cm1502 chapter 2 -2013-14
TRANSCRIPT
-
8/21/2019 CM1502 Chapter 2 -2013-14
1/40
Electron configuration
and chemical periodicity.
1
Chapter 2
CM1502
1
-
8/21/2019 CM1502 Chapter 2 -2013-14
2/40
Need to now solve:
212121
,,, rrrrrr EH
Our wavefunction now depends on r1and r2,
i.e., (x1, y1, z1)and (x2, y2, z2)
Consider the He Atom
If a second electron is added to our atom (eg: H-or He), two newinteractions come into existence.
1. Attraction of the second electron to the nucleus, and
2.repulsion of the second electron by the first.
The Hamiltonian should include these interactions.
K.E. for e 1
12
2
2
2
1
2
0
21
22
4
1
r
e
r
e
r
eKKH
K.E. for e 2P.E. e 1 to nuc
P.E. e 2 to nuc
P.E. e-e rep
Adding a Second Electron
2
-
8/21/2019 CM1502 Chapter 2 -2013-14
3/40
No Exact Solution
!"#$# &' () #*+,- ')./-&)( -) -"&' #0/+-&)(1 !"# %!"
"&'&( )&2
3*+,- ')./-&)(' ,+( )(.4 #*&'- 5)$ '4'-#6' 7&-" )(#
#.#,-$)(1 &*+*1 81 8#91 :&;91 8;91 #-,2
!"&' &' + -"$##4 ?$)=.#61 @/'- .&A# -"# )$=&- )5 -"#
B/(
-
8/21/2019 CM1502 Chapter 2 -2013-14
4/40
Solving the Schrdinger Equation
G)$ '6+.. +-)6' +(> 6).#,/.#'1 7# ,+( >) -"&' ()7 5)$ +..?$+,-&,+. >#H$##' )5 ?$#,&'&)(1 /'&(H ,)6?/-#$'
I '&6?.# +??$)*&6+-&)(-) "#.? ').J# -"# B,"$K>&(H#$ 30/+-&)( &'-"# ') ,"#&-&"#&". -!(.,%/& 01#&/2
!"+- &'1 7# 7$&-#: (r1,r2 1(r1)2(r2).
8#$# 4L&' -"# +-)6&, )$=&-+. )5 #.#,-$)( L -"+- 6)J#' +' &51#.#,-$)( ; &' ()- ?$#'#(-2
B) 7"#( 4)/ 7$&-# L';5)$ -"# ,)(5&H/$+-&)( )5 8#1 7"+- 4)/ +$#+,-/+..4 7$&-&(H &'M (r1,r2 s(r1) s(r2)
4
-
8/21/2019 CM1502 Chapter 2 -2013-14
5/40
Atomic Orbital(AO) Energy and Total
Electronic Energy Solution to Schrdinger equation for systems with more than one electron
(using computers) results in two types of energies, 1. AO energies and
2. the total electronic energy.
For the H atom, the energy of an AO is equal to the total electronic energyof the H atom since it has only 1 electron.
Energy of a electron in a particular AO depends on several factors,the three relevant ones here are
The attraction felt by the electronbetween itself and thenucleus. i.e., the effective nuclear charge that the electron
experiences, Zeff. The repulsion of the electron with remaining electrons in theatom. e-e repulsion
Orbital Shape
This means the energy of an electron in 4s AO in one atom,is different to
the energy of an electron in the 4s AO of another atom. 5
-
8/21/2019 CM1502 Chapter 2 -2013-14
6/40
Zeffand Screening
Consider He
electron 1 blocks out some of the positivecharge of the nucleus so that electron 2does not get to see the full +2 charge(andvise versa).
Because of screening the effective nuclearcharge, Zeff, of He is 1.69 instead of 2.
It is illustrated in this movie(ILVE workbin-videos-Effective nuclear charge)
6
http://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/042_EffectiveNuc.movhttp://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/042_EffectiveNuc.mov -
8/21/2019 CM1502 Chapter 2 -2013-14
7/40
7
355#,-&J# (/,.#+$ ,"+$H# >#?#(>' )(
L2 N/,.#+$ ,"+$H#
;2 B".>&(H =4 -"# #.#,-$)(' &( -"# '+6# #(#$H4 .#J#.
O2 B".>&(H =4 -"# #.#,-$)(' &( -"# &((#$ #(#$H4 .#J#.
-
8/21/2019 CM1502 Chapter 2 -2013-14
8/40
Zeffand Screening
For the H atom, the 2sand 2porbital have the same energy.
