`
\ojh m`\^on rdoc \ijoc`m \ojh di \ ^c`hd^\g m`\^odji' doȱn oc` cdbc(`i`mbt `g`^omjin oc\o \m` diqjgq`_)
Ndi^` doȱn jigt oc` cdbc(`i`mbt `g`^omjin oc\o k\mod^dk\o` di \ ^c`hd^\g m`\^odji' doȱn jigt oc` cdbc(`i`mbt
`g`^omjin oc\o r` rdgg ^ji^`mi pn rc`i r` r\io oj _`o`mhdi` oc` ^c`hd^\g kmjk`mod`n ja \ k\mod^pg\m `g`h`io)
Epno cjr Ȱcdbcȱ di `i`mbt _j`n \i `g`^omji i``_ oj ]` oj k\mod^dk\o` di \ ^c`hd^\g m`\^odji: R`gg' di hjno
^c`hd^\g m`\^odjin' oc` jigt `g`^omjin diqjgq`_ \m` oc` `g`^omjin di oc` cdbc`no `i`mbt g`q`g) Di joc`m rjm_n'
oc` `g`^omjin rdoc oc` cdbc`no q\gp` ja n #oc` kmdi^dk\g lp\ioph iph]`m$' k\mod^dk\o` di ^c`hd^\g m`\^odjin'
rcdg` oc` `g`^omjin rdoc gjr`m q\gp`n ja n \m` ^\gg`_ ȳ^jm` `g`^omjin'ȴ \m` ^gjn`m oj oc` ip^g`pn \i_' \n \
-/2
rrr)^f,-)jmb
m`npgo' _jiȱo b`o diqjgq`_) Oc` `g`^omjin rdoc oc` cdbc`no q\gp` ja n \m` fijri \n q\g`i^` `g`^omjin) >jm`
`g`^omjin \m` \gnj m`a`mm`_ \n iji(q\g`i^` `g`^omjin) Orj _dz`m`io `g`h`ion c\q` ndhdg\m ^c`hd^\g
kmjk`mod`n rc`i oc`t c\q` oc` n\h` iph]`m ja q\g`i^` `g`^omjin di oc`dm jpo`mhjno `i`mbt g`q`g)
@g`h`ion di oc` n\h` ^jgphi ja oc` K`mdj_d^ O\]g` c\q` ndhdg\m ^c`hd^\g kmjk`mod`n) Nj rc\o _j`n oc\o
h`\i \]jpo oc`dm q\g`i^` `g`^omjin: Tjp bp`nn`_ do @g`h`ion di oc` n\h` ^jgphi ja oc` K`mdj_d^ O\]g`
c\q` oc` n\h` iph]`m ja q\g`i^` `g`^omjin ȭ oc\oȱn rct oc`t c\q` ndhdg\m ^c`hd^\g kmjk`mod`n) G`oȱn n`` da
ocdn dn omp` ajm njh` ja oc` `g`h`ion di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g`)
@s\hkg` ,5
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm ct_mjb`i (H))
Admno' tjp i``_ oj {i_ ct_mjb`i ji oc` K`mdj_d^ O\]g`) O\f` \ gjjf \o oc` K`mdj_d^ O\]g` \]jq`) Tjp
fijr oc\o ct_mjb`i dn di oc` {mno ^jgphi' \i_ da tjp gjjf ^\m`apggt' tjpȱgg n`` oc\o ct_mjb`i \gnj c\kk`in
oj ]` \o oc` ojk ja oc` {mno ^jgphi) Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm ct_mjb`i
dn Z = 1' ocpn ct_mjb`i c\n 1 kmjoji) I`pom\g ct_mjb`i rdgg \gnj c\q` 1 `g`^omji) Tjp i``_ oj rmdo` oc`
`g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 1 `g`^omji)
<n ncjri di oc` {bpm` ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj ct_mjb`i (H))
Oc`m`ajm`' r` rmdo` oc` `g`^omji ^ji{bpm\odji ajm H : 1s1 )
M`h`h]`m' rc`i tjp rmdo` `g`^omji ^ji{bpm\odjin' oc` iph]`m jpo di amjio \gr\tn di_d^\o`n oc` kmdi^dk\g
lp\ioph iph]`m' n' ja \ k\mod^pg\m jm]do\g' ocpn 1s2 c\n n = 1' rcdg` 3s1 c\n n = 3) Rc\o dn oc` cdbc`no
kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di ct_mjb`iȱn `g`^omji ^ji{bpm\odji: Doȱn n = 1' nj \gg `g`^omjin
rdoc n = 1 \m` q\g`i^` `g`^omjin) Ct_mjb`i c\n 1 q\g`i^` `g`^omji di \i s jm]do\g)
@s\hkg` -5
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm gdocdph (Li))
Admno' tjp {i_ gdocdph ji oc` K`mdj_d^ O\]g`) Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm
gdocdph dn Z = 3' ocpn gdocdph c\n 3 kmjojin) I`pom\g gdocdph rdgg \gnj c\q` 3 `g`^omjin) Tjp i``_ oj rmdo`
oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 3 `g`^omjin)
<n dggpnom\o`_ di oc` {bpm` ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj gdocdph (Li)) iji(q\g`i^` `g`^omjin5 1s2 )
rrr)^f,-)jmb
-/3
Oc`m`ajm`' r` rmdo` oc` `g`^omji ^ji{bpm\odji ajm Li : 1s2 2s1 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di gdocdphȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 2' nj \gg `g`^omjin rdoc n = 2 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 2 \m` iji(q\g`i^`
`g`^omjin) Gdocdph c\n 1 q\g`i^` `g`^omji di \i s jm]do\g)
@s\hkg` .5
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm nj_dph (Na))
Admno' tjp {i_ nj_dph ji oc` K`mdj_d^ O\]g`) Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm
nj_dph dn Z = 11' ocpn nj_dph c\n 11 kmjojin) I`pom\g nj_dph rdgg \gnj c\q` 11 `g`^omjin) Tjp i``_ oj
rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 11 `g`^omjin)
<n ncjri ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj nj_dph (Na)) iji(q\g`i^` `g`^omjin5 1s2 2s2 2p6 )
Oc`m`ajm`' r` rmdo` oc` `g`^omji ^ji{bpm\odji ajm Na : 1s2 2s2 2p6 3s1 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di nj_dphȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 3' nj \gg `g`^omjin rdoc n = 3 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 3 \m` iji(q\g`i^`
`g`^omjin) #?jiȱo ]` ajjg`_ ]t oc` 2p6 jm]do\gn) @q`i ocjpbc oc`t \m` p jm]do\gn' ijo s jm]do\gn' oc`t c\q`
n = 2' nj oc`t \m` iji(q\g`i^` `g`^omjin$ Nj_dph c\n 1 q\g`i^` `g`^omji di \i s jm]do\g)
Da tjp gjjf \o oc` g\no gdi` di @s\hkg` ,' @s\hkg` -' @s\hkg` . tjp ncjpg_ ijod^` \ k\oo`mi)
Ct_mjb`i c\n 1 q\g`i^` `g`^omji di \i s jm]do\g
Gdocdph c\n 1 q\g`i^` `g`^omji di \i s jm]do\g
Nj_dph c\n 1 q\g`i^` `g`^omji di \i s jm]do\g
Di a\^o' \gg `g`h`ion di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 1 q\g`i^` `g`^omji di \i s jm]do\g)
Oc`m`ajm`' r` rjpg_ `sk`^o \gg ja oc`n` `g`h`ion oj c\q` ndhdg\m ^c`hd^\g kmjk`mod`n ȭ \i_ oc`t _j)
-/4
rrr)^f,-)jmb
#Ct_mjb`i dn nk`^d\g ]`^\pn` do dn oc` {mno `g`h`io di oc` K`mdj_d^ O\]g`) <n \ m`npgo' ct_mjb`i c\n jigt
ji` kmjoji \i_ ji` `g`^omji' rcd^c bdq` do nk`^d\g ^c`hd^\g kmjk`mod`n) Njh`odh`n n^d`iodnon _jiȱo di^gp_`
ct_mjb`i di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g`' ]po dino`\_ bdq` do don jri Ȱnk`^d\gȱ ^jgphi oj m`|`^o
don nk`^d\g kmjk`mod`n ȭ r` rjiȱo _j oc\o c`m`' ]po tjp ncjpg_ m`\gdu` oc\o ct_mjb`i _j`n ijo c\q` \gg oc`
n\h` ^c`hd^\g kmjk`mod`n \n oc` m`no ja oc` `g`h`ion di don ^jgphi)$
Oc` `g`h`ion di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g` #joc`m oc\i ct_mjb`i$ \m` fijri \n Bmjpk ,<
h`o\gn' jm <gf\gd H`o\gn) Rc`i tjp ^jhk\m` oc` ^c`hd^\g kmjk`mod`n ja oc`n` `g`h`ion #gdocdph' nj_dph'
kjo\nndph' mp]d_dph' ^`ndph' \i_ am\i^dph$' rc\o tjpȱgg ijod^` dn oc\o oc`t \m` \gg m`h\mf\]gt ndhdg\m)
Bmjpk ,< `g`h`ion \m` h`o\gn' ndgq`m(^jgjm`_' \i_ njao) Oc`n` `g`h`ion \m` `som`h`gt m`\^odq`) N`q`m\g ja
oc`h `skgj_` da tjp kpo oc`h di r\o`m)
<n kd^opm`_ ]`gjr' ijod^` cjr oc` `g`h`ion gdocdph (Li)' nj_dph (Na)' \i_ kjo\nndph (K) \gg gjjf \gdf`)
Oc`t \m` \gg njao' ndgq`m h`o\gn) Ndi^` Li, Na \i_ K \m` \gg Bmjpk ,< h`o\gn' oc`t \gg nc\m` ndhdg\m ^c`hd^\g
kmjk`mod`n) #Njpm^`5 cook5**`i)rdfdk`_d\)jmb*rdfd*Adg`5Gdh`o\g)EKB' cook5**`i)rdfdk`_d\)jmb*
rdfd*Adg`5I\h`o\g)EKB)ekb' cook5**`i)rdfdk`_d\)jmb*rdfd*Dh\b`5Fh`o\g)ekb) >>(=T(N<$
<i_ {i\ggt' ]`^\pn` oc`t \m` nj m`\^odq`' Bmjpk ,< `g`h`ion \m` ijo ajpi_ di oc`dm `g`h`io\g ajmh di
i\opm` ȭ di joc`m rjm_n' tjp _jiȱo {i_ kpm` nj_dph jm kpm` kjo\nndph di i\opm`)
<n ncjri ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj mp]d_dph (Rb)) iji(q\g`i^` `g`^omjin5 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 )
Bmjpk -< @g`h`ion C\q` Orj n @g`^omjin
<gg ja oc` `g`h`ion di oc` {mno ^jgphi ja oc` k`mdj_d^ o\]g` c\q` 1 q\g`i^` `g`^omji di \i s np]g`q`g) Cjr
_j tjp ocdif oc` `g`h`ion di oc` n`^ji_ ^jgphi ja oc` k`mdj_d^ o\]g` _dz`m: G`oȱn {i_ jpo ]t o\fdib \
