Effective Atomic Number (EAN)

Effective Atomic Number (EAN)

1. Effective Nuclear
Charge

2. Shielding or screening effect
•Inamulti-electronatomthevalence-shellelectronsare
attractedbythenucleusandalsoatthesametimerepelled
bytheelectronspresentbetweenthenucleusandthe
valence-shellelectrons.
•Thusthenucleusexertsanattractiveforceonthevalence
shellelectronswhiletheinner-shellelectronsexerta
repulsiveforceonthevalence-shellelectrons.
•Thecombinedeffectofthesetwoforcesisthattheactual
forceexertedbythenucleusonthevalence-shellelectrons
ispartiallydecreasedorweakenedbythepresenceof
repulsiveforcesexertedbytheinner-shellelectronsonthe
valence-shellelectrons.
•Thusthevalenceshellelectronsexperiencelessattraction
orpulltowardsthenucleus.

3. Figure:The valence shell electron experience less attraction
from the nucleus due to the presence of inner shell electrons
called shielding or screening effect of inner shell electrons.

4. "This decrease in the attractive force exerted by the
nucleus on the valence shell electron, which is obviously
due to the presence of the electrons lying between the
nucleus and valence shell electrons (called intervening
electrons) is called shielding effect or screening effect".
•Inotherwords,theinterveningelectronsscreenorshield
thevalence-shellelectronsfromthenucleus.
•Thisconcepthasthefollowingapplications:
–Theconceptofshieldingeffecthasbeenusedto
explainwhytheionizationpotentialvaluesofthe
elementsofagivengroupdecreaseondescendingthe
group.
–Thisconcepthasalsobeenusedtoexplainthatwhen
weproceedfromaninertgastoalkalimetal,alarge
decreaseintheionizationpotentialisobserved.

5. Effective nuclear charge (Z
eff
)
•Withthedecreaseintheforceofattractioncausedbythe
shieldingeffectofinterveningelectrons,theactual
nuclearcharge(whichisequaltotheatomicnumber,Zof
theelement)isdecreasedbythequantity,σ(sigma)which
iscalledscreeningconstant.
•Thedecreasednuclearchargewhichisobviouslyequalto
(Z-σ)iscalledeffectivenuclearchargeandisdenotedby
Z
eff
.
•Thus:
•σisameasureoftheextenttowhichtheintervening
electronsscreentheouter-mostshellelectronfromthe
nuclearpullonit.

6. •Aboveequationsuggeststhateffectivenuclearcharge
(Z
eff
)isdefinedas:
"The actual nuclear charge (Z or Z
actual
) minus the
screening constant (σ) produced by the electrons residing
between the nucleus and the outer-most shell electron
(intervening electrons)".
Factorsaffectingthemagnitudeofσ(screeningconstant)
andZ
eff
andtheirvariationintheperiodictable
•Followingaretheimportantfactorswhichaffectthe
magnitudeofσandZ
eff
andpredicttheirvariationinthe
periodictable.
Numberofinterveningelectrons
•Greateristhenumberofelectronsinterveningbetweenthenucleus
andtheoutermostshell(i.e.,interveningelectrons),morewillbe
themagnitudeofσandhencethemagnitudeofZ
eff
willdecrease
(Z
eff
=Z
actual
-σ)toagreaterextent.

7. •Whenwemovedownagroup,thenumberofinterveening
electronsincreasesandhencethemagnitudeofσalso
increases.
•Theincreaseinthevalueofσ,decreasesthevalueofZ
eff
.
•Thusongoingdownagroup,themagnitudeofZ
eff
goes
ondecreasing.
•ForexampleintheelementsofgroupIA,withthe
increaseofthenumberofinnershellsandelectronsin
them,theshieldingeffectcausedbytheseelectronsonthe
valence-shellelectronalsoincreasesfromLitoCsas
shownbelow:

8. Sizeoftheatom
•Withtheincreaseinthesizeoftheatom,Z
eff
decreases.
•Thus:
–Sinceatomicsizeincreasesingoingdownagroup,Z
eff
decreasesinthesamedirection.
–Sincethesizeofatomsdecreasesaswemovealonga
periodfromlefttoright,Z
eff
increasesinthesame
direction.

9. Slater'srulesforeffectivenuclearcharge
•Thissetofsimplerulesforapproximatingtheeffective
nuclearchargewasproposedanumberofyearsagoby
ProfessorJohnC.Slater,aformerfacultymemberat
M.I.T.
Slater'srulesforcalculatingσandZ
eff
•ThevalueofσandhencethatofZ
eff
canbecalculatedby
usingSlater'srules.
•Accordingtotheserulesthevalueofσforagiven
electronisestimatedasfollows:
1)Writedownthecompleteelectronicconfigurationoftheelement
anddividetheelectronsintothefollowingorbitalgroupsstarting
fromtheinsideoftheatom.
•Orbitalswithinabracketaresaidtobelongtothesamegroup.

