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(n, l, ml, ms) ATOMIC ORBITALS
n l ml orbitals designation
1 0 0 1 1s
2 0 0 1 2s
1 -1,0,+1 3 2px,2py,2pz
3 0 0 1 3s
1 -1,0,+1 3 3px,3py,3pz
2 -2,-1,0,+1,+2 5 3dxy,3dyz,3dxz,
3dx2-y2,3dz2
4 … … … …
H Atom Orbital Energies
energy level diagram H atom
3s 3p 3d
2s 2p
1s
E
energy depends only on principal quantum number
orbitals with same n but different l are degenerate
1s
E
2s2p
3s3p
3d4s
4p5s
4d
MULTI-ELECTRON ATOM
orbitals with same n and different l are not degenerate
energy depends on n and ml
EXAMPLES [Xe]
EXP I
Periodic Table of the Elements
period
group
chemical reactivity - valence electrons
ns1 ns2
ns2np6
ns2(n-1)dx
cations are smaller than their atoms
anions are larger than their atoms
Na is 186 pm and Na+ is 95 pm
F is 64 pm and F- is 133 pm
same nuclear charge and repulsion among electrons increases radius
one less electron electrons pulled in by nuclear charge
O < O– < O2–
EXAMPLES
Which is bigger?
Na or Rb Rb higher n, bigger orbitals
K or Ca K poorer screening for Ca
Ca or Ca2+ Ca bigger than cation
Br or Br- Br smaller than anion
QUESTIONThe species F-, Na+,Mg2+ have relative sizes in the order
1 F-< Na+<Mg2+ 2 F-> Na+>Mg2+
3 Na+>Mg2+> F- 4 Na+=Mg2+= F-
5 Mg2+> Na+>F-
QUESTION
1 F-< Na+<Mg2+
2 F-> Na+>Mg2+
3 Na+>Mg2+> F-
4 Na+=Mg2+= F-
5 Mg2+> Na+>F-
Na+ is 95 pm
Mg2+ is 66 pm
F- is 133 pm
ALL 1s22s22p6
ALL are isoelectronic
3. IONIZATION ENERGIES
M(g) M+(g) + e-
energy required to remove an electron from a gas phase atom in its electronic ground state
I1 > 0
first ionization energy(photon)
M+(g) M2+(g) + e-
M2+(g) M3+(g) + e-
second ionization energy
third ionization energy
I2 > 0
I3 > 0
I1 > I2 > I3
Why?
electrons closer to nucleus more tightly held
ION
IZA
TIO
N E
NE
RG
Y
ION
IZA
TIO
N E
NE
RG
Y
first ionization energies decrease
d shell insertion
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9
GROUP NUMBER
ION
IZA
TIO
N E
NE
RG
Y(k
J/m
ol)
1 2 13 14 15 16 17 18
n=1
n=2
n=3
n=4
1. closed shells are energetically most stable
2. half-filled shells are energetically very stable
DERIVATION OF IONIZATION ENERGIES
4. ELECTRON AFFINITIES
the energy change associated with the addition
of an electron to a gaseous atom
X(g) + e– X–(g)
electron affinity can be positive or negative
-200
-100
0
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
ATOMIC NUMBER
-ELE
CT
RO
N A
FF
INIT
Y
H
He
Li
Be
B
C
N
O
F
Ne
Na
Mg
Al
Si
P
S
Cl
Ar