gjjf \o \ a`r `s\hkg`n)
@s\hkg` /5
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm ]`mtggdph (Be))
Admno' tjp {i_ ]`mtggdph ji oc` K`mdj_d^ O\]g`) Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm
]`mtggdph dn Z = 4' ocpn ]`mtggdph c\n 4 kmjojin) I`pom\g ]`mtggdph rdgg \gnj c\q` 4 `g`^omjin) Tjp i``_
oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 4 `g`^omjin)
rrr)^f,-)jmb
-0+
Oc`m`ajm`' r` rmdo` oc` `g`^omji ^ji{bpm\odji ajm Be : 1s2 2s2 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di ]`mtggdphȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 2' nj \gg `g`^omjin rdoc n = 2 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 2 \m` iji(q\g`i^`
`g`^omjin) =`mtggdph c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g)
<n ncjri ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj ]`mtggdph (Be)) iji(q\g`i^` `g`^omjin5 1s2 )
@s\hkg` 05
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm h\bi`ndph (Mg))
Admno' tjp {i_ h\bi`ndph ji oc` K`mdj_d^ O\]g`) Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m
ajm h\bi`ndph dn Z = 12' ocpn h\bi`ndph c\n 12 kmjojin) I`pom\g h\bi`ndph rdgg \gnj c\q` 12 `g`^omjin)
Tjp i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 12 `g`^omjin)
Oc`m`ajm`' oc` `g`^omji ^ji{bpm\odji ajm Mg : 1s2 2s2 2p6 3s2 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di nomjiodphȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 3' nj \gg `g`^omjin rdoc n = 3 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 3 \m` iji(q\g`i^`
`g`^omjin) H\bi`ndph c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g)
Ijod^` oc\o5
=`mtggdph c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g)
H\bi`ndph c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g)
<n kd^opm`_ ]`gjr' nkjmon _mdifn am`lp`iogt ^jio\di oc` `g`^omjgto` ^\g^dph ^cgjmd_`) #Njpm^`5 >F(,Ajpi_\odji) >>(=T(N<$
-0,
rrr)^f,-)jmb
Tjp ^\i kmj]\]gt bp`nn oc` iph]`m \i_ otk` ja q\g`i^` `g`^omjin di \i \ojh ja ^\g^dph (Ca)' nomjiodph
(S r)' ]\mdph (Ba) jm m\_dph (Ra)) Da tjp bp`nn`_ 2 `g`^omjin di \i s jm]do\g' oc`i tjp bp`nn`_ mdbco <gg
`g`h`ion di oc` n`^ji_ ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g)
Oc` `g`h`ion di oc` n`^ji_ ^jgphi ja oc` K`mdj_d^ O\]g` \m` fijri \n Bmjpk -< h`o\gn' jm <gf\gdi`
@\moc H`o\gn) <n tjp hdbco `sk`^o' ]`^\pn` \gg Bmjpk -< h`o\gn c\q` 2 q\g`i^` `g`^omjin di \i s
jm]do\g' oc`t \gg nc\m` ndhdg\m ^c`hd^\g kmjk`mod`n) Bmjpk -< `g`h`ion \m` h`o\gn' ndgq`m ^jgjm`_ \i_ \m`
lpdo` m`\^odq` ocjpbc oc`t \m` ijo i`\mgt \n m`\^odq` \n oc` Bmjpk ,< `g`h`ion)
Bmjpk .< @g`h`ion C\q` n \i_ ,k @g`^omjin
<gg ja oc` `g`h`ion di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 1 q\g`i^` `g`^omji di \i s np]g`q`g \i_ \gg
ja oc` `g`h`ion di oc` n`^ji_ ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 2 q\g`i^` `g`^omjin di \i s np]g`q`g) >\i
tjp h\f` \it km`_d^odji \]jpo oc` q\g`i^` `g`^omjin di oc` ocdm_ ^jgphi ja oc` K`mdj_d^ O\]g`: Rc`m`
dn oc` ocdm_ ^jgphi ja oc` K`mdj_d^ O\]g`: Do opmin jpo oc\o oc`m` \m` m`\ggt orj _dz`m`io Ȱocdm_ ^jgphinȱ
di oc` K`mdj_d^ O\]g`) O\f` \ ^gjn` gjjf \o oc` {bpm` ja oc` K`mdj_ O\]g` #oc` {mno {bpm` ja ocdn g`nnji$)
>\i tjp nkjo oc` ^jgphi g\]`g`_ Ȱ.<ȱ: >\i tjp nkjo oc` ^jgphi g\]`g`_ Ȱ.=ȱ: Ijod^` oc\o oc` nh\gg`no
\ojh di oc` Ȱ.=ȱ ^jgphi c\n Z = 21 #N^\i_dph' S c$' rcdg` oc` nh\gg`no \ojh di oc` Ȱ.<ȱ ^jgphi c\n Z = 5
#=jmji' B$) VTjp i``_ oj ijo` oc\o oc`m` dn \i \go`mi\o` r\t oj i\h` .< `g`h`ion6 oc` ^\i \gnj ]` m`a`mm`_
oj \n bmjpk 13 ndi^` oc`n` `g`h`ion \m` di oc` 13th ^jgphi ja oc` K`mdj_d^ O\]g`)X Oc`m`ajm`' do j]qdjpngt
h\f`n n`in` oj _dn^pnn oc` .< ^jgphi {mno) G`oȱn {bpm` jpo cjr h\it q\g`i^` `g`^omjin \ojhn di oc` .<
^jgphi c\q`5
@s\hkg` 15
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm ]jmji (B))
Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm ]jmji dn Z = 5' ocpn ]jmji c\n 5 kmjojin) I`pom\g
]jmji rdgg \gnj c\q` 5 `g`^omjin) Tjp i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 5 `g`^omjin)
Oc`m`ajm`' oc` `g`^omji ^ji{bpm\odji ajm B : 1s2 2s2 2p1 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di ]jmjiȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 2' nj \gg `g`^omjin rdoc n = 2 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 2 \m` iji(q\g`i^`
rrr)^f,-)jmb
-0-
`g`^omjin) =joc oc` `g`^omji di oc` 2p jm]do\g \i_ oc` `g`^omjin di oc` 2s jm]do\g \m` q\g`i^` `g`^omjin)
=jmji c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g' \i_ 1 q\g`i^` `g`^omji di \ p jm]do\g' ajm \
ojo\g ja 3 q\g`i^` `g`^omjin)
<n kd^opm`_ ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj ]jmji #=$)
@s\hkg` 25
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm \gphdiph (Al))
Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm \gphdiph dn Z = 136 ocpn i`pom\g \gphdiph c\n
13 kmjojin \i_ 13 `g`^omjin) Tjp i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 13 `g`^omjin)
Oc`m`ajm`' oc` `g`^omji ^ji{bpm\odji ajm Al : 1s2 2s2 2p6 3s2 3p1 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di \gphdiphȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 3' nj \gg `g`^omjin rdoc n = 3 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 3 \m` iji(q\g`i^`
`g`^omjin) =joc oc` `g`^omji di oc` 3p jm]do\g \i_ oc` `g`^omjin di oc` 3s jm]do\g \m` q\g`i^` `g`^omjin)
<gphdiph c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g' \i_ 1 q\g`i^` `g`^omji di \ p jm]do\g' ajm
\ ojo\g ja 3 q\g`i^` `g`^omjin)
Amjh @s\hkg` 2 \i_ @s\hkg` 3' r` c\q`5
=jmji c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ , q\g`i^` `g`^omji di \ p jm]do\g
<gphdiph c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ , q\g`i^` `g`^omji di \ p jm]do\g
Di a\^o' \gg `g`h`ion di oc` .< ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g
\i_ 1 q\g`i^` `g`^omji di \ p jm]do\g) Oc\oȱn \ ojo\g ja 3 q\g`i^` `g`^omjin ajm \ojhn di oc` .< ^jgphi)
<b\di' oc` ^c`hd^\g kmjk`mod`n ja .< `g`h`ion \m` ndhdg\m' ]`^\pn` oc`t c\q` oc` n\h` iph]`m \i_ otk`
ja q\g`i^` `g`^omjin)
Bmjpk /<(3< >jiodip` oj <__ k @g`^omjin oj oc` Jpo`mhjno
@i`mbt G`q`g
=t ijr' tjp h\t c\q` ijod^`_ \ k\oo`mi m`g\odib oc` iph]`m ja q\g`i^` `g`^omjin oj oc` ^jgphi iph]`m)
Bmjpk ,< `g`h`ion c\q` 1 q\g`i^` `g`^omji) Bmjpk -< `g`h`ion c\q` 2 q\g`i^` `g`^omjin) Bmjpk .<
`g`h`ion c\q` 3 q\g`i^` `g`^omjin) Bmjpk /< `g`h`ion c\q`ȹ r`gg' r` c\q`iȱo gjjf`_ \o oc`h t`o' ]po
rc\o rjpg_ tjp bp`nn: Doȱn km`oot j]qdjpn) Bmjpk /< `g`h`ion c\q` 4 q\g`i^` `g`^omjin) Ndhdg\mgt' Bmjpk
0< `g`h`ion c\q` 5 q\g`i^` `g`^omjin) Di a\^o' oc` k\oo`mi ^jiodip`n \gg oc` r\t pk oj Bmjpk 3< `g`h`ion'
rcd^c c\q` 8 q\g`i^` `g`^omjin) G`oȱn o\f` \ gjjf \o \ a`r `s\hkg`n di jm_`m oj {bpm` jpo `s\^ogt rc\o
otk`n ja q\g`i^` `g`^omjin \m` diqjgq`_) Admno' r`ȱgg ^jind_`m \ Bmjpk /< `g`h`io)
@s\hkg` 35
-0.