Screening occurs when there is more than 1 electron (cf. He).
The third electron in Li occupies 2s sublevel rather than 2p.Why?
Zeffis larger for the 2sthan 2p, but why?
We have to consider orbital shapes, that is radial probabilitydistributions.
8
-
8/21/2019 CM1502 Chapter 2 -2013-14
9/40
Orbital Penetration
2p orbital (orange curve) is slightly closer
to the nucleus than the maxima of the 2s
orbital (blue curve).
But small portion of 2s radial probabilitydistribution peaks with the 1s region.
Thus an electron in the 2s orbital spends
part of its time penetrating very close tothe nucleus.
9
-
8/21/2019 CM1502 Chapter 2 -2013-14
10/40
10
Penetration has two effects:
It increases the nuclear attraction for a 2s electron overthe 2p electron
It decreases the shielding of a 2s electron by the 1s
electron.
As a result an energy level splits into sublevels of differingenergy. The lower the /value of the sublevel, the
penetration is higher and hence greater the attraction
to the nucleus. Order of sublevel energies: s
-
8/21/2019 CM1502 Chapter 2 -2013-14
11/40
Electron spin quantum number This is the property of an electron and not the orbital.
Each electron behaves like a spinning charge and generates atiny magnetic field.
The two fields have opposing directions.
So half of the electrons are attracted by the large external
magnetic field while other half is repelled.
This gives rise to the spin quantum number mswith allowed
values of +1/2(spin up) or -1/2 (spin down)
11
-
8/21/2019 CM1502 Chapter 2 -2013-14
12/40
Paulis Exclusion Principle
N) -7) #.#,-$)(' &( + H&J#( +-)6 ,+( "+J# -"# #*+,-
'+6# '#- )5 0/+(-/6 (/6=#$'2
G)$ -"# 8# +-)61 -"# ,)(5&H/$+-&)( L';6#+(' -"+-
)(# #.#,-$)( "+' -"# 0/+(-/6 (/6=#$'"P L1 /P Q1 0/P Q1 02P 9R1+(> -"# )-"#$
"P L1 /P Q1 0/P Q1 02P ()- "+J# -"# ,)(5&H/$+-&)( L'O1 '&(,# -"#
-"&$> #.#,-$)( 7)/.> "+J# -) H#- -"# '+6# '#- )5
0/+(-/6 (/6=#$' +' )(# )5 -"# )-"#$ -7)2
12
-
8/21/2019 CM1502 Chapter 2 -2013-14
13/40
The Aufbau Principle
E' + $/.# 5)$ 5&(>&(H -"# .)7#'- #(#$H4#.#,-$)( ,)(5&H/$+-&)(5)$ +-)6'2
E- '-+-#' -"+- 4)/ 6/'- !## .3& &/&%.(1"241"& !. ! .,0&4 ,".1 .3& 1(),.!/2 .3!.
516/# 0!7& .3& !.10 012. 2.!)/&4 )6.1)&8,"+ .3& 9!6/, &:%/62,1" -(,"%,-/& !.
!// .,0&22
S4 T6)'- '-+=.#U 7# 6#+( .)7#'- J+./#
-) -)-+. #.#,-$)(&, #(#$H4132
13
-
8/21/2019 CM1502 Chapter 2 -2013-14
14/40
Stable Electronic Configurations
!"# )$>#$ )5 5&..&(H IV &' =#'-$#6#6=#$#> =4 ?&,-/$&(H -"#?#$&)>&, -+=.# &( 4)/$ 6&(>2
!"# -+=.# -) -"# $&H"- &../'-$+-#'-"&'2
1s2s 2p
3s 3p
4s 3d 4p
5s 4d 5p
6s 4f 5d 6p
7s 5f 6d 7p
Orbitals Filled
You should be able to give
ground state (most stable
state) electronic
configurations for any
element in the periodic tablegiven the Z only.
14
-
8/21/2019 CM1502 Chapter 2 -2013-14
15/40
Hunds Rule of Maximum Multiplicity
W+$- LM X#H#(#$+-# )$=&-+.' Y/Z Q[ +$# +.7+4' 5&..#> 7&-" '&(H.##.#,-$)(' =#5)$# +(4 )5 -"#6 +$# >)/=.4 ),,/?>2
D !"&' $#>/,#' #.#,-$)( -) -")'# ?+&$' 7"#$# -"#&$
'?&(' +$# )??)'&-#2D !"&' .#+>' -) #J#( .#'' #.#,-$)(
-
8/21/2019 CM1502 Chapter 2 -2013-14
16/40
Orbital Occupancy Diagram
The species with unpaired electrons
exhibits paramagnetism;it is attracted byan external magnetic field.
