ki1101-2012-kd lec04a thequantummechanicsofatom
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Chapter 8Chapter 8
The Quantum Mechanical AtomThe Quantum Mechanical Atom
Achmad Rochliadi
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Summary HighlightSummary Highlight
Model of Atomic Theory Electromagnetic Energy
Atomic Spectra
Matter Wave
Electron Configuration
Shape of !r"ital
Atomic propertie
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&alton ' Each element i compoed of mall particle
called atom,
Atom are neither created nor detroyed inchemical reaction,
All atom of a given element are identical
Compound are formed +hen atom of more
than one element com"ine
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Thompon ' The atom of the element conit of a
num"er of negatively electrifiedcorpucle encloed in a phere ofuniform poitive electrification,
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Rutherford The atom of an element conit of a mall* poitively
charged nucleu in the centre* +hich carrie almot theentire ma of the atom,
The electron are revolving around the nucleu at high
peed, The num"er of electron in an atom i e/ual to the
num"er of proton, Hence it i electrically neutral, The volume of the nucleu i negligi"ly mall
compared to the volume of the atom, Mot of the pace in the atom i empty
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Rutherford Simple &eignRutherford Simple &eign
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(iel -ohr' Atom i a mall* poitively charged nucleu
urrounded "y electron that travel in circular
or"it around the nucleu0imilar in tructure
to the olar ytem* "ut +ith electrotatic force
providing attraction* rather than gravity,
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The Quantum Mechanical AtomThe Quantum Mechanical Atom
-y the late $8%%1 it +a clear that claicalphyic +a incapa"le of decri"ing atom
and molecule
E)periment ho+ed that electron actedli2e tiny charged particle in ome
e)periment and +ave in other
The phyic that decri"e o"3ect +ithwave/particle dualityi called quantum
mechanicsor quantum theory
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Energy can "e tranferred "et+een thing a
light or radiation Radiation carrie energy through pace a
wavesor ocillation moving out+ard from
a ditur"ance Electromagnetic +ave 4radiation5 may "e
characteri6ed "y their .height7 or
amplitudeand the num"er that occur perecond or frequency4v5
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ight Act A A Waveight Act A A Wave
Wavelength ()the ditance light travel tocomplete one cycle
Frequency () the num"er of +ave cyclein one econd
unit are cycle per econd 4cp5* Hert6 4H65 H6 9 :$
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atoms12
Frequency And Wavelength Are RelatedFrequency And Wavelength Are Related
(ote that a the fre/uency of the +aveincreae* the +avelength decreae
Regardle of the fre/uency* light travel at
the ame peed* c
c9;,??@?>B8 < $%8m
Learning Check' Df the fre/uency of a radiotation i %%, MH6* +hat i the +avelength
in mF 0.999 m
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7.1 Electromagnetic radiation provides the clue to the electronic structuresof atoms
13
Radiant nergy !pectrumRadiant nergy !pectrumhigh energy,
short waves
low energy,
long waves
"h t l t i ff t #" ti l $h %f"h t l t i ff t #" ti l $h %f
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@,$ Electromagnetic radiation provide the clue to the electronic tructure of atom $
"hotoelectric ffect #"article $heory %f"hotoelectric ffect #"article $heory %f
Light&Light&
Al"ert Eintein 4$?%B5 E9h= Shining light on a clean metal urface may
e3ect electron
There i a threhold level needed to e3ect theelectron 4a +or2 function pecific to the
metal5
Dncreaing intenity doe not caue the effect
Dncreaing thefrequencyof the light doe
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The unit of fre/uency are the hert'4('5
The minimum and ma)imum amplitude of
electromagnetic radiation are evenly paced
The pea2:to:pea2 ditance i called thewavelength
5econd4$$$H6$ :$
54
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The product of fre/uency and +avelength
give the peed of light 4c5
Electromagnetic radiation come in a "roadrange of fre/uencie called the
electromagnetic spectrum
The electromagnetic pectrum i dividedinto region according to the +avelength
of radiation
m$%,%% 8 c
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What +e call lighti a mall lice of the
electromagnetic pectrum +ith +avelength"et+een a"out %% and @%% nm
Thi i called the visi)le region"ecaue +e can
.ee7 thee +avelength of the electromagneticpectrum
Gamma ray* ray* and ultraviolet radiation
have +avelength horter than the vii"le region
Micro+ave* infrared radiation* and radio +avehave +avelength longer than vii"le light
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The +ay a u"tance a"or"
electromagnetic radiation can "e ued to
characteri6e it
Ior e)ample* each u"tance a"or" a
uni/uely different et of infrared
fre/uencie
A plot of +avelength a"or"ed veru the
a"orption i called an infrared a)sorption
spectrum
Dt can "e ued to identify a u"tance
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The ocillating magnetic and electric field
of an electromagnetic +ave interact +ith
particle that it pae
A charged particle can pic2 up energy at the
e)pene of the radiation ource
Infraredasorptionspectrum
of woodalcohol!methanol".