rrr)^f,-)jmb
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm ^\m]ji (C))
Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm ^\m]ji dn Z = 6' ocpn i`pom\g ^\m]ji c\n 6 kmjojin
\i_ 6 `g`^omjin) Tjp i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 6 `g`^omjin)
Oc`m`ajm`' oc` `g`^omji ^ji{bpm\odji ajm C : 1s2 2s2 2p2 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di ^\m]jiȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 2' nj \gg `g`^omjin rdoc n = 2 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 2 \m` iji(q\g`i^`
`g`^omjin) =joc oc` `g`^omjin di oc` 2p jm]do\gn \i_ oc` `g`^omjin di oc` 2s jm]do\g \m` q\g`i^` `g`^omjin)
>\m]ji c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g' \i_ 2 q\g`i^`n `g`^omji di p jm]do\gn' ajm \
ojo\g ja 4 q\g`i^` `g`^omjin)
Dggpnom\o`_ ]`gjr' oc` _d\bji\g mpg` \kkgd`_ oj ^\m]ji (C)) iji(q\g`i^` `g`^omjin5 1s2 )
Ijr g`oȱn ^jind_`m \ Bmjpk 0< `g`h`io)
@s\hkg` 45
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm idomjb`i (N))
Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm idomjb`i dn Z = 7' i`pom\g idomjb`i c\n 7 kmjojin
\i_ 7 `g`^omjin) Tjp i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 7 `g`^omjin)
Oc`m`ajm`' oc` `g`^omji ^ji{bpm\odji ajm N : 1s2 2s2 2p3 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di kcjnkcjmpnȱn `g`^omji ^ji{bpm\odji: Doȱn
n = 2' nj \gg `g`^omjin rdoc n = 2 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 2 \m` iji(q\g`i^`
`g`^omjin) =joc oc` `g`^omjin di oc` 2p jm]do\gn \i_ oc` `g`^omjin di oc` 2s jm]do\g \m` q\g`i^` `g`^omjin)
Idomjb`i c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g' \i_ 3 q\g`i^` `g`^omjin di p jm]do\gn ajm \
ojo\g ja 5 q\g`i^` `g`^omjin)
<n \ {i\g `s\hkg`' g`oȱn o\f` \ gjjf \o \ Bmjpk 1< `g`h`io #jm Bmjpk ,1$)
@s\hkg` ,+5
Rmdo` oc` `g`^omji ^ji{bpm\odji ajm jstb`i (O))
Oc` K`mdj_d^ O\]g` o`ggn tjp oc\o oc` \ojhd^ iph]`m ajm jstb`i dn Z = 86 i`pom\g jstb`i c\n 8 kmjojin
\i_ 8 `g`^omjin) Tjp i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm \i \ojh rdoc 8 `g`^omjin)
Oc`m`ajm`' oc` `g`^omji ^ji{bpm\odji ajm O : 1s2 2s2 2p4 )
Rc\o dn oc` cdbc`no kmdi^dk\g lp\ioph iph]`m oc\o tjp n`` di jstb`i ȱn `g`^omji ^ji{bpm\odji:
Doȱn n = 2' nj \gg `g`^omjin rdoc n = 2 \m` q\g`i^` `g`^omjin' \i_ \gg `g`^omjin rdoc n < 2 \m` iji(q\g`i^`
`g`^omjin) =joc oc` `g`^omjin di oc` 2p jm]do\gn \i_ oc` `g`^omjin di oc` 2s jm]do\g \m` q\g`i^` `g`^omjin)
Jstb`i c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g' \i_ 4 q\g`i^` `g`^omjin di p jm]do\gn' ajm \
ojo\g ja 6 q\g`i^` `g`^omjin)
rrr)^f,-)jmb
-0/
Nj g`oȱn nphh\mdu` rc\o r` fijr nj a\m5
Bmjpk ,< `g`h`ion c\q` 1 q\g`i^` `g`^omji di \i s jm]do\g
Bmjpk -< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g
Bmjpk .< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 1 q\g`i^` `g`^omji di \ p jm]do\g
Bmjpk /< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 2 q\g`i^` `g`^omjin di p jm]do\gn
Bmjpk 0< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 3 q\g`i^` `g`^omjin di p jm]do\gn
Bmjpk 1< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 4 q\g`i^` `g`^omjin di p jm]do\gn
>\i tjp bp`nn cjr oc` q\g`i^` `g`^omjin di ^jgphin 7A #Bmjpk ,2$ \i_ 3< #Bmjpk ,3$ \m` \mm\ib`_:
Bmjpk 2< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 5 q\g`i^` `g`^omjin di p jm]do\gn
Bmjpk 3< `g`h`ion c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 6 q\g`i^` `g`^omjin di p jm]do\gn
Ijod^` oc\o' \ao`m ^jgphi .<' `\^c ^jgphi ji` no`k apmoc`m oj oc` mdbco c\n ji` \__dodji\g q\g`i^` p
`g`^omji) Bmjpk /< `g`h`ion c\q` ji` hjm` q\g`i^` p `g`^omji oc\i Bmjpk .< `g`h`ion) Ndhdg\mgt' Bmjpk
0< `g`h`ion c\q` ji` hjm` q\g`i^` p `g`^omji oc\i Bmjpk /< `g`h`ion) =po rc\o c\kk`in rc`i tjp
m`\^c Bmjpk 3< `g`h`ion: Rct _j`n oc` K`mdj_d^ O\]g` `i_ \o ^jgphi 3<: G`oȱn ocdif \]jpo oc\o
^\m`apggt) Bmjpk 3< `g`h`ion c\q` 6 q\g`i^` `g`^omjin di p jm]do\gn) Di oc` g\no ^c\ko`m' tjp g`\mi`_ oc\o
oc` h\sdhph iph]`m ja p `g`^omjin \o \it `i`mbt g`q`g dn 6) Oc`m`ajm`' oc`m` ^jpg_iȱo ]` \ Ȱ4<ȱ ^jgphi'
]`^\pn` \ Ȱ4<ȱ ^jgphi rjpg_ c\q` 7p `g`^omjin di oc` q\g`i^` `i`mbt g`q`g' rcd^c dn dhkjnnd]g`)
Oc` a\^o oc\o Bmjpk 3< `g`h`ion c\q` ^jhkg`o`gt {gg`_ q\g`i^` s np]g`q`g \i_ p np]g`q`g dn dhkjmo\io di
o`mhn ja oc`dm ^c`hd^\g kmjk`mod`n) Bmjpk 3< `g`h`ion \m` ^\gg`_ Ij]g` B\n`n)
Oc`t \m` \gg b\n`n' \i_ oc`t \m` ijo q`mt m`\^odq` \o \gg)
G`nnji Nphh\mt
ȸ <gg fijri `g`h`ion \m` jmb\idu`_ dioj oc` K`mdj_d^ O\]g` di np^c \ r\t oc\o `g`h`ion di oc` n\h`
^jgphi c\q` ndhdg\m ^c`hd^\g kmjk`mod`n)
ȸ Jigt oc` cdbc`no `i`mbt `g`^omjin #q\g`i^` `g`^omjin$ \m` diqjgq`_ di ^c`hd^\g m`\^odjin) Oc`m`ajm`' do
dn jigt oc`n` cdbc(`i`mbt `g`^omjin oc\o \m` dhkjmo\io di _`o`mhdidib \i `g`h`ion ^c`hd^\g kmjk`mod`n)
ȸ Orj _dz`m`io `g`h`ion \m` gdf`gt oj c\q` ndhdg\m ^c`hd^\g kmjk`mod`n rc`i oc`t c\q` oc` n\h` iph]`m
ja q\g`i^` `g`^omjin)
ȸ @g`h`ion rdoc oc` n\h` iph]`m ja q\g`i^` `g`^omjin \m` ajpi_ di oc` n\h` ^jgphi ja oc` K`mdj_d^
O\]g`)
ȸ <gg `g`h`ion di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 1 q\g`i^` `g`^omji di \i s jm]do\g) Oc`n`
`g`h`ion \m` fijri \n Bmjpk ,< h`o\gn jm \gf\gd h`o\gn)
ȸ <gg `g`h`ion di oc` n`^ji_ ^jgphi ja oc` K`mdj_d^ O\]g` c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g)
Oc`n` `g`h`ion \m` fijri \n Bmjpk -< h`o\gn jm \gf\gdi` `\moc h`o\gn)
ȸ <gg `g`h`ion di ^jgphi .< ja oc` K`mdj_d^ O\]g` c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ , q\g`i^`
`g`^omji di \ p jm]do\g)
ȸ <gg `g`h`ion di ^jgphi /< ja oc` K`mdj_d^ O\]g` c\q` 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 2 q\g`i^`
`g`^omjin di p jm]do\gnȹ`o^)
ȸ >jgphi 3< c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 6 q\g`i^` di p jm]do\gn) Ndi^` \it bdq`i `i`mbt
g`q`g ^\i c\q` \o hjno 6p `g`^omjin' ^jgphi 8A `g`h`ion c\q` \ {gg`_ p np]g`q`g) Oc`m`ajm`' oc`t \m`
di`mo #iji(m`\^odq`$' ]`^\pn` oc`t \m` pigdf`gt oj `doc`m b\di jm gjn` `g`^omjin) Bmjpk 3< `g`h`ion
\m` ^\gg`_ Ij]g` B\n`n)
-00
rrr)^f,-)jmb
M`qd`r Lp`nodjin
,) O\f` \ gjjf \o oc` K`mdj_d^ O\]g`) Cjr rjpg_ tjp _`n^md]` do: Rct _j tjp ocdif do c\n np^c \ apiit
nc\k`:
-) >\i tjp npbb`no cjr `g`h`ion di oc` n\h` ^jgphi ja oc` K`mdj_d^ O\]g` hdbco ]` ndhdg\m:
.) >cjjn` oc` ^jmm`^o no\o`h`io)
#\$
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Mg c\n jigt 1 q\g`i^` `g`^omji di \i s jm]do\g
F c\n jigt 1 q\g`i^` `g`^omji di \i s jm]do\g
O c\n jigt 1 q\g`i^` `g`^omji di \i s jm]do\g
Kr c\n jigt 1 q\g`i^` `g`^omji di \i s jm]do\g
Fr c\n jigt 1 q\g`i^` `g`^omji di \i s jm]do\g
/) >dm^g` oc` \kkmjkmd\o` `g`h`io ajm `\^c ]g\if)
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(Al/Li/Na) c\n 1 q\g`i^` `g`^omji di \ p jm]do\g
0) >cjjn` oc` ^jmm`^o no\o`h`io)
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2) ?`^d_` rc`oc`m `\^c ja oc` ajggjrdib no\o`h`ion dn omp` jm a\gn`)
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Ge c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g
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B c\n 3 q\g`i^` `g`^omjin di p jm]do\gn
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3) H\o^c oc` `g`h`io oj don q\g`i^` `g`^omjin)
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S r ( d) \ ojo\g ja 8 q\g`i^` `g`^omjin
I ( dd) \ ojo\g ja 2 q\g`i^` `g`^omjin