10. 2)Nowselecttheelectronforwhichthevalueofσistobe
calculated.
•Forthiscalculationaddupthecontributionstoσforthe
otherelectronsaccordingtothefollowingrules:
Type of electron
Contribution to σ for each
electron of this type
aAllelectronsingroupsoutsidethe
electronchosen
0
bAllotherelectronsinthesame
groupaschosenone
0.35 (or 0.30 for 1s electron)
cAllelectronsinshellimmediately
inside
0.85
dAllelectronsfurtherinside 1.00

11. 3)Slater'sRulesisnowbrokenintotwocases:
–Theshieldingexperiencedbyans-orp-electron
–Theshieldingexperiencedbyad-orf-electron

12. s-andp-Orbitalelectrons
Fornsornpvalenceelectrons:
–Electronswithinsamegroupshield0.35,exceptthe
1swhichshield0.30
–Electronswithinthen-1groupshield0.85
–Electronswithinthen-2orlowergroupsshield1.00
d-andf-Orbitalelectrons
Forndornfvalenceelectrons:
–Electronswithinsamegroupshield0.35
–Electronswithinthelowergroupsshield1.00
•Theserulesaresummarizedinthefollowingtable.

13. Table: Slater's rules for calculating shieldings.
Inordertounderstandtheaboverulesletusconsiderthe
followingexamples.

14. YouTubeLectures
•EffectiveNuclearCharge
–https://www.youtube.com/watch?v=IvSmfgxCSNQ
•EffectiveNuclearCharge,Shieldingeffect,&PeriodicProperties
–https://www.youtube.com/watch?v=hs5t-6iq6-c
•HowToUseSlater'sRuletoEstimateTheEffectiveNuclear
Charge
–https://www.youtube.com/watch?v=TaYUOiEe6OA
•UsingSlater'sRules:3Examples
–https://www.youtube.com/watch?v=7wrTWlXI2IY
•LearnSlater'sRule|EffectiveNuclearChargeCalculation
–https://www.youtube.com/watch?v=F4Fx6zbcddU
•TrickforSlater'sRule,calculationofscreeningconstantand
effectivenuclearcharge
–https://www.youtube.com/watch?v=iz2_J4fjJdY

19. Variation of screening effect or σin the periodic table

20. Variation of effective nuclear charge in the periodic table

21. ApplicationsofSlater'srulesandconceptofeffective
nuclearcharge
•Slater'srulesandtheconceptofeffectivenuclearcharge
havebeenusedtoexplainthefollowing:
Whyis4sorbitalfilledearlierthan3dorbitalsin
potassiumatom(Z=19)?
(4s Orbital is filled before 3d orbitals)
•WeknowthattheconfigurationofAr(Z=18)whichis
thelastelementof3
rd
periodoftheperiodictableis:
1s
2
, 2s
2
p
6
, 3s
2
p
6
•Thus3
rd
shellisnotcompletelyfilledinAratom,since3d
orbitalsremainvacantinit.
•After3porbitalshavebeenfilledcompletelyinAr,the
19
th
electroninK(Z=19)doesnotenter3dorbitals;
ratheritgoesto4sorbital.

22. •Why4sorbitalisfilledinpreferenceto3dorbitalscanbe
explainedasfollows:
•Thetwoconfigurationsthataretheoreticallypossiblefor
K-atomare:
•ThecalculatedvalueofZ
eff
experiencedby4s
1
electronof
K-atom[configuration(a)]equalto2.20.
•ThevalueofZ
eff
experiencedby3delectronofK-atom
[configuration(b)]canbecalculatedasfollows:
–σfor3delectroninstructure(b)=0.35x0+1.0x18=18
–Z
eff
experiencedby3delectron=19–18=1.0
4s
1
→Z
eff
→ 2.20
3d
1
→Z
eff
→ 1.0

23. •SinceZ
eff
for4s
1
electronisgreaterthanthatfor3d
1
electron,theattractionbetween4s
1
electronandthe
nucleusisgreaterthanthatbetweenthe3d
1
electronand
nucleusofK-atom.
•Lowervalueofeffectivenuclearchargeactingon3d
electronascomparedtothatactingon4selectronmakes
itevidentthatinpotassiumatom3delectronislesstightly
boundtothenucleusthanthe4selectron.
•Consequentlytheadditionalelectroninpotassiumatom
preferstoenter4sorbitalthan3dorbital.
•Thus1s
2
,2s
2
p
6
,3s
2
p
6
,4s
1
configurationwouldbemore
stablethan1s
2
,2s
2
p
6
,3s
2
p
6
d
1
configuration.
•Inotherwords4sorbitalisfilledearlierthan3dorbital.