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The energy tranfer i not decri"e correctly
"y claical phyic
Dn $?%% the German cientit Ma) #lanc2
propoed that the electromagnetic radiation
could "e vie+ed a a tream of tiny energy
pac2et or quanta+e no+ call photons
#hoton travel at the peed of light
#lanc2 propoed* and Eintein confirmed*that the energy of a photon is proportional
to its frequency
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Thi mean that )othelectron and
electromagnetic radiation can "e
repreented a either +ave or particle The vii"le pectrum i a continuous
pectrum "ecaue it contain a continuou
ditri"ution of light of all color E)cited atom can emit light
J$%K,K>Kcontant#lanc2L
photonofenergy
:
h
hE
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>>
Ilame EmiionIlame Emiion Element e)hi"it characteritic color +hen
"urned
The characteritic pectra are alo o"erved
+hen element are u"3ect to trong electrical
field a in ga dicharge tu"e,
(ote that the
light from the
dicharge tu"e i
actually everal
different colored
line a een on
the urface of the
C&
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The atomic spectrumor emission
spectrumi a erie of individual linecalled a line spectrum
Atomic pectra are uni/ue for each element
#ight emitted y
e$cited atoms is
comprised of a
few narrow eams
with fre%uencies
characteristic of
the element.
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Dn general* the line pectrum of an element
i rather complicated
The line pectrum of hydrogen* +ith a
ingle electron* i the implet
The Ryd)erg equationcan "e ued to
calculated all the pectral line of hydrogen
n1and n> are poitive integers
#attern Dn Atomic ine Spectra
$
=
RH$
n$>
$
n>>
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The firt theoretical model that uccefully
accounted for the Ryd"erg e/uation +a
propoed in $?$ "y (iel -ohr
&ontinuous !a" and discrete
!" potential energy of a
tortoise. 'he potential energy
of the tortoise in !" is
%uanti(ed.
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@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie >8
Electron move around the nucleu in fi)edpath or orbitsmuch li2e the planet move
around the un
!r"it poition* la"eled +ith the integer n*have pecific potential energy
The lo+et energy tate of an atom i called
theground state4an electron +ith n9 $ for ahydrogen atom5
-ohr1 Model !f The Atom-ohr1 Model !f The Atom
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@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie >?