Ne ( ddd) \ ojo\g ja 5 q\g`i^` `g`^omjin
N ( dq) \ ojo\g ja 7 q\g`i^` `g`^omjin
4) Adgg di oc` ]g\ifn)
rrr)^f,-)jmb
-01
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Ba c\n ZZ q\g`i^` `g`^omji#n$ di \i s jm]do\g' \i_ ZZ q\g`i^` `g`^omji#n$ di p jm]do\gn
S n c\n ZZ q\g`i^` `g`^omji#n$ di \i s jm]do\g' \i_ ZZ q\g`i^` `g`^omji#n$ di p jm]do\gn
S c\n ZZ q\g`i^` `g`^omji#n$ di \i s jm]do\g' \i_ ZZ q\g`i^` `g`^omji#n$ di p jm]do\gn
Po c\n ZZ q\g`i^` `g`^omji#n$ di \i s jm]do\g' \i_ ZZ q\g`i^` `g`^omji#n$ di p jm]do\gn
Na c\n ZZ q\g`i^` `g`^omji#n$ di \i s jm]do\g' \i_ ZZ q\g`i^` `g`^omji#n$ di p jm]do\gn
,+) Gdno \gg ja oc` `g`h`ion rdoc `s\^ogt - q\g`i^` `g`^omjin di p jm]do\gn)
,,) <i `g`h`io c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 4 q\g`i^` `g`^omjin di p jm]do\gn) Da oc` `g`h`io
dn di oc` n`^ji_ mjr ja oc` K`mdj_d^ O\]g`' rcd^c `g`h`io dn do:
,-) <i `g`h`io c\n 2 q\g`i^` `g`^omjin di \i s jm]do\g \i_ 6 q\g`i^` `g`^omjin di p jm]do\gn) Da oc` `g`h`io
dn di oc` n\h` mjr \n Di' rcd^c `g`h`io dn do:
Apmoc`m M`\_dib * Npkkg`h`io\g Gdifn
ȸ cook5**rrr)rjp)`_p*g\n*kctn^d*^c/,-*k`mcdno)coh
ȸ cook5**rrr)\dk)jmb*cdnojmt*^pmd`*k`mdj_d^)coh
ȸ cook5**r`])]p__tkmje`^o)jmb*r`]+,2*r`]+,2*cdnojmt)cohg
ȸ cook5**rrr)_\t\c)^jh*k`mdj_d^
ȸ cook5**rrr)^c`hopojm)^jh*k`md^c)coh
Qj^\]pg\mt
K`mdj_d^ O\]g` N^d`iodnon pn` oc` K`mdj_d^ O\]g` oj nphh\mdu` rc\o oc`t fijr \]jpo oc` `sdnodib
`g`h`ion) @g`h`ion ja ndhdg\m ndu` \m` ajpi_ di oc` n\h` mjr' rcdg` `g`h`ion rdoc ndhdg\m ^c`hd^\g
kmjk`mod`n \m` ajpi_ di oc` n\h` ^jgphi)
^c`hd^\g kmjk`mod`n Oc` r\tn di rcd^c \i `g`h`io m`\^on rdoc \ijoc`m `g`h`io jm ^jhkjpi_)
q\g`i^` `g`^omjin Oc` `g`^omjin di \i \ojh rdoc oc` cdbc`no q\gp` ja n #oc` `g`^omjin di oc` cdbc`no
`i`mbt g`q`g$)
iji(q\g`i^` `g`^omjin <gg `g`^omjin di \ojh rcd^c \m` ijo q\g`i^` `g`^omjin) Iji(q\g`i^` `g`^omjin \m`
ijo dhkjmo\io di _`o`mhdidib \i `g`h`ioȱn ^c`hd^\g kmjk`mod`n ]`^\pn` oc`t m\m`gt b`o diqjgq`_ di
^c`hd^\g m`\^odjin)
\gf\gd h`o\gn Bmjpk ,< h`o\gn) Oc`n` \m` `g`h`ion ajpi_ di oc` {mno ^jgphi ja oc` K`mdj_d^ O\]g`'
`s^gp_dib ct_mjb`i)
\gf\gdi` `\moc h`o\gn Bmjpk -< h`o\gn) Oc`n` \m` `g`h`ion ajpi_ di oc` n`^ji_ ^jgphi ja oc` K`mdj_d^
O\]g`)
ij]g` b\n`n Bmjpk 3< `g`h`ion) Oc`n` \m` `g`h`ion ajpi_ di oc` `dbco ^jgphi ja oc` K`mdj_d^ O\]g`)
Oc`t \m` di`mo' rcd^c h`\in oc\o oc`t \m` q`mt iji(m`\^odq`)
-02
rrr)^f,-)jmb
3)- Jm]do\g >ji{bpm\odjin
G`nnji J]e`^odq`n
ȸ ?m\r jm]do\g _d\bm\hn)
ȸ ?`{i` Cpi_ȱn Mpg`)
ȸ Pn` Cpi_ȱn Mpg` oj _`^d_` cjr `g`^omjin {gg np]g`q`gn rdoc hjm` oc\i ji` jm]do\g)
Diomj_p^odji
Di oc` @g`^omji >ji{bpm\odjin ja H\di Bmjpk @g`h`ion g`nnji' tjp g`\mi`_ \ gdoog` ]do \]jpo q\g`i^`
`g`^omjin) Tjp n\r cjr oc` iph]`m \i_ otk` ja q\g`i^` `g`^omjin \m` dhkjmo\io di _`o`mhdidib oc`
^c`hd^\g kmjk`mod`n ja \ k\mod^pg\m `g`h`io) Bmjpk ,< h`o\gn r`m` cdbcgt m`\^odq`' ]`^\pn` oc`t c\q` \
nomjib o`i_`i^t oj gjn` oc`dm ndibg` q\g`i^` s `g`^omjin) Bmjpk -< h`o\gn \m` m`\^odq` \n r`gg' ]po g`nn
nj' ]`^\pn` oc`t c\_ 2 q\g`i^` s `g`^omjin) Adi\ggt' Bmjpk 3< `g`h`ion r`m` di`mo #ijo m`\^odq` \o \gg$'
]`^\pn` oc`t c\_ ^jhkg`o`gt {gg`_ q\g`i^`n \i_ p np]g`q`gn' h`\idib oc`t ^jpg_ i`doc`m gjn` ijm b\di
`g`^omjin q`mt `\ndgt) Ijr tjp hdbco ]` rji_`mdib rct r` _d_iȱo o\gf hp^c \]jpo oc` ^c`hd^\g kmjk`mod`n
ja oc` `g`h`ion di ^jgphin /<(2<) Do opmin jpo oc\o pi_`mno\i_dib oc` ]`c\qdjm ja oc`n` `g`h`ion m`lpdm`n
\ ]do hjm` diajmh\odji) Nk`^d{^\ggt' r` i``_ oj fijr cjr oc` `g`^omjin {gg pk oc` p jm]do\gn) >\m]ji'
ajm dino\i^`' dn \ Bmjpk /< `g`h`io' nj do c\n 2 q\g`i^` s `g`^omjin' \i_ 2 q\g`i^` p `g`^omjin) J]qdjpngt'
oc` 2 q\g`i^` s `g`^omjin \m` k\dm`_ ojb`oc`m di oc` s jm]do\g' ]po rc\o \]jpo oc` 2 q\g`i^` p `g`^omjin:
<m` oc` q\g`i^` p `g`^omjin k\dm`_ di \ ndibg` p jm]do\g' jm \m` oc`t `\^c di oc`dm jri p jm]do\g #m`h`h]`m'
oc`m` \m` \ ojo\g ja ocm`` p jm]do\gn oc\o oc` q\g`i^` p `g`^omjin ^jpg_ ]` ajpi_ di$) Rc\o \]jpo idomjb`i:
Idomjb`i dn \ Bmjpk 0< `g`h`io' nj do c\n 2 q\g`i^` s `g`^omjin' \i_ 3 q\g`i^` p `g`^omjin) <b\di' oc` 2
q\g`i^` s `g`^omjin hpno ]` k\dm`_ di oc` s jm]do\g' ]po rc\o \]jpo oc` 3 q\g`i^` p `g`^omjin: <m` orj ja
oc`h k\dm`_ di \ ndibg` p jm]do\g' jm _j \gg ocm`` c\q` oc`dm jri p jm]do\gn:
Jm]do\g M`km`n`io\odji
=`ajm` r` _dn^pnn oc` jm_`m \i_ h\ii`m di rcd^c oc` jm]do\gn di \ p np]g`q`g \m` {gg`_' r` c\q` oj diomj_p^` \
nth]jgd^ ijo\odji oc\o n^d`iodnon pn` oj ncjr jm]do\g {ggdib) Am`lp`iogt' n^d`iodnon rdgg pn` ]js`n oj m`km`n`io
jm]do\gn)
Oc` {bpm` ]`gjr ncjrn \ n`o ja ]js`n ajm jm]do\gn pk oj oc` n = 2 `i`mbt g`q`g) Oc` ]js`n \m` _`kd^odib
`g`^omji jm]do\gn ajm oc` n = 1 \i_ n = 2 `i`mbt g`q`gn) Ijod^` oc\o ajm n = 1' oc`m` dn \ ndibg` s jm]do\g'
rcdg` ajm n = 2 oc`m` dn ji` s jm]do\g \i_ ocm`` p jm]do\gn)
Rc`i \ Ȱnkdi(pkȱ `g`^omji dn km`n`io di \i jm]do\g' n^d`iodnon _m\r \i pkr\m_ kjdiodib \mmjr di oc\o jm]do\gȱn
]js) Ocdn g`\_n oj rc\o dn fijri \n \i jm]do\g _d\bm\h) Ajm `s\hkg`' ct_mjb`i c\n \ ndibg` `g`^omji di
oc` 1s jm]do\g) Da oc\o ndibg` `g`^omji r`m` \ nkdi(pk' oc` jm]do\g _d\bm\h ajm ct_mjb`i rjpg_ ]`5
Dggpnom\o`_ ]`gjr' oc` jm]do\g _d\bm\h ajm ct_mjb`i' \nnphdib oc\o ct_mjb`iȱn ndibg` `g`^omji dn Ȱnkdi(pkȱ
(m s = +1/2))
rrr)^f,-)jmb
-03
Rc`i \ Ȱnkdi(_jriȱ `g`^omji dn km`n`io di \i jm]do\g' n^d`iodnon _m\r \ _jrir\m_ kjdiodib \mmjr di oc\o
jm]do\gȱn ]js) C`gdph' ajm dino\i^`' c\n orj `g`^omjin di oc` 1s jm]do\g) R` fijr oc\o ji` ja oc`n` `g`^omjin
hpno ]` Ȱnkdi(pkȱ \i_ oc` joc`m hpno ]` Ȱnkdi(_jri'ȱ nj oc` jm]do\g _d\bm\h ajm c`gdph rjpg_ ]`5
<n ncjri ]`gjr' oc` jm]do\g _d\bm\h ajm c`gdph) Ijod^` oc\o rc`i `g`^omjin \m` k\dm`_ di \i jm]do\g' ji`
ja oc` `g`^omjin dn Ȱnkdi(pk'ȱ rcdg` oc` joc`m dn Ȱnkdi(_jri)ȱ
=t ^jhk\mdib oc` {mno orj jm]do\g m`km`n`io\odji {bpm`n' do ncjpg_ ]` a\dmgt j]qdjpn oj tjp' rcd^c `g`^omjin
\m` k\dm`_ \i_ rcd^c \m` pik\dm`_) Oc\o dn ji` ja oc` \_q\io\b`n ja \i jm]do\g _d\bm\h) <i jm]do\g _d\bm\h
dn \ ^g`\m r\t ja ncjrdib `s\^ogt cjr h\it k\dm`_ \i_ pik\dm`_ `g`^omjin oc`m` \m` di \ k\mod^pg\m \ojhȱn
`g`^omjid^ ^ji{bpm\odji)
Ijr tjp hdbco ]` rji_`mdib \]jpo oc` pik\dm`_ `g`^omjin ȭ cjr _j tjp fijr rc`oc`m oj _m\r oc`h
\n Ȱnkdi(pk'ȱ jm Ȱnkdi(_jri)ȱ O`^cid^\ggt nk`\fdib' oc` {mno `g`^omji di \ np]g`q`g #1s, 2s, 2p' `o^$ ^jpg_ ]`
`doc`m Ȱnkdi(pkȱ jm Ȱnkdi(_jri)ȱ Di joc`m rjm_n' ajm ct_mjb`i (1s1 )' tjp ^jpg_ _m\r oc` \mmjr di oc` 1s
jm]do\g ]js kjdiodib `doc`m pk jm _jri) Ndhdg\mgt' ajm ]jmji (1s2 2s2 2p1 )' tjp ^jpg_ _m\r oc` \mmjr di oc`
2p jm]do\g ]js kjdiodib `doc`m pk jm _jri) Ji^` tjpȱq` ^cjn`i oc` nkdi ja oc` {mno `g`^omji di \ np]g`q`g'
ocjpbc' oc` nkdin ja \gg ja oc` joc`m `g`^omjin di oc\o np]g`q`g _`k`i_ ji oc` nkdi tjp ^cjn` ajm oc` {mno)
Oj \qjd_ ^jiapndji' n^d`iodnon ȱ\gr\tn _m\r oc` {mno `g`^omji di \i jm]do\g \n Ȱnkdi(pk)ȱȱ Da tjp nod^f rdoc
ocdn mpg`' tjpȱgg i`q`m b`o dioj omjp]g`)
Da tjp dindno ji ]m`\fdib ocdn mpg`' tjp hdbco _m\r \i jm]do\g _d\bm\h oc\o dn di^jmm`^o' \n ncjri di oc`
{bpm` ]`gjr) =t ^jiq`iodji' n^d`iodnon pnp\ggt _m\r \gg pik\dm`_ `g`^omjin \n Ȱnkdi(pk)ȱ Ocdn km`q`ion oc`h
amjh _m\rdib di^jmm`^o jm]do\g _d\bm\hn gdf` oc` ji` ncjri di #^$) Di oc` i`so n`^odji' tjpȱgg g`\mi oc\o
oc` jm]do\g _d\bm\h di #^$ dn di^jmm`^o ]`^\pn` do _j`n ijo j]`t Cpi_ȱn Mpg`)
-04
rrr)^f,-)jmb