The species with all of its electrons
paired exhibits diamagnetism; it is not
attracted by an external magnetic field.
16
-
8/21/2019 CM1502 Chapter 2 -2013-14
17/40
17
-
8/21/2019 CM1502 Chapter 2 -2013-14
18/40
Distribution of electrons
The electron configuration
nl#of electrons in the sublevel
as s,p, d, f
The orbital diagram (box or circle)
!"#$# +$# -7) ,)66)( 7+4' -) &(>&,+-# -"# >&'-$&=/-&)( )5 #.#,-$)('2
These configurations actually
represent electronic wave
functions i.e., approximatesolutions to the Schrdinger
equation.
The electronic configurations
and AO stability is responsible
for the periodic properties
observed in the elements.
The method of writing the electronic configuration
is illustrated in this movie(ILVE workbin-videos-Electronic configuration) 18
http://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/042_EffectiveNuc.movhttp://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/042_EffectiveNuc.mov -
8/21/2019 CM1502 Chapter 2 -2013-14
19/40
A periodic table of partial, ground-state electron
configurations.
19
-
8/21/2019 CM1502 Chapter 2 -2013-14
20/40
Stability of AOs with different nand l
7"4 >)#' ] +(> ^+ ),,/?4 -"# _' IV =#5)$# -"# O>F
_' ?#(#-$+-#' =#--#$ &(-) -"# L';;';;?`O';O?`,)$# -"+( +(4 O> IV >)#'2
7"4 +$# #.#,-$)(' $#6)J#> 5$)6 -"# _' IV /?)( &)(&a+-&)( )5 + -$+('&-&)(6#-+.' &( -"# _-"?#$&)>1
&*+*G#;9"+' -"# ,)(5&H/$+-&)( bI$c_'QO#`F
!"# O> IV &' $+?&>.4 =#,)6&(H 6)$# '-+=.# 5)$ 5/$-"#$ #.#6#(-'2 d"4F
D S4 +>>&(H L #.#,-$)( -) -"# _' &( ]1 7# 5&(> -"+- -"&' "+$>.4 ',$##(' -"# O>YO> 6+*&6/6 ,.)'#$ -"+( -"# _' 6+&( 6+*&6/6[1 ') +(4 O> # 7)/.> H+&( +(+.6)'- 5/.. &(,$#+'# )5 9L 5)$ &-';#552
D G)$ -"# '+6# $#+')(1 +>>&(H + '#,)(> #.#,-$)( -) -"# _' &( ^+1 "+$>.4',$##(' +(4 #.#,-$)( -"+- 6&H"- =# 5)/(> &( -"# O>
D -"/' -"# O> )$=&-+. >$)?' '-&.. 5/$-"#$ &( #(#$H42
D G&(+..4 +- B,1 -"# O> IV )&%10&2 !"#$2.!)/& .3!"
-"# _' IV1 +(> $#6+&(' ') 5)$ -"# $#'- )5 -"##(-&$# ?#$&)>&, -+=.#2
20
-
8/21/2019 CM1502 Chapter 2 -2013-14
21/40
Why isnt the lowest energy electronic
configuration of Sc [Ar]4s03d3?
The answer to this question lies
in electron-electron repulsion.
The extent of an n= 3AO is
significantly less than n= 4 AO.
Electrons in the 3d AO repel
each other more than electrons
in a 4s AO.
erepulsion(3d,3d) > erepulsion(3d,4s) > erepulsion(4s,4s).
E
21
-
8/21/2019 CM1502 Chapter 2 -2013-14
22/40
Anomalous Configurations 1
8#$# #
-
8/21/2019 CM1502 Chapter 2 -2013-14
23/40
AnomalousConfigurations 2
^/ "+' -"# ,)(5&H/$+-&)( _'LO>LQ
!"# #(#$H4 H+? =#-7##( O> +(> _' &' .+$H# #()/H"-) )J#$,)6# -"# &(,$#+'# &( #(#$H4 >/# -) #2
D !"# $#+')( 5)$ +()6+.' 5)$ f/1 f"1 W> +(> IH+$# -"# '+6# +' 7#..1 #*,#?- 7# +$# -+.A&(H +=)/--"# _> +(> e' $+-"#$ -"+( -"# O> +(> _' IV'2
23
-
8/21/2019 CM1502 Chapter 2 -2013-14
24/40
The consistent changes in properties such as atomic size, Ionization
energies etc within a group or period are called periodic properties.