A"orption And EmiionA"orption And Emiion
Electron thatabsorbenergy areraied to a higherenergy level
A particularfre/uency of light iemitted+hen an
electron fall to alo+er energy level
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@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie %
Thi e/uation allo+ the calculation of the energy*
E* of any or"it
"9 -ohr1 contant
n i the or"it location
J$%>,$8"
n"E
$8
>
-ohr E/uation 4$?$5-ohr E/uation 4$?$5
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@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie $
-ohr1 4theoretical5 e/uation e)plain thee)perimental 4empirical5 Ryd"erg e/uation
The com"ination of contant* b/hc* ha a
value +hich differ from the e)perimentallyderived value ofRH"y only %,%BN
>>
>>
>>
$$$$
$$
or
+ith
54
hl
hl
lh
nnhc
b
lhnn
n
b
n
blh
hc
nnb
EEE
-ohr1 Model #redict Energy evel-ohr1 Model #redict Energy evel
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@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie >
Oour TurnNOour TurnN
Which energy i not poi"le according to -ohr1ModelF
A, :B,B
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@,> Atomic line pectra are evidence that electron in atom have /uanti6ed energie
Theory +a not
a"le to e)plain
the pectra of
atom +ith more
than one electron Theory doen1t
e)plain the
collaping atom
parado)
-ohr1 Model Iail-ohr1 Model Iail
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@, Electron have propertie of "oth particle and +ave
ight E)hi"it Dnterferenceight E)hi"it Dnterference
Constructive interference:+ave .in:
phae7 create +ave of greater amplitude
4 they add5 estructive interference: +ave .out:of:
phae7 create +ave of lo+er amplitude
4they cancel out5
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@, Electron have propertie of "oth particle and +ave B
ight e)hi"it interference* and it alo haparticle nature
Electron* 2no+n to "e particle* alo
demontrate interference
&iffraction And Electron&iffraction And Electron
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An electron that .ecape7 from the nucleu
ha infinity for it /uantum num"er and6ero energy
-ohr1 4theoretical5 e/uation e)plain the
4empirical5 Ryd"erg e/uation
>>
>>
>>
$$$$
$$
or
+ith
54
hl
hl
lh
nnhc
b
lhnn
n
b
n
blh
hc
nnb
EEE
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The com"ination of contant* b/hc* ha a
value +hich differ from the e)perimentallyderived value ofRH"y only %,%B
-ohr1 effort to develop a general theory
of electronic tructure +a doomed "y the+aveparticle duality of electron
&e -roglie uggeted that the +avelength
of a particle of ma mmoving at peed v i
mvh
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Thi relation provide the lin2 "et+een the
decription a a particle and a a +ave Heavy o"3ect have very .hort7
+avelength o their matter +ave and the
+ave propertie go unnoticed Tiny particle +ith mall mae have
.long7 +avelength o their +ave propertie
are an important part of their "ehavior Wave com"ine in t+o +ay
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The contructive and detructiveinterference i called diffraction
Electron produce imilar pattern
!a" )aves in phase interfere constructively. !" *ut of phase
waves produce destructive interference. !c" )aves passing
through holes fan out and produce an interference pattern.
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There are t+o type of +ave' traveling
and standing
A tanding +ave i produced +hen a guitar
tring i pluc2ed' the center of the tringvi"rate* "ut the end remain fi)ed
#oint of 6ero +ave amplitude are called
nodes
'he wind produces
traveling waves on the
surfaces of la+es and
oceans.
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Ior guitar tring the only +ave are thoefor +hich a half:+avelength i repeated
e*actlya +hole num"er of time
Ior a trength of length+ith nan integerthi can "e +ritten
tanding waves on a guitar
string.
nn >
>'grearranginor
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Thee reult can "e ued to ho+ ho+
/uantum theory unite the +ave and particle
decription of a "ound electron
Conider the claical particle model of the
."ead on a +ire7
Df the electron 4particle5 ha ma mand
peedv
The 2inetic energy of the moving electron i
>
>$ mvE
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The &e -roglie relation connect model
4a5 and 4"5
!a" - classical model of theelectron as a ead on a wire. -nyenergy is possile and position ise$actly +nown. !" &lassicalmodel of the electron as astanding wave. !c" uantummechanical model comines !a"and !". /ar+ areas indicate
proale electron positions.
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The electron energy i /uanti6ed "ecaue it
depend on the integer n
The lo+et energy allo+ed i for n9$ or
E!h"/#m"4the energy cannot )e 'ero5
>
>>
>
>
8
>
>
>
>$>
>$
giveuing
'ngu"titutior
m
hn
n
m
hmh
mh
mvh
E
mmvE
v
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Electron trapped on a +ire have ome
reidual 2inetic energy* 3ut li2e electrontrapped in atom
'he spacing
etween levels is
proportional to
#
2
.
!a" - long wire. !"
- short wire.
'he
onger the wire, the
sma er the spacing
etween a owed
energy eve s.