Ijod^` oc\o ]t _m\rdib oc` {mno `g`^omji di `\^c jm]do\g \n Ȱnkdi(pk'ȱ \gg ja oc` pik\dm`_ `g`^omjin di oc`
np]g`q`g c\q` oc` n\h` nkdi' `q`i da oc`t \m` di _dz`m`io jm]do\gn Ocdn dn _p` oj \ kmdi^dkg` fijri \n
Cpi_ȱn Mpg`) R`ȱgg _dn^pnn Cpi_ȱn Mpg` di hjm` _`o\dg di oc` i`so n`^odji)
Jm]do\gn di k Np]g`q`g Adgg Di_dqd_p\ggt =`ajm` K\dmdib
Km`qdjpngt r` g`\mi`_ oc\o oc` `i`mbt ja \i `g`^omji di \it bdq`i jm]do\g _`k`i_n ji oc` `i`mbt g`q`g ja oc`
jm]do\g #rcd^c dn _`o`mhdi`_ ]t oc` kmdi^dk\g lp\ioph iph]`m' n$ \i_ oc` np]g`q`g ja oc` jm]do\g #s, p, d'
`o^) rcd^c dn _`o`mhdi`_ ]t oc` \udhpoc\g lp\ioph iph]`m5 !$) R` \gnj g`\mi`_ oc\o \^^jm_dib oj oc`
<pa]\p kmdi^dkg`' `g`^omjin rdgg {gg oc` gjr`no `i`mbt jm]do\gn {mno' \i_ oc`i hjq` pk oj cdbc`m `i`mbt
jm]do\gn jigt \ao`m oc` gjr`m `i`mbt jm]do\gn \m` apgg) Da tjp ocdif ^\m`apggt' ocjpbc' tjpȱgg m`\gdu` oc\o
oc`m`ȱn nodgg \ kmj]g`h) >`mo\digt' 1s jm]do\gn ncjpg_ ]` {gg`_ ]`ajm` 2s jm]do\gn' ]`^\pn` oc` ,n jm]do\gn
c\q` \ gjr`m q\gp` ja n' \i_ ocpn \ gjr`m `i`mbt) Ndhdg\mgt' 2s jm]do\gn ncjpg_ ]` {gg`_ ]`ajm` 2p jm]do\gn'
]`^\pn` 2s jm]do\gn c\q` \ gjr`m q\gp` ja !(! = 0)' \i_ ocpn \ gjr`m `i`mbt) Rc\o \]jpo oc` ocm`` _dz`m`io
2p jm]do\gn: Di rc\o jm_`m _j `g`^omjin {gg oc` 2p jm]do\gn: Oj \inr`m ocdn lp`nodji' r` i``_ oj opmi oj \
kmdi^dkg` fijri \n Cpi_ȱn Mpg`) Cpi_ȱn Mpg` no\o`n oc\o5 #,$ @q`mt jm]do\g di \ np]g`q`g dn ndibgt j^^pkd`_
]`ajm` \it jm]do\g dn _jp]gt j^^pkd`_) #-$ <gg ja oc` `g`^omjin di ndibgt j^^pkd`_ jm]do\gn c\q` oc` n\h`
nkdi)
<^^jm_dib oj oc` {mno mpg`' `g`^omjin rdgg \gr\tn j^^pkt \i `hkot jm]do\g ]`ajm` oc`t k\dm pk) Ocdn ncjpg_
h\f` n`in` bdq`i rc\o tjp fijr \]jpo `g`^omjin) @g`^omjin \m` i`b\odq`gt ^c\mb`_ \i_' \n \ m`npgo' oc`t
m`k`g `\^c joc`m) Ndi^` `g`^omji(`g`^omji m`kpgndji m\dn`n oc` `i`mbt ja oc` `g`^omjin diqjgq`_' `g`^omjin
o`i_ oj hdidhdu` m`kpgndji #\i_ ocpn hdidhdu` oc`dm `i`mbd`n$ ]t j^^pktdib oc`dm jri jm]do\g' m\oc`m oc\i
nc\mdib \i jm]do\g rdoc \ijoc`m `g`^omji) O\f` \ gjjf \o oc` {bpm` ]`gjr)
rrr)^f,-)jmb
-1+
Ijod^` cjr oc` orj 2p `g`^omjin di oc` jm]do\g _d\bm\h ji oc` g`ao \m` di n`k\m\o` jm]do\gn' rcdg` oc` orj 2p
`g`^omjin di oc` jm]do\g _d\bm\h ji oc` mdbco \m` nc\mdib \ ndibg` jm]do\g) Oc` jm]do\g _d\bm\h ji oc` g`ao
dn oc` ^jmm`^o jm]do\g _d\bm\h' ]`^\pn` do j]`tn Cpi_ȱn Mpg`' h`\idib oc\o oc`m` dn g`nn `g`^omji(`g`^omji
m`kpgndji \i_' \n \ m`npgo' oc` `g`^omjin c\q` gjr`m `i`mbd`n #m`h`h]`m' `g`^omjin \gr\tn hdidhdu` oc`dm
`i`mbd`n$)
Oc` {bpm` \]jq` dggpnom\odib jm]do\g _d\bm\hn ajm idomjb`i dn ndhdg\m oj oc` jm]do\g _d\bm\h ajm ^\m]ji di
oc` {mno {bpm`) Ijod^` cjr \gg ocm`` 2p `g`^omjin di oc` jm]do\g _d\bm\h ji oc` g`ao \m` di n`k\m\o` jm]do\gn'
rcdg` orj ja oc` ocm`` 2p `g`^omjin di oc` _d\bm\h ji oc` mdbco \m` nc\mdib \ ndibg` jm]do\g) Oc` jm]do\g
_d\bm\h ji oc` g`ao dn oc` ^jmm`^o jm]do\g _d\bm\h' ]`^\pn` do j]`tn Cpi_ȱn Mpg`) <b\di' ocdn h`\in oc\o
oc`m` dn g`nn `g`^omji(`g`^omji m`kpgndji \i_' \n \ m`npgo' oc` `g`^omjin c\q` gjr`m `i`mbd`n)
Oc` {bpm` \]jq` ncjrn kjnnd]g` `g`^omji ^ji{bpm\odjin ajm \i \ojh rdoc ajpm 2p `g`^omjin) Ocdn odh`' orj
ja oc` `g`^omjin c\q` ij ^cjd^` ȭ oc`t hpno k\dm pk) Oc` joc`m orj `g`^omjin' cjr`q`m' ^jpg_ `doc`m k\dm
pk' \n ncjri di oc` jm]do\g _d\bm\h ji oc` mdbco' jm j^^pkt oc`dm jri jm]do\gn' \n ncjri di oc` jm]do\g
_d\bm\h ji oc` g`ao) Rcd^c _j tjp ocdif dn ^jmm`^o: J]qdjpngt' oc` jm]do\g _d\bm\h ji oc` g`ao' ]`^\pn` do
hdidhdu`n `g`^omji(`g`^omji m`kpgndji) Oc` jm]do\g _d\bm\h ji oc` g`ao dn \gnj oc` jm]do\g _d\bm\h' rcd^c
ajggjrn Cpi_ȱn Mpg`' ndi^` \gg jm]do\gn \m` ndibgt j^^pkd`_ ]`ajm` \it \m` _jp]gt j^^pkd`_) Oc` jm]do\g
_d\bm\h ji oc` mdbco _j`n ijo ajggjr Cpi_ȱn Mpg`' ndi^` oc` {mno orj jm]do\gn \m` _jp]gt j^^pkd`_ ]`ajm`
oc` ocdm_ dn ndibgt j^^pkd`_)
Rcdg` doȱn `\nt oj pi_`mno\i_ rct `g`^omjin rjpg_ j^^pkt `hkot jm]do\gn ]`ajm` k\dmdib pk' doȱn \ gjo c\m_`m
oj pi_`mno\i_ rct pik\dm`_ `g`^omjin di _dz`m`io jm]do\gn hpno \gg c\q` oc` n\h` nkdi) @g`^omji nkdin di
_dz`m`io jm]do\gn \gdbi #\gg kjdio di oc` n\h` _dm`^odji$' ]`^\pn` nkdin' rcd^c \m` \gdbi`_ c\q` gjr`m `i`mbt
oc\i nkdin rcd^c \m` ijo \gdbi`_) Ijod^` oc\o \n gjib \n tjp \gr\tn _m\r oc` {mno `g`^omji di \i
jm]do\g \n Ȱnkdi(pkȱ tjp rdgg \gr\tn _m\r nkdin rcd^c \m` \gdbi`_) M`a`m ]\^f oj oc` {bpm` dggpnom\odib
pik\dm`_ `g`^omjin \n ȱnkdi(pk)ȱ Ijr oc\o tjp fijr Cpi_ȱn Mpg`' do ncjpg_ ]` j]qdjpn rct oc` jm]do\g
_d\bm\h di 4.c dn di^jmm`^o ȭ oc` orj `g`^omjin di oc` ndibgt j^^pkd`_ 2p jm]do\gn c\q` _dz`m`io nkdin' \i_
ocpn ocdn jm]do\g _d\bm\h _j`n ijo j]`t Cpi_ȱn Mpg`) >jhk\m` oc` jm]do\g _d\bm\h di 4.c oj oc` jm]do\g
_d\bm\h di 4.d) Oc` jm]do\g _d\bm\h di 4.d _j`n j]`t Cpi_ȱn Mpg`' ]`^\pn` oc` orj `g`^omjin di oc` ndibgt
j^^pkd`_ 2p jm]do\gn c\q` oc` n\h` nkdi)
Idomjb`i C\n Ocm`` Pik\dm`_ @g`^omjin
Ijr oc\o r` fijr \]jpo jm]do\g _d\bm\hn \i_ Cpi_ȱn mpg`' r` ^\i ]`bdi oj `skg\di oc` ^c`hdnomt ja oc`
`g`h`ion di Bmjpkn /< ocmjpbc 2<) G`oȱn o\f` \ gjjf \o idomjb`i \n \i `s\hkg`)
@s\hkg` ,5
-1,
rrr)^f,-)jmb
?m\r oc` jm]do\g _d\bm\h ajm idomjb`i)
Admno' r` i``_ oj rmdo` oc` `g`^omji ^ji{bpm\odji ajm idomjb`i epno \n r` _d_ km`qdjpngt5 rcd^c bdq`n
1s2 2s2 2p3 ) Oj _m\r oc` jm]do\g _d\bm\h r` rdgg rmdo` oc` ajggjrdib5 oc` {mno orj `g`^omjin rdgg k\dm pk di
oc` ,n jm]do\g6 oc` i`so orj `g`^omjin rdgg k\dm pk di oc` 2s jm]do\g) Oc\o g`\q`n 3 `g`^omjin' rcd^c hpno
]` kg\^`_ di oc` 2p jm]do\gn) <^^jm_dib oj Cpi_ȱn Mpg`' \gg jm]do\gn rdgg ]` ndibgt j^^pkd`_ ]`ajm` \it
dn _jp]gt j^^pkd`_) Oc`m`ajm`' r` fijr oc\o `\^c p jm]do\g b`on ji` `g`^omji) Cpi_ȱn Mpg` \gnj o`ggn pn
oc\o \gg ja oc` pik\dm`_ `g`^omjin hpno c\q` oc` n\h` nkdi) F``kdib rdoc ^jiq`iodji' r` _m\r \gg ja oc`n`
`g`^omjin \n Ȱnkdi(pk'ȱ rcd^c bdq`n)
Jm]do\g _d\bm\hn ^\i c`gk tjp oj h\f` km`_d^odjin \]jpo oc` r\tn di rcd^c ^`mo\di `g`h`ion rdgg m`\^o'
\i_ oc` ^c`hd^\g Ȱ^jhkjpi_nȱ jm Ȱhjg`^pg`nȱ oc\o _dz`m`io `g`h`ion rdgg ajmh) R` \m`iȱo m`\_t oj _dn^pnn
^jhkjpi_n' jm hjg`^pg`n t`o) Oc` kmdi^dkg`n oc\o tjpȱm` g`\midib ijr rdgg c`gk tjp oj pi_`mno\i_ oc`
]`c\qdjm ja \gg ^c`hd^\gn' amjh oc` hjno ]\nd^ `g`h`ion gdf` ct_mjb`i \i_ c`gdph' oj oc` hjno ^jhkg`s
kmjo`din #cpb` ]djgjbd^\g ^c`hd^\gn h\_` ja ocjpn\i_n ja _dz`m`io \ojhn ]jpi_ ojb`oc`m$ ajpi_ di tjpm
]j_t)
G`nnji Nphh\mt
ȸ Jm]do\g _d\bm\hn \m` _m\ri ]t m`km`n`iodib `\^c jm]do\g \n \ ]js' `\^c Ȱnkdi(pkȱ `g`^omji di \i jm]do\g
\n \i pkr\m_ kjdiodib \mmjr di oc` ]js' \i_ `\^c Ȱnkdi(_jriȱ `g`^omji di \i jm]do\g \n \ _jrir\m_
kjdiodib \mmjr di oc` ]js) Tjp ^\i jigt c\q` orj \mmjrn di `\^c ]js' \i_ oc`t hpno ]` kjdiodib di
jkkjndo` _dm`^odjin)
ȸ N^d`iodnon pn` oc` ^jiq`iodji oc\o oc` {mno `g`^omji di \it jm]do\g dn Ȱnkdi(pk'ȱ oc`m`ajm`' oc` {mno
\mmjr di \i jm]do\g Ȱ]jsȱ ncjpg_ kjdio pk) Cpi_ȱn Mpg` no\o`n5
#,$ @q`mt jm]do\g di \ np]g`q`g dn ndibgt j^^pkd`_ ]`ajm` \it jm]do\g dn _jp]gt j^^pkd`_)
#-$ <gg ja oc` `g`^omjin di ndibgt j^^pkd`_ jm]do\gn c\q` oc` n\h` nkdi)
ȸ @g`^omjin rdgg j^^pkt n`k\m\o` jm]do\gn m\oc`m oc\i k\dmdib pk' ndi^` ocdn hdidhdu`n `g`^omji(`g`^omji
m`kpgndjin' oc`m`]t hdidhdudib `i`mbt) @g`^omji nkdin di _dz`m`io jm]do\gn rdocdi oc` n\h` np]g`q`g
\gdbi ]`^\pn` \gdbi`_ nkdin c\q` gjr`m `i`mbt)
rrr)^f,-)jmb
-1-
M`qd`r Lp`nodjin
,) Rcd^c ja oc` ajggjrdib dn \ q\gd_ jm]do\g _d\bm\h:
-)
.)