24. Formationofcationsfromtheisolatedgaseousatomsof
transitionmetals
(4s Electrons are removed before 3d electrons in the
conversion of 3d transition elements into cations)
•Whentransitionmetalsareconvertedintocations,itisns
electrons,andnot(n–1)delectrons,whichareremoved
firstfromtheisolatedgaseousatomsoftransitionmetals.
•Inordertoexplainthisfactletusconsiderthe
configurationofvanadiumatom(atomicnumber=23)
whichis1s
2
,2s
2
p
6
,3s
2
p
6
d
3
,4s
2
.
•SupposethisatomistobeconvertedintoV
2+
cation.
•Quiteobviouslythiscationisformedbytheremovalof
twoelectronsfrom4sorbitalandnotfrom3dorbital.
•Thus:

25. •Why4selectronsprefertoberemovedthan3delectrons
canbeexplainedbycalculatingthevalueofeffective
nuclearchargeactingononeofthe4sor3delectrons.
•Effectivenuclearchargeactingononeofthe4selectrons
isgivenby:
Z
eff(4s)
=Z–σ
•Effectivenuclearchargeactingononeofthe3delectrons
isgivenby:
Z
eff(3d)
=Z–σ

26. •Greatervalueofeffectivenuclearchargeactingononeof
the3delectronsascomparedtothatactingononeofthe
4selectronsinvanadiumatommakesitevidentthatin
thisatom3delectronsaremoretightlyboundtothe
nucleusthanthe4selectrons.
•Consequentlyintheconversionofvanadiumatominto
V
2+
cationtheelectronstoberemovedare4selectrons
andnot3delectrons.

27. Acationissmallerinsizethanitsparentatom
•Acationisformedbythelossofoneormoreelectrons
fromanatom.
•Itmayberepresentedas:
M → M
n+
+ ne
-
•Thedecreaseintheradiusorsizeofcationascomparedto
itsparentatomcanbeexplainedonthebasisofthe
conceptofeffectivenuclearcharge.
•Acationisformedbytheremovalofoneormore
electronsfromtheparentatom.
•Thusacationhaslessernumberofelectrons,thanits
parentatom.
•Withthedecreaseofthenumberofelectrons,the
magnitudeofthescreeningconstant,σ,alsodecreases.
•Thedecreaseinthevalueofσincreasesthemagnitudeof
effectivenuclearcharge.

28. •Theincreasedeffectivenuclearchargepullstheelectron
cloudofcationinwardnearertothenucleusandthus
makesthecationsmallerinsizethanitsparentneutral
atom.
•Thesizeofthecationsofthesameelementindifferent
oxidationstatesdecreasewiththeincreaseinthe
oxidationstate.
•Forexampleincaseofpair:Fe
2+
-Fe
3+
,theradiusofFe
2+
isgreater
thanthatofFe
3+
ion(Fe
2+
=76pm,Fe
3+
=64pm).
•Thesameargumentalsoappliestothisdecreaseasexplained
above.

29. Ananionislargerinsizethanitsparentatom
•Ananionisformedbythegainofoneormoreelectrons.
•Theincreaseinthesizeofanionascomparedtoitsparent
atomcanalsobeexplainedonthebasisoftheconceptof
effectivenuclearcharge.
•Withtheincreaseinthenumberofelectronsthe
magnitudeofscreeningconstant,σ,alsoincreases.
•Theincreaseinthemagnitudeofσdecreasesthe
magnitudeofeffectivenuclearchange,whichpullsthe
electroncloudofanionlesstightlyfromthenucleusand
thusmakestheanionlargerinsizethanitsparentatom.
•Thushalidesionsarebiggerinsizethanthehalogen
atoms.

30. Variationofatomicandionicradiioftheatomsof
representativeelementsinaperiodandagroup
a)Inaperiod
•Weknowthatthenumberofshellsinalltheelementsofa
givenperiodremainsthesamebutthevalueofeffective
nuclearcharge,ascalculatedbySlater'srules,increases
fromlefttoright.
•Theincreasedeffectivenuclearchargepullstheelectron
cloudoftheatomnearertothenucleusandthusthesize
oftheatomsandionsgoesondecreasingfromleftto
right.