Periodic Properties of the Elements
An understanding of how Zeffand nvary in the periodic table as wellas the most stable electronic configurations, helps us to understandthe trends in the following properties:
Ionization Energy.
Electron Affinity.
Atomic Radius.
Electronegativity.
Oxidation states (which we will not discuss, but you may reviewfor your own interest in the movie(IVLE workbin-videos-Oxidations states)
24
http://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/045_CommonOxiSta.movhttp://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/045_CommonOxiSta.mov -
8/21/2019 CM1502 Chapter 2 -2013-14
25/40
25
Moving across a period,
nis constant, and Zeffincreases.
Moving down a group
Zeffincreases somewhat, but nincreases by
one unit
Zeffand n
-
8/21/2019 CM1502 Chapter 2 -2013-14
26/40
Atomic Radii There are different types of atomic radii.
Covalent radii (also unfortunatelysometimes called Atomic radii)
!the distance between the nuclei of single bondedatoms, e.g., Cl2
Metallic radius is one-half the shortestdistance between nuclei of adjacent individual atoms in a
crystal of an element, e.g., Fe(S)
Ionic radii Obtained from solids that exhibit ionic bonding, e.g.,
NaCl.
van der Waals radii
The radius of the sphere surrounding the nucleus that
contains 98% of the electron density. 26
P i di it i At i R dii
-
8/21/2019 CM1502 Chapter 2 -2013-14
27/40
27
Periodicity in Atomic Radii
P i di it i At i R dii
-
8/21/2019 CM1502 Chapter 2 -2013-14
28/40
Varies in a systematic way along the group and the period.
Review the trend in the movie (IVLE-workbin-videos-atomicradii)
From the radial distribution for a hydrogenic atomwe have
rnln2/Zeff
,
where nand lrefer to the highest occupied AO (HOAO).
Moving across a period,nis constant, but Zeffincreases,so the radii decrease.
Moving down a groupZeffincreases somewhat, but n2
increases more, so the radii increase.
28
Periodicity in Atomic Radii
-
8/21/2019 CM1502 Chapter 2 -2013-14
29/40
Ionic Radii
E- &' + 6#+'/$# )5 '&a# )5 +( &)(+(> &' )=-+&(#> 5$)6
-"# >&'-+(,# =#-7##( -"# (/,.#& )5 +>@+,#(- &)(' &( +,$4'-+..&(# &)(&, ,)6?)/(>2
^+-&)(' +$# '6+..#$-"+( ?+$#(- +-)6' +(> +(&)('
+$# .+$H#$-"+( -"#&$ ?+$#(- +-)6'2
^+-&)( '&a# >#,$#+'# 7&-" -"# ,"+$H#
#2HM G#O9&' '6+..#$ -"+( G#;9
X)7( -"# H$)/? &)(&, '&a# &(,$#+'#'2
I,$)'' -"# ?#$&)> -"# ?+--#$( &' ,)6?.#*2
29
-
8/21/2019 CM1502 Chapter 2 -2013-14
30/40
Ionic Vs Atomic radii
30
Notice the trend in
the sizes for anisoelectronicseries like N3-, O2-,F-, Na+, Mg2+, Al3+.
Isoelectronic the sameelectronicconfiguration
(s2p6).
-
8/21/2019 CM1502 Chapter 2 -2013-14
31/40
Ionization Energy (IE)
The first IE is defined as the energy needed to remove the most weakly
bound electroni.e., the electron from the Highest Occupied Atomic Orbital
(HOAO).
This process requires energy to overcome their electrostatic attraction.
Hence IE is always positive.
The second, third and continuing IE correspond to removing theeasiest electron from A+, A2+, etc.
For a given element there is an increase in IE1, IE2,IE3..etc
This is because each electron is pulled away from a species witha higher positive charge.
31
Review the trend seen in the 1st, 2nd, and 3rd IE via the movie
(IVLE workbin-videos-Ionization Energy)
http://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/047_IonizationEner.movhttp://users/MinhT/Dropbox/NUS/CM1502/Lecture%20note/047_IonizationEner.mov -
8/21/2019 CM1502 Chapter 2 -2013-14
32/40
Periodicity in the first IE For a given period as wemove from left to right,the IE increases.
This is because Zeffincreases from left toright.