/)
0)
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jstb`i' O) Pn` do oj \inr`m oc` ajggjrdib lp`nodjin5
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pik\dm`_ q\g`i^` `g`^omjin
k\dm`_ q\g`i^` `g`^omjin
k\dm`_ iji(q\g`i^` `g`^omjin
pik\dm`_ iji(q\g`i^` `g`^omjin
1) ?m\r oc` jm]do\g _d\bm\h ajm i`ji' Ne) Pn` do oj \inr`m oc` ajggjrdib lp`nodjin5
#\$
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pik\dm`_ q\g`i^` `g`^omjin
k\dm`_ q\g`i^` `g`^omjin
k\dm`_ iji(q\g`i^` `g`^omjin
pik\dm`_ iji(q\g`i^` `g`^omjin
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@q`mt jm]do\g di \ np]g`q`g dn _jp]gt j^^pkd`_ ]`ajm` \it jm]do\g dn ndibgt j^^pkd`_)
@q`mt jm]do\g di \ np]g`q`g dn ndibgt j^^pkd`_ ]`ajm` \it jm]do\g dn _jp]gt j^^pkd`_)
<gg `g`^omjin di ndibgt j^^pkd`_ jm]do\gn c\q` oc` n\h` nkdi)
Oc` orj `g`^omjin di \ ndibg` jm]do\g c\q` oc` n\h` nkdi)
<gg `g`^omjin di ndibgt j^^pkd`_ jm]do\gn c\q` _dz`m`io nkdin)
Oc` orj `g`^omjin di \ ndibg` jm]do\g c\q` _dz`m`io nkdin)
3) ?m\r oc` jm]do\g _d\bm\h ajm kcjnkcjmpn P)
4) ?m\r \i jm]do\g _d\bm\h ajm ndgd^ji' S i) Pn` do oj \inr`m oc` ajggjrdib lp`nodjin5
#\$
#]$
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\
\
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ndgd^ji
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c\n
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c\n
c\n
ZZZ
ZZZ
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pik\dm`_ q\g`i^` `g`^omjin
k\dm`_ q\g`i^` `g`^omjin
k\dm`_ iji(q\g`i^` `g`^omjin
pik\dm`_ iji(q\g`i^` `g`^omjin
,+) ?m\r \i jm]do\g _d\bm\h ajm Mn) Pn` do oj _`o`mhdi` oc` ojo\g iph]`m ja pik\dm`_ `g`^omjin di \i
Mn \ojh)
-1.
rrr)^f,-)jmb
Apmoc`m M`\_dib * Npkkg`h`io\g Gdifn
ȸ cook5**rrr)^c`hkm\^od^`)^jh*_mdggn*e\q\Z<J)kck
ȸ cook5**gd]m\mt)ocdiflp`no)jmb*.104*nomp^opm`n*`g`^omji^jiadb)cohg
ȸ cook5**rrr)^c`h)g\o`^c)`_p*y_`__t*G`^oijo`*>c\k2=)cohg
ȸ cook5**rrr)hd)hpi)^\*pn`mn*`_pmiajm*,,++*\ojhd^ -+nomp^opm`*ng_+.1)coh
Qj^\]pg\mt
jm]do\g _d\bm\h Jm]do\g _d\bm\hn \m` _m\ri ]t m`km`n`iodib `\^c jm]do\g \n \ ]js' `\^c Ȱnkdi(pkȱ `g`^(
omji di \i jm]do\g \n \i pkr\m_ kjdiodib \mmjr di oc` ]js' \i_ `\^c Ȱnkdi(_jriȱ `g`^omji di \i jm]do\g
\n \ _jrir\m_ kjdiodib \mmjr di oc` ]js)
Cpi_ȱn mpg` @q`mt jm]do\g di \ np]g`q`g dn ndibgt j^^pkd`_ ]`ajm` \it jm]do\g dn _jp]gt j^^pkd`_) <gg ja
oc` `g`^omjin di ndibgt j^^pkd`_ jm]do\gn c\q` oc` n\h` nkdi)
3). Oc` K`mdj_d^ O\]g` \i_ @g`^omji >ji{bpm\(
odjin
G`nnji J]e`^odq`n
ȸ M`g\o` \i `g`h`ioȱn kjndodji di oc` KO oj oc` `i`mbt g`q`g ja don q\g`i^` `g`^omjin #`s^gp_dib om\indodji
h`o\gn' g\ioc\id_`n' \i_ \^odid_`n$)
ȸ M`g\o` \i `g`h`ioȱn kjndodji di oc` KO oj oc` np]g`q`g ja don cdbc`no `i`mbt q\g`i^` `g`^omjin)
ȸ @skg\di rct oc`m` \m` jigt orj `g`h`ion di oc` {mno mjr ja oc` KO)
Diomj_p^odji
Rdoc rc\o r` c\q` \gm`\_t _dn^pnn`_' tjp hdbco m`\gdu` oc\o epno \n `g`^omji ^ji{bpm\odjin ^\i ]` pn`_
oj `skg\di oc` nc\k` \i_ jmb\idu\odji ja oc` K`mdj_d^ O\]g`' oc` nc\k` \i_ jmb\idu\odji ja oc` K`mdj_d^
O\]g` ^\i' di opmi' ]` pn`_ oj km`_d^o `g`^omji ^ji{bpm\odjin) Di a\^o' da tjp ^\i gj^\o` \i `g`h`io ji oc`
K`mdj_d^ O\]g`' tjp ^\i pn` oc` `g`h`ioȱn kjndodji oj {bpm` jpo oc` `i`mbt g`q`g ja oc` `g`h`ioȱn q\g`i^`
`g`^omjin) Apmoc`mhjm`' \i `g`h`ioȱn kjndodji ji oc` K`mdj_d^ O\]g` o`ggn tjp oc` np]g`q`g ja oc` `g`h`ioȱn
cdbc`no `i`mbt q\g`i^` `g`^omjin) Di ocdn g`nnji' r`ȱgg o\f` \ ^gjn` gjjf \o cjr oc` K`mdj_d^ O\]g` m`g\o`n oj
oc` `g`^omji ^ji{bpm\odjin)
Mjrn <^mjnn ji oc` KO \m` >jindno`io Rdoc oc` @i`mbt G`q`g di
<i <ojh
Admno' g`oȱn omt oj {bpm` jpo rc\o r` ^\i g`\mi amjh \i `g`h`ioȱn mjr jm k`mdj_ di oc` K`mdj_d^ O\]g`)
Oc` {bpm` ]`gjr ncjrn cjr oc` _dz`m`io mjrn di oc` K`mdj_d^ O\]g` \m` iph]`m`_) Oc` om\indodji h`o\gn
\i_ oc` g\ioc\id_`n \i_ \^odid_`n c\q` ]``i jhdoo`_) #Njpm^`5 >F(,- Ajpi_\odji) >>(=T(N<$
rrr)^f,-)jmb
-1/
Oj pi_`mno\i_ rc\o ocdn h`\in di o`mhn ja \i `g`h`ioȱn `g`^omji ^ji{bpm\odji' g`oȱn ^jind_`m oc` Bmjpk
,< h`o\gn) Da r` rmdo` oc` `g`^omji ^ji{bpm\odji ajm oc` Bmjpk ,< h`o\g amjh `\^c mjr ja oc` K`mdj_d^
O\]g`' r` c\q`5
mjr
2
Li :
1s2 2s1
mjr
3
Na :
1s2 2s2 2p6 3s1
mjr
4
K:
1s2 2s2 2p6 3s2 3p6 4s1
mjr
5
Rb :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1
mjr
6
Cs :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s1
mjr
7
Fr :
s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4 f 14 5d10 6p6 7s1
?j tjp n`` \it k\oo`mi: Ajm Bmjpk ,< h`o\gn' do n``hn oc\o `g`h`ioȱn mjr ^jmm`nkji_n oj oc` `i`mbt g`q`g
ja oc\o `g`h`ioȱn q\g`i^` `g`^omji) Gdocdph (Li)' ajm dino\i^`' dn ajpi_ di mjr 2 ja oc` K`mdj_d^ O\]g`' \i_
don q\g`i^` `g`^omji dn ajpi_ di oc` n = 2 `i`mbt g`q`g) >`ndph (Cs) dn ajpi_ di mjr 6 ja oc` K`mdj_d^ O\]g`'
\i_ don q\g`i^` `g`^omji dn ajpi_ di oc` n = 6 `i`mbt g`q`g) G`oȱn n`` da ocdn n\h` k\oo`mi cjg_n ajm Bmjpk
-< h`o\gn5
mjr
2
Li :
1s2 2s2
mjr
3
Na :
1s2 2s2 2p6 3s2
mjr
4
K:
1s2 2s2 2p6 3s2 3p6 4s2
mjr
5
Rb :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2
mjr
6
Cs :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2
mjr
7
Fr :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4 f 14 5d10 6p6 7s2
Ajm Bmjpk -< h`o\gn' oc` n\h` mpg` \kkgd`n H\bi`ndph (Mg) dn ajpi_ di mjr 3 ja oc` K`mdj_d^ O\]g`' \i_
don q\g`i^` `g`^omjin \m` ajpi_ di oc` n = 3 `i`mbt g`q`g) Ndhdg\mgt' M\_dph (Ra) dn ajpi_ di mjr 7 ja oc`
K`mdj_d^ O\]g`' \i_ don q\g`i^` `g`^omjin \m` ajpi_ di oc` n = 7 `i`mbt g`q`g)
-10
rrr)^f,-)jmb
Nj a\m nj bjj_ ȭ ]po _j`n oc` n\h` k\oo`mi \kkgt oj oc` Bmjpk .< ( 3< `g`h`ion #\gnj fijri \n Bmjpkn
13ȭ18$) G`oȱn {i_ jpo ]t rmdodib oc` `g`^omji ^ji{bpm\odji ajm oc` Bmjpk .< `g`h`io di `\^c mjr)
mjr
2
B:
1s2 2s2 2p1
mjr
3
Al :
1s2 2s2 2p6 3s2 3p1
mjr
4
Ga :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1
mjr
5
In :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p1
mjr
6
Tl :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 5d10 6p1
@q`i ocjpbc oc` q\g`i^` `g`^omjin di Bmjpk .< `g`h`ion \m` ajpi_ di ]joc s \i_ p jm]do\gn' do opmin jpo
oc\o \i `g`h`ioȱn mjr nodgg ^jmm`nkji_n oj oc` `i`mbt g`q`g ja oc\o `g`h`ioȱn q\g`i^` `g`^omjin) Ajm `s\hkg`'
B\ggdph (Ga) dn ajpi_ di mjr 4 ja oc` K`mdj_d^ O\]g`' \i_ don q\g`i^` `g`^omjin \m` ajpi_ di oc` n = 4
`i`mbt g`q`g) Gdf`rdn`' Oc\ggdph (T l) dn ajpi_ di mjr 6 ja oc` K`mdj_d^ O\]g`' \i_ don q\g`i^` `g`^omjin \m`