31. •Thusingoingfromlefttorightinaperiodofs-andp-
blockelementsatomicandionicradiidecreasewiththe
increaseofatomicnumber.
•Thisfactcanbeillustratedbyconsideringtheatomic
(covalent)andionicradiioftheelementsof2ndperiodas
shownbelow:

32. •Thusinanyperiodthealkalimetals(thatarepresentat
theextremeleftoftheperiodictable)havethelargestsize
whilethehalogens(thatarepresentattheextremeright,
excludingzerogroupelements)havethesmallestsize.
•However,thesizeoftheatomsofinertgasesislargerthan
thatoftheprecedinghalogen.
b)Inagroup
•Ingoingdownagroupofs-andp-blockelementsthe
atomicandionicradiibothincreasewiththeincreaseof
atomicnumber.
•Forexampletheatomic(covalent)andionicradiiofalkali
metalsincreaseonproceedingfromLitoCsasshown
below:

33. •Wehaveseenthatondescendingagroupthemagnitudeof
effectivenuclearchargeactingonthevalence-shellelectronofthe
elementsremainsthesame(thefirstelementisatypicalcase).
•Thustheconceptofeffectivenuclearchargecannotbeusedto
explainthesuccessiveincreaseintheatomicorionicradiiofthe
elementsofagivengroup.

34. •However,theotherfactornamelythenumberofshellsor
principalquantumnumber(n)canbeusedtoexplainthe
increaseinradii.
•Asthenumberofshellsorprincipalquantumnumber(n)
increasesfrom2(incaseofLi)to6(incaseofCs),the
outer-mostshellelectronsgetfartherandfartheraway
fromthenucleusandhenceatomicandionicradii
increase.
•Thusitisduetotheprogressiveadditionofanewshell
(ortheincreaseinthenumberofshells)thattheatomic
orionicradiiincreasewhenweproceedfromtopto
bottominagroup.
•Thevariationofatomicandionicradiiofrepresentative
elements(s-andp-blockelement)inaperiodanda
groupoftheperiodictablecanbeshownasgivenin
followingfigure.

36. Variationofelectronegativityvaluesinaperiodanda
groupofrepresentativeelements
a)Inaperiod
•Ingoingfromlefttorightinaperiodofs-andp-block
elements,theelectronegativityvaluesincrease.
•Thisincreasecanbeexplainedonthebasisofanyofthe
followingfacts.
i)Onmovingfromlefttorightinaperiod,thereisa
decreaseinthesizeoftheatoms.
•Smalleratomshavegreatertendencytoattractthe
electronstowardsthemselvesi.e.smalleratomshave
higherelectronegativityvalues.
ii)Onmovingfromlefttorightinaperiodthereisanincreaseof
ionisationenergyandelectronaffinityoftheelements.
•Theatomsoftheelementswhichhavehighervalueofionisation
energiesandelectronaffinitiesalsohavehigherelectronegativities.

37. b)Inagroup
•Ingoingdownagroupofs-andp-blockelements,the
electronegativityvaluesdecrease.
•Thisdecreasecanalsobeexplainedonthebasisofanyof
thefollowingfacts.
i)Aswemovedownagroup,thereisanincreaseinthesize
oftheatoms.
•Withtheincreaseinsizeoftheatoms,their
electronegativityvaluesdecrease.
ii)Ionisationenergyandelectronaffinityonwhich
electronegativitydependsdecreaseasthegroupis
descended.
•Withthedecreaseofthesequantitiestheelectronegativity
valuesalsodecrease.
•TheheavierelementsofgroupIIIA(i.e.Ga,InandTI)
showreversetrendduetotheinterveningtransitionseries.

38. •Thevariationofelectronegativityvaluesdiscussedabovereveals
thatthehalogens(VIIAgroupelements)whichlieonthe
extremerightoftheperiodictablearethemostelectronegative
(i.e.leastelectropositive)elementsandthealkalimetals(IA
groupelements)whichlieontheextremeleftoftheperiodic
tablearetheleastelectronegative(i,e.mostelectropositive)
elements.
•Thusweseethatthemostelectronegativeelementisflourine
whichoccursatthetoprighthandcornerandtheleast
electronegativeelementiscesiumwhichoccursatthebottom
lefthandcorneroftheperiodictable.
•Beingthemostelectronegative,Fdoesnotshowanybasic
character,i.e.,ithasnotendencytoformpositiveionsinanyof
itsknowncompounds.
•Ontheotherhand,thereis,however,evidencetoshowthatCl,
BrandIhaveatendencytoformpositiveions.
•Thevariationofelectronegativityinaperiodandagroupof(s•
andp•blockelements)isshowninfollowingfigure.

40. Variationinthevaluesofsuccessiveionisationenergies
ofagivenelement
•Thesuccessiveionisationenergies(IE
1
,IE
2
,1E
3
etc.)ofa
givenelement(M)increasesintheorder:
IE
1
< IE
2
< IE
3
< …..
•Thisorderhasbeenexplainedonthebasisoftheconcept
ofeffectivenuclearchargeexperiencedbythelast
electroninM,M
+
,M
2+
etc.

41. Applications of Slater's rules
•Also see from Satya Parakashand HaqNawaz
•SelfStudy–shouldbeincludedinsyllabus…

42. The End