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The +ave that correpond to the electron i
called a wave function The amplitude of the +ave function at a
given point can "e related to the
pro)a)ilityof finding the electron there
According to /uantum mechanic there are
region of the +ire +here the electron +ill
not "e found
Region of 6ero +ave function amplitude
are called node
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Dt i generally true that the more nodes an
electron has, the higher its energy Er+in SchrPdinger +a the firt to
uccefully apply the concept of the +ave
nature of matter to electronic tructure
He developed an e/uation that can "e
olved to give +ave function and energy
level for electron trapped in them
Wave function for electron in atom are
called or)itals
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!r"ital are characteri6ed "y a et of three
/uantum num"er'
n9 principle /uantum num"er, All
or"ital +ith the ave principle
/uantum num"er are in the ame shell,Allo+ed value' the et of poitive
integer,
l 9 econdary /uantum num"er +hichdivide the or"ital in a hell into
maller group called su)shells,
Allo+ed value' from % to 4n $5,
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1elationships etween
n
, , and
m
.
umer of
n m
ushell *ritals
0 0 s
2 0 0 2
s
, 0, 2
p
3
3 0 0 3s
, 0, 3p 3
2 2, , 0, , 2 3d 4
5 0 0 5s
, 0, 5
p
3
2 2, , 0, , 2 5d 4
3 3, 2, , 0, , 2, 3 5f 7
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The appro)imate energie of the u"hellin an atom +ith more than one electron'
Electron "ehave li2e tiny magnet
'he %uantum
numersassociated withthe first twoshells areshown.
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Electron +ithin atom interact +ith amagnet field in one of t+o +ay'
Electron pin i important in determiningelectronic tructure
Electrons can spin in either
direction in the presence of an
e$ternal magnetic field. 'his
gives rise to the spin %uantum
numer,
m
s
with allowed
values of 6 2 !spin up8" or 9
2 !spin down8".
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According to the "auli e*clusion principle
no two electrons in the same atom can haveidentical values for all four quantum
numbers
Thu t+o electron can occupy the ame
or"ital only if they have oppoite pin and
are aid to "e paired
A u"tance +ith more pin in one direction
i aid to contain unpairedelectron
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Su"tance +ith unpaired electron arelightly attracted to a magnet and are called
paramagnetic
Su"tance in +hich all electron are pairedare called diamagnetic
The ditri"ution of electron among the
or"ital of an atom i called the electronic
structureor electronic configuration
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To indicate the ground tate electronconfiguration +e can'
$5 it the u"hell that contain electron andindicate their electron population +ith aupercript,
>5 Repreent each or"ital +ith a circle and uearro+ to indicate the pin of each electron,
Electron configuration mut "e conitent+ith the #auli principle* auf"au principle*and Hund1 rule
E)ample' ( $s>>s>>p* (a $s>>s>>pKs$
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Electron configuration e)plain the
tructure of the periodic ta"le
'he periodic tale isdivided into regionsof 2, :, 10, and 15columns which is
the ma$imumnumer of electronsin s, p, d, and fsulevels.
ushells that fillacross the periods.
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Ior the repreentative element 4A Group5
the electron +ith the highet n value or
valence shellare normally the only
electron important for chemical propertie
Ior thee element the valence electrons
consist of just the s and p subshells
encountered crossing the period that
contains the element in question
E)ample' the valence configuration of"romine i
-r s>pB
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There are fe+ important e)ception to the
.e)pected7 electronic figuration of
commonly encountered element
Iollo+ing the rule for Cr* Cu* Ag* and Au
uing no"le ga notation'
$$%>?
$$%>?
$$%>?