ajpi_ di oc` n = 6 `i`mbt g`q`g)
Do m`\ggt _j`n n``h \n da r` ^\i km`_d^o oc` `i`mbt g`q`g ja \i `g`h`ioȱn q\g`i^` `g`^omjin pndib oc` mjr
iph]`m ajm oc\o `g`h`io di oc` K`mdj_d^ O\]g`) G`oȱn omt ji` g\no `s\hkg`' ocjpbc' epno oj ]` npm` ]t
rmdodib oc` `g`^omji ^ji{bpm\odji ajm oc` Bmjpk 2< `g`h`io di `\^c mjr)
mjr
2
B:
1s2 2s2 2p5
mjr
3
Al :
1s2 2s2 2p6 3s2 3p5
mjr
4
Ga :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
mjr
5
In :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p5
mjr
6
Tl :
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 5d10 6p5
Ji^` \b\di' \i `g`h`ioȱn mjr ^\i ]` pn`_ oj _`o`mhdi` oc` `i`mbt g`q`g ja oc\o `g`h`ioȱn q\g`i^` `g`^omjin)
>cgjmdi` (Cl)' ajm dino\i^`' dn ajpi_ di mjr 3 ja oc` K`mdj_d^ O\]g`' \i_ don q\g`i^` `g`^omjin \m` ajpi_
di oc` n = 3 `i`mbt g`q`g) Ndhdg\mgt' Dj_di` (I) dn ajpi_ di mjr 5 ja oc` K`mdj_d^ O\]g`' \i_ don q\g`i^`
`g`^omjin \m` ajpi_ di oc` n = 5 `i`mbt g`q`g)
Tjp ncjpg_ h\f` ijo` ja ji` {i\g kjdio rc`i do ^jh`n oj `i`mbt g`q`gn \i_ cjr oc`t m`g\o` oj oc` K`mdj_d^
O\]g`) Jpm mpg` ajm _`o`mhdidib oc` `i`mbt g`q`g ja \i `g`h`ioȱn q\g`i^` `g`^omjin pndib oc` `g`h`ioȱn mjr
di oc` K`mdj_d^ O\]g` rjmfn ajm Bmjpk ,< ȭ 3< `g`h`ion) Ocdn mpg` _j`niȱo \kkgt' cjr`q`m' oj oc` Bmjpk
,= ȭ 3= #\gnj fijri \n Bmjpkn . ȭ ,-$ `g`h`ion) Oc` `g`h`ion di oc\o gjr`m kjmodji ja oc` K`mdj_d^ O\]g`
#oc` hd__g` kjmodji ja oc` K`mdj_d^ O\]g` Ȱ]g\^f`_ jpoȱ di Adbpm` ,$ \m` fijri \n om\indodji h`o\gn) Oc`t
]`c\q` _dz`m`iogt' \i_ tjp ^\iȱo \kkgt oc` n\h` mpg`n oj oc`h \n a\m \n q\g`i^` `g`^omjin \m` ^ji^`mi`_)
Oc` n\h` bj`n ajm oc` dnjg\o`_ gjr`m kjmodji ja oc` K`mdj_d^ O\]g` #\gnj Ȱ]g\^f`_ jpoȱ di oc` {bpm` ja oc`
K`mdj_d^ O\]g` \]jq`$) Ocdn ]gj^f ^jio\din `g`h`ion fijri \n g\ioc\id_`n \i_ \^odid_`n) Gdf` om\indodji
h`o\gn' g\ioc\id_`n \i_ \^odid_`n _j ijo j]`t oc` n\h` mpg`n \n oc` Bmjpk ,< ( 3< `g`h`ion rc`i do ^jh`n
oj q\g`i^` `g`^omjin \i_ q\g`i^` `g`^omji `i`mbt g`q`gn)
Ct_mjb`i \i_ C`gdph J^^pkt oc` Admno K`mdj_
Tjp kmj]\]gt ijod^`_ oc\o' di oc` g\no n`^odji' r` _d_iȱo h`iodji oc` {mno mjr \o \gg) Dino`\_' r` \gr\tn
no\mo`_ amjh mjr 2) Oc` {mno mjr di oc` K`mdj_d^ O\]g` dn \ Ȱnk`^d\g mjrȱ ajm n`q`m\g m`\njin) Oj ]`bdi rdoc'
oc` {mno mjr ja oc` K`mdj_d^ O\]g` ^jio\din jigt orj `g`h`ion ȭ ct_mjb`i \i_ c`gdph) >\i tjp {bpm` jpo
rct oc`m` \m` jigt orj `g`h`ion di oc` {mno mjr:
<^^jm_dib oj rc\o r` g`\mi`_ di oc` g\no n`^odji' \i `g`h`ioȱn mjr iph]`m ^jmm`nkji_n oj oc` `i`mbt g`q`g
ja oc\o `g`h`ioȱn q\g`i^` `g`^omjin) Oc`m`ajm`' oc` {mno mjr hpno ^jio\di `g`h`ion rdoc q\g`i^` `g`^omjin
rrr)^f,-)jmb
-11
di oc` n = 1 `i`mbt g`q`g) =t ijr tjp ncjpg_ fijr oc\o oc`m` dn jigt ji` jm]do\g di oc` n = 1 `i`mbt g`q`g)
Oc\o jm]do\g' ja ^jpmn`' dn oc` ,n jm]do\g) Ct_mjb`i c\n ji` q\g`i^` `g`^omji di oc` ,n jm]do\g' #don `g`^omji
^ji{bpm\odji dn 1s1 $' \i_ c`gdph c\n orj q\g`i^` `g`^omjin di oc` ,n jm]do\g #don `g`^omji ^ji{bpm\odji dn
1s2 $) Ndi^` doȱn dhkjnnd]g` oj {o hjm` oc\i orj `g`^omjin dioj oc` ,n jm]do\g' \ojhn rdoc \ ojo\g ja ocm`` jm
hjm` `g`^omjin hpno c\q` q\g`i^` `g`^omjin di \i `i`mbt g`q`g rdoc n = 2 jm bm`\o`m) >g`\mgt' oc`i' \ojhn
rdoc \ ojo\g ja ocm`` jm hjm` `g`^omjin _j ijo ]`gjib di oc` {mno mjr ja oc` K`mdj_d^ O\]g`)
Oc` {mno mjr ja oc` K`mdj_d^ O\]g` dn \gnj nk`^d\g ]`^\pn` don `g`h`ion c\q` nk`^d\g kmjk`mod`n) Ct_mjb`i'
ajm `s\hkg`' dn ijo \ h`o\g gdf` oc` m`no ja oc` Bmjpk ,< `g`h`ion) Dino`\_' ct_mjb`i \ojhn m`\^o rdoc `\^c
joc`m \i_ ajmh rc\oȱn fijri \n ct_mjb`i b\n' H2 ) <n r\n h`iodji`_ di oc` g\no g`nnji' njh` n^d`iodnon
rdgg kpo ct_mjb`i di \ ^\o`bjmt \gg ]t don`ga' m\oc`m oc\i di^gp_dib do \o oc` ojk ja oc` ,< ^jgphi) R`
rjiȱo _j oc\o c`m`' ]po tjp ncjpg_ \gr\tn f``k di hdi_ oc` a\^o oc\o ct_mjb`i dn Ȱ_dz`m`io'ȱ \i_ oc\o tjp
ncjpg_iȱo ^jhk\m` oc` ct_mjb`iȱn ^c`hd^\g kmjk`mod`n rdoc oc` ^c`hd^\g kmjk`mod`n ja oc` joc`m Bmjpk ,<
`g`h`ion)
C`gdph dn \gnj \ nk`^d\g \ojh) Tjp hdbco rji_`m rct c`gdph \kk`\mn \o oc` a\m mdbco(c\i_ nd_` ja oc`
K`mdj_d^ O\]g`' m\oc`m oc\i mdbco i`so oj ct_mjb`i) <b\di' c`gdphȱn kg\^`h`io di oc` K`mdj_d^ O\]g` m`|`^on
don nk`^d\g ^c`hd^\g kmjk`mod`n) @\mgd`m tjp g`\mi`_ oc\o Bmjpk 3< `g`h`ion r`m` Ȱdi`moȱ \i_ oc\o di^gp_`n
c`gdph) @q`i ocjpbc c`gdph jigt c\n orj q\g`i^` `g`^omjin' rcdg` oc` m`no ja oc` Bmjpk 3< `g`h`ion c\q`
`dbco q\g`i^` `g`^omjin' c`gdph dn kg\^`_ ji oc` ojk ja oc` 3< ^jgphi ndi^` c`gdphȱn ^c`hd^\g ]`c\qdjm dn
ndhdg\m oj oc` ^c`hd^\g ]`c\qdjm ja oc` joc`m Ij]g` B\n`n ]`^\pn` do c\n \ ^jhkg`o`_ jpo`m `i`mbt g`q`g)
Oc` n Np]g`q`g =gj^f ji KO
Nj a\m r` fijr oc\o' rdoc oc` `s^`kodji ja om\indodji h`o\gn' g\ioc\id_`n \i_ \^odid_`n' r` ^\i pn` oc`
mjr di rcd^c \i `g`h`io dn ajpi_ oj _`o`mhdi` oc` `i`mbt g`q`g ja oc\o `g`h`ioȱn q\g`i^` `g`^omjin) >\i
oc` jmb\idu\odji ja oc` K`mdj_d^ O\]g`' \i_ oc` kg\^`h`io ja \i `g`h`io rdocdi oc` K`mdj_d^ O\]g`' o`gg pn
\itocdib `gn` \]jpo oc` `g`h`ion `g`^omji ^ji{bpm\odji: Oc` \inr`m dn ȭ Ȱt`n)ȱ M`h`h]`m oc\o oc` cdbc`no
`i`mbt q\g`i^` `g`^omjin di Bmjpk ,< \i_ Bmjpk -< `g`h`ion \m` \gr\tn di s jm]do\gn) Di a\^o' oc` jigt
q\g`i^` `g`^omjin di Bmjpk ,< \i_ Bmjpk -< `g`h`ion \m` di s jm]do\gn Gdocdph' (Li) ajm dino\i^`' c\n
oc` `g`^omji ^ji{bpm\odji 1s2 2s1 ) Ijod^` oc\o gdocdphȱn ndibg` q\g`i^` `g`^omji dn di \i s jm]do\g) Ndhdg\mgt'
h\bi`ndph (Mg) c\n oc` `g`^omji ^ji{bpm\odji 1s2 2s2 2p6 3s2 ) <b\di' ijod^` oc\o h\bi`ndphȱn orj q\g`i^`
`g`^omjin \m` di \i s jm]do\g) Ndi^` \gg ja oc` q\g`i^` `g`^omjin di Bmjpk ,< \i_ Bmjpk -< `g`h`ion `sdno
di s jm]do\gn' oc` {mno orj ^jgphin ja oc` K`mdj_d^ O\]g` #^jgphin ,< \i_ -<$ \m` fijri \n oc` Ȱs
np]g`q`g ]gj^f)ȱ Oc` s np]g`q`g ]gj^f dn ncjri di oc` {bpm` ]`gjr) Ijod^` oc\o oc` s np]g`q`g ]gj^f ^jindnon
ja \gg ja oc` h`o\gn amjh Li _jri oj Fr di ^jgphi ,<' \i_ \gg ja oc` h`o\gn amjh =` _jri oj M\ di ^jgphi
-<) Ct_mjb`i dn ijo di^gp_`_ di oc` s np]g`q`g ]gj^f' \b\di' ]`^\pn` ja don nk`^d\g kmjk`mod`n)
<n kd^opm`_ ]`gjr' oc` s np]g`q`g ]gj^f ja oc` K`mdj_d^ O\]g` di^gp_`n oc` Bmjpk ,< h`o\gn \i_ oc` Bmjpk
-< h`o\gn) #Njpm^`5 >F(,- Ajpi_\odji) >>(=T(N<$
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Rc\o ^\i r` n\t \]jpo oc` q\g`i^` `g`^omjin di Bmjpk .<( Bmjpk 3< `g`h`ion: Di k\mod^pg\m' rc\o ^\i