The IE falls slowly downa group.
nincreases as wemove down a group,Zeffalso increases, but
slowly.
The increase in ndominates over the
gradual increase in Zeff.
322
2
eff
n
ZkE
n
Orbital energies very roughly follow
the Bohr formula:
-
8/21/2019 CM1502 Chapter 2 -2013-14
33/40
33
Little glitches occur at Be-B and N-O.
For Be-B, With the 2p> 2sthe
IE is therefore lower in B cf. Be.
For N-O, N has half filledpsub-shell, so the 4thelectron to enter thepsub shell in O is forced topair with another electron and produces significante-e repulsion. This increases the orbital energy,and hence reduces the IE.
-
8/21/2019 CM1502 Chapter 2 -2013-14
34/40
34
Electron AffinityDefined as the energy required to remove the least tightly
bound electron from an singly charged anion, A-.
Forming an A-depends on the stability and availabilityof an AO to hold the extra electron.
EA are always smaller than IE because there is very
little attraction between an e and a neutral atom at longdistances compared with an e and a positively charged
atom.
-
8/21/2019 CM1502 Chapter 2 -2013-14
35/40
35
Periodicity in the first EA
Those elements that require energy to add an electron are assigned an EA of zero.
!"# -$#(>' +$#
()- $#H/.+$2
!"#$# &' +()J#$+.. &(,$#+'#
5$)6 .#5- -) $&H"-
+(> >#,$#+'#
>)7( -"# H$)/?2
-
8/21/2019 CM1502 Chapter 2 -2013-14
36/40
Trends in metallic behavior.
!"# -4?&,+. =#"+J&)$ )5 6#-+.' &' -).)'# #.#,-$)(' -) ()(#,$#+'#
&( '&a#1 +( &(,$#+'# &( E3 +(> +
6)$# 5+J)/$+=.# 3I
E- &(,$#+'#' >)7( -"# H$)/?&(
-"# ?#$&)>&, -+=.#
+ >#,$#+'# &( E32
36
-
8/21/2019 CM1502 Chapter 2 -2013-14
37/40
Redox and Acid base behavior
!"# #.#6#(-' 7&-" .)7 E3 +(> '6+..3I Y#HMH?L1;[ +$# '-$)(H $#>/,&(H+H#(-'2
!"# #.#6#(-' 7&-" "&H" E3 +(> .+$H#3I Y#HM H? L` +(> Lg[ +$# '-$)(H
)*&>&a&(H +H#(-'2
I' -"# #.#6#(-' =#,)6# 6)$#6#-+..&,>)7( -"# H$)/?1 -"#&$)*&>#' =#,)6# 6)$# =+'&,2
I' -"# #.#6#(-' =#,)6# .#''6#-+..&, +,$)'' + ?#$&)>1 -"#&$ )*&>#'=#,)6# 6)$# +,&>&,2
37
-
8/21/2019 CM1502 Chapter 2 -2013-14
38/40
Electronegativity ()
Several definitions exist, but all give very similar results.
is proportional to the average of the ionization energy and electron affinity.
has no units(review its overall trend in the movie (IVLE workbin-videos-electronegativity).
If an element can readily give up an electron (low IE), and is not interested inaccepting an electron (small EA), then it will have a low , e.g., Na.
If an element does not easily ionize (high IE), and is quite interested in acceptingan electron (large EA), then it will have a high , e.g., F.
Small values of favor electron donation, whereas large values favor acceptingelectrons.
Metals have small values of , whereas nonmetals have large values.
Chemical bonds between atoms with large differences in have strong ioniccharacter.
Chemical bonds between atoms with similar valuesare largely covalent.
38
-
8/21/2019 CM1502 Chapter 2 -2013-14
39/40
39
IE (eV), EA (eV) and EN(Pauling scale) of elements
-
8/21/2019 CM1502 Chapter 2 -2013-14
40/40
Summary Anomalous electronic configurations can be understood by considering the
overall stability of a particular electronic configuration.
An understanding of how Zeffand nvary in the periodic table as well as the most
stable electronic configurations is enough to understand the trends in the
following properties.
Ionization Energy
Roughly follows Zeff2/n2, with some differences seen in the transition metals.
Electron Affinity
Depends on the stability and availability of an AO in a neutral atom to hold
the extra electron.
Atomic Radius Roughly follows n2/Zeff.
Electronegativity.
Proportional to the average of IE and AE.
Provides much insight into the nature of chemical bonds (covalent, ionic, and
b l t d t th h th t i d ti !)40