$B>
KSeTBKSeTBCu
BSUrTBSUrTAg
SArTSArTCu
SArTSArTCr
alE)perimentE)pectedElement
sdsd
sdsd
sdsd
sdsd
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Apparently* half:filled and filled u"hell
are particularly ta"le
Similar irregularitie occur among the
lanthanide and actinide element
The poition of an electron mut "e
decri"ed +ith pro"a"ilitie
Heien"erg1 uncertainty principleay
that it i impoi"le to meaure +ith
complete preciion the velocity andpoition of a particle imultaneouly
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Thee limitation are not important for large
o"3ect "ut are very important for mall
particle li2e electron
Quantum mechanic re/uire that +e tal2
a"out the pro"a"ility of finding an electron
in a particular region of pace
Thi pro"a"ility i often repreented a an
electron clouda"out the nucleu
The pro"a"ility varie +ith ditance from
the nucleu
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Thi type of plot ho+ that electron
densityvarie from place to place Electron denity variation define the hape*
i6e* and orientation of or"ital
!a" - dotdensity
diagram for an
electron in a
s
orital. !" ;raph
of proaility
versus distance.
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por"ital are /uite different fromsor"ital
They poe a nodial plane +hich include
the nucleu and eparate the .lo"e7 ofhigh pro"a"ility
*ritals get larger as the
principle %uantum numer n
increases. odes, or regions
of (ero electron density,
appear eginning with the 2s
orital.
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Recall that there are three different or"italin eachpu"hell
/otdensity diagrams of
the cross section of the
proaility distriution of a
single !a" 2pand !" 3p
orital showing the nodal
plane.
'he directions of ma$imum electron
density lie along lines that are
mutually perpendicular. It is
convenient to lael the oritals as p
$
,
p
y
, and p
(
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The hape and orientation of dor"ital are
more complicated than forpor"ital
Shape and directional propertie of the
five dor"ital in a du"hell, Thefor"ital are even more comple) than
the dor"ital
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The amount of poitive charge .felt7 "y
outer electron in atom other than
hydrogen i called the effective nuclearcharge
Dt i lo+er than the atomic num"er "ecaue
of shielding
If the 2 charge of the1s2core of lithium were100< effective at
shielding the 2selectronfrom the nucleus, thevalence electron wouldsee8 a charge of 61.
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The effective nuclear charge felt "y outer
electron i determined primarily "y the
difference "et+een the charge on the
nucleu and the charge on the core
Effective nuclear charge control a num"er
of propertie
Atomic i6e increae top to "ottom in a group
"ecaue of increaing n and get maller left to
right in a group "ecaue the effective nuclearcharge increae
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Variation in atomic and ionic radii, Value
in picometer 4$%:$>m5
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The i6e trend in ion can "e ummari6ed'
#oitive ion are al+ay maller than the atom
they are formed
(egative ion al+ay larger than the atom
from +hich they are formed
-dding electrons leads toan increase in si(e of aparticle, as illustrated for
fluorine. emoving electronsdecreases the si(e of theparticle, as shown forlithium and iron.
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+oni'ation energy4DE5 i the energy
re/uired to remove an electron from an
iolated* gaeou atom
Succeive ioni6ation are poi"le until no
electron remain
The trend in DE are the oppoite of thetrend in atomic i6e
eg$g$ 5454
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=ariations in first
ioni(ationenergies.
Elements with the
largest ioni(ation
energies are in the
upper right of the
periodic tale. 'hose
with the smallest
ioni(ation energy are
at the lower left.
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=ariations in
successive
ioni(ation
energies. ote
that it is
e$tremely
difficult to rea+
into the nole
gas core !2
nd
through >
th
ioni(ations for #i
through ?,
respectfully.
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The electron affinity4EA5 i the potential
energy change aociated +ith the addition
of an electron to a gaeou atom or ion in it
ground tate
The addition of one electron to a neutral
atom i e)othermic for nearly all atom
The addition of more electron re/uire
energy
5454 g$eg$
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Conider the addition of electron to
o)ygen'
The reult for firt electron affinitie can
"e generali6ed
: :
: : >:
: >:
Change EA42Jmol5
!4g5 e ! 4 5 :$$
! 4g5 e ! 4 5 8
(et' !4g5 >e ! 4 5 @%
g
g
g
+
+ +
+ +
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Dn general' EA increae from left to right in a period
EA increae "ottom to top in a group
Meauring atomic maeMeauring atomic mae
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Meauring atomic maeMeauring atomic mae