r` n\t \]jpo oc` cdbc`no `i`mbt q\g`i^` `g`^omjin: Da tjp gjjf ^\m`apggt' tjpȱgg ijod^` oc\o ajm Bmjpk .<
Bmjpk 3< #jm da tjp km`a`m' Bmjpkn 13ȭ18$ `g`h`ion' oc` cdbc`no `i`mbt q\g`i^` `g`^omjin \m` \gr\tn di p
jm]do\gn) =jmji' (B) ajm dino\i^`' c\n oc` `g`^omji ^ji{bpm\odji 1s2 2s2 2p1 ) Rcdg` ]jmji c\n ]joc 2s \i_
2p q\g`i^` `g`^omjin' oc` 2p q\g`i^` `g`^omjin \m` cdbc`m di `i`mbt) Ndhdg\mgt' Fmtkoji (Kr) c\n oc` `g`^omji
^ji{bpm\odji 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 ) <b\di' rcdg` fmtkoji c\n ]joc 4s \i_ 4p q\g`i^` `g`^omjin' oc`
4p q\g`i^` `g`^omjin \m` cdbc`m di `i`mbt) Ndi^` oc` cdbc`no `i`mbt q\g`i^` `g`^omjin di Bmjpk .< Bmjpk
3< `g`h`ion `sdno di p jm]do\gn' oc` {i\g nds ^jgphin ja oc` K`mdj_d^ O\]g` #^jgphin .< ocmjpbc 3<$
\m` fijri \n oc` Ȱk np]g`q`g ]gj^f)ȱ Oc` p np]g`q`g ]gj^f dn ncjri di oc` {bpm` ]`gjr) <__dodji\ggt'
\n dggpnom\o`_ di oc` {bpm` ]`gjr oc` p np]g`q`g ]gj^f ^jindnon ja \gg ja oc` `g`h`ion amjh B _jri oj T l di
^jgphi .<' \gg ja oc` `g`h`ion amjh C _jri oj K] di ^jgphi /<' \gg ja oc` `g`h`ion amjh N _jri oj Bi
di ^jgphi 5A' \gg ja oc` `g`h`ion amjh O _jri oj Po di ^jgphi 1<' \gg ja oc` `g`h`ion amjh F _jri oj <o
di ^jgphi 2< \i_' {i\ggt' \gg ja oc` `g`h`ion amjh Ne _jri oj Rn di ^jgphi 3<) C`gdph dn ijo di^gp_`_
di oc` p np]g`q`g ]gj^f' rcd^c ncjpg_ h\f` n`in`' ndi^` c`gdph c\n ij p `g`^omjin
<n dggpnom\o`_ ]`gjr' oc` p np]g`q`g ]gj^f ja oc` K`mdj_d^ O\]g` di^gp_`n oc` Bmjpk .< ȭ Bmjpk 3< `g`h`ion)
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Epno \n oc` K`mdj_d^ O\]g` c\n \i s np]g`q`g ]gj^f \i_ \ p np]g`q`g ]gj^f' do \gnj c\n \ d np]g`q`g ]gj^f \i_
\i f np]g`q`g ]gj^f) ?`{idib q\g`i^` `g`^omjin di oc` d \i_ f np]g`q`g ]gj^fn ^\i ]` hjm` _dzd^pgo ]po' di
b`i`m\g' hjno ja oc` cdbc `i`mbt q\g`i^` `g`^omjin di oc` d np]g`q`g ]gj^f \m` di d jm]do\gn rcdg` hjno ja
oc` cdbc `i`mbt q\g`i^` `g`^omjin di oc` f np]g`q`g ]gj^f \m` di f jm]do\gn)
<n dggpnom\o`_ di oc` {bpm` ]`gjr' oc` K`mdj_d^ O\]g` dn _dqd_`_ dioj oc` s np]g`q`g ]gj^f' oc` p np]g`q`g
]gj^f' oc` d np]g`q`g ]gj^f' \i_ oc` f np]g`q`g ]gj^f) #Njpm^`5 >F(,- Ajpi_\odji) >>(=T(N<$
< ^jhkg`o` nphh\mt ja oc` K`mdj_d^ O\]g`' \i_ oc` diajmh\odji do ^jio\din \]jpo \i `g`h`ioȱn q\g`i^` `g`^(
omjin dn ncjri di oc` {bpm` ]`gjr) #Njpm^`5 cook5**`i)rdfdk`_d\)jmb*rdfd*Adg`5KO\]g`Znomp^opm`)
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@\mgd`m tjp g`\mi`_ oc\o oc` K`mdj_d^ O\]g` r\n \ ^jiq`id`io r\t oj nphh\mdu` \gg ja oc` diajmh\odji oc\o
n^d`iodnon fijr \]jpo oc` _dz`m`io `g`h`ion ajpi_ di jpm rjmg_) Oc` K`mdj_d^ O\]g` kmj]\]gt `q`i gjjf`_
apiit oj tjp' ]`^\pn` tjp c\_ ij r\t ja pi_`mno\i_dib rc\o don nc\k` \i_ jmb\idu\odji h`\io) Ijr oc\o
r`ȱq` _dn^pnn`_ `g`^omji jm]do\gn \i_ `g`^omji `i`mbt g`q`gn' ocjpbc' oc` K`mdj_d^ O\]g` ncjpg_iȱo n``h nj
nom\ib` \ithjm`) Di a\^o' oc` nc\k` ja oc` K`mdj_d^ O\]g` \^op\ggt m`|`^on oc` r\t di rcd^c `g`^omjin \m`
jmb\idu`_ di \ojhn ja oc` _dz`m`io `g`h`ion)
Oc` ajggjrdib r`]k\b`' K`mdj_d^ O\]g` #cook5**rrr)dpi)`_p*y^k\ic_*k`mdj_d^o\]g`)cohg$ ^jio\din
\i dio`m\^odq` k`mdj_d^ o\]g` oc\o \ggjrn tjp oj ^gd^f ji oc` `g`h`io \i_ oc` r`] k\b` oc`i ncjrn \ iph]`m
ja kctnd^\g ^jino\ion ajm oc\o `g`h`io) Oc` _\o\ di^gp_`n' i\h`' _`indot' `g`^omji ^ji{bpm\odji' c`\o ja
q\kjmdu\odji' c`\o ja apndji' h`godib kjdio' ]jdgdib kjdio' nk`^d{^ c`\o' \i_ `g`^omji`b\odqdot)
G`nnji Nphh\mt
ȸ Ajm Bmjpk ,<' -<' .<' /<' 0<' 1<' 2< \i_ 3< `g`h`ion' oc` mjr di rcd^c \i `g`h`io dn ajpi_
^jmm`nkji_n oj oc` `i`mbt g`q`g ja oc\o `g`h`ioȱn q\g`i^` `g`^omjin) Ajm `s\hkg`' gdocdph (Li) dn di
mjr -' \i_ don q\g`i^` `g`^omjin \m` di oc` n = 2 `i`mbt g`q`g)
ȸ Tjp ^\i km`_d^o oc` `i`mbt g`q`g ja \i `g`h`ioȱn q\g`i^` `g`^omjin pndib oc` `g`h`ioȱn mjr iph]`m di
oc` K`mdj_d^ O\]g`)
ȸ @g`h`ion di oc` {mno mjr c\q` nk`^d\g kmjk`mod`n)
ȸ Ct_mjb`i dn ijo \i \gf\gd h`o\g' \i_ dn pnp\ggt ajpi_ \n \ b\n)
ȸ C`gdph dn \ Ij]g` B\n' \i_ `scd]don ^c`hd^\g kmjk`mod`n ndhdg\m oj oc` joc`m Ij]g` B\n`n ajpi_ di
Bmjpk 3<)
ȸ Oc` K`mdj_d^ O\]g` ^\i ]` _dqd_`_ dioj s, d, p \i_ f np]g`q`g ]gj^fn)
ȸ Ajm `g`h`ion di oc` s np]g`q`g ]gj^f' \gg q\g`i^` `g`^omjin \m` ajpi_ di s jm]do\gn)
ȸ Ajm `g`h`ion di oc` p np]g`q`g ]gj^f' oc` cdbc`no `i`mbt q\g`i^` `g`^omjin \m` ajpi_ di p jm]do\gn)
M`qd`r Lp`nodjin
,) Pn` oc` K`mdj_d^ O\]g` oj _`o`mhdi` oc` `i`mbt g`q`g ja oc` q\g`i^` `g`^omjin di `\^c ja oc` ajggjrdib
`g`h`ion)
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.) Pn` oc` K`mdj_d^ O\]g` oj _`o`mhdi` oc` `i`mbt g`q`g \i_ np]g`q`g ja oc` cdbc`no `i`mbt `g`^omjin di
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Li c\n q\g`i^` `g`^omjin di oc` n = 1 `i`mbt g`q`g)
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Ga c\n q\g`i^` `g`^omjin di oc` n = 3 `i`mbt g`q`g)
Xe c\n q\g`i^` `g`^omjin di oc` n = 5 `i`mbt g`q`g)
P c\n q\g`i^` `g`^omjin di oc` n = 2 `i`mbt g`q`g)
0) H\o^c oc` `g`h`io oj oc` np]g`q`g ]gj^f do dn ajpi_ di5
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4) Rcd^c `i`mbt g`q`g _j`n oc` {mno mjr di oc` d np]g`q`g ]gj^f ^jmm`nkji_ oj:
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Tjp \m` m`lpdm`_ oj m`bdno`m ]`ajm` tjp ^\i r\o^c oc` qd_`jn ]po oc`m` dn ij ^c\mb`) Oc` r`]ndo` c\n ji`
qd_`j oc\o \kkgd`n oj ocdn g`nnji ^\gg`_ Oc` K`mdj_d^ O\]g`)
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Oc` cdbc`no `i`mbt `g`^omjin di om\indodji h`o\gn \m` ajpi_ di _ jm]do\gn)
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`g`^omjin di g\ioc\id_`n \i_ \^odid_`n \m` ajpi_ di f jm]do\gn)
s np]g`q`g ]gj^f Oc` `g`h`ion di oc` K`mdj_d^ O\]g` di ^jgphin ,< \i_ 2A #`s^gp_dib ct_mjb`i$) <gg
q\g`i^` `g`^omjin ajm `g`h`ion di oc` s np]g`q`g ]gj^f \m` di s jm]do\gn)
p np]g`q`g ]gj^f Oc` `g`h`ion di oc` K`mdj_d^ O\]g` di ^jgphin .< ocmjpbc 8A #`s^gp_dib c`gdph$)
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d np]g`q`g ]gj^f Oc` `g`h`ion di oc` K`mdj_d^ O\]g` di ^jgphin ,= ocmjpbc 8B #\gnj fijri \n om\indodji
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f np]g`q`g ]gj^f Oc` `g`h`ion di oc` g\ioc\id_` \i_ \^odid_` mjrn ja oc` K`mdj_d^ O\]g`)
ij]g` b\n`n Bmjpk 3< `g`h`ion) Oc`n` \m` `g`h`ion ajpi_ di oc` `dbco ^jgphi ja oc` K`mdj_d^ O\]g`)
Oc`t \m` di`mo' rcd^c h`\in oc\o oc`t \m` q`mt iji(m`\^odq`)
di`mo Iji(m`\^odq`)
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