MULTIELECTRON ATOMS
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ELECTRON SPIN:
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PAULI'S EXCLUSION PRINCIPLE
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Electron has intrinsic angular momentum - “spin”; it behaves
as if it were “spinning”, i.e. rotating around its axis.
rotating charge  magnetic field - the electron is a magnetic
dipole.
S = sħ with s = 
remember: ħ = h/2 is the “unit of angular momentum”
(In units of angular momentum,) the electron has “spin”; it is a
member of the family of particles with “half-integer spin”,
called “Fermions”.
Fermions obey Pauli's exclusion principle.
direction of spin is “quantized”, i.e. only certain directions are
allowed.
For spin 1/2, only two directions are allowed - called “up” and
“down”.
No quantum mechanical state can be occupied by more
than one fermion of the same kind (e.g. more than one
electron).
MULTIELECTRON ATOMS
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The hydrogen atom, having only one electron, is a very simple
system; this is why Bohr's simple model worked for it.
Complications in atoms with many electrons:
 in addition to the force between electron and nucleus,
there are also forces between the electrons;
 “shielding”: electrons in outer orbits are shielded from
the force of the nucleus by electrons in the inner orbits.
  need to solve Schrödinger equation to describe multielectron atoms.
QUANTUM NUMBERS
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Schrödinger equation applied to atom :
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electron's energy, magnitude and direction of angular
momentum are quantized (i.e. only certain values
allowed);
no well-defined orbit, only probability of finding
electron at given position “orbital”;
the state of an electron is described by a set of four
quantum numbers:
 n, the principal quantum number
 l , the orbital quantum number
 ml= lz, the orbital magnetic quantum number
 ms= sz, the spin quantum number
Meaning of quantum numbers:
 the energy level of a state is determined by n and l

most probable value of distance grows with n

n = 1,2,3,….

l = 0,1,2,3,…, n -1 (i.e. n different values);
measures magnitude of angular momentum
in units of ħ ; value of l influences the energy and
the shape of the orbital:




l = 0 : spherical
l = 1 : dumbbell shaped,....
ml = 0, 1, 2,  l , i.e. (2 l + 1)
different values;
specifies direction of angular momentum (gives
component of angular momentum vector in specified
direction)  determines orientation of orbital
ms =   denotes direction of spin:
ms = +  “spin up”
ms =   “spin
orbitals
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Orbital shapes
Electron “shells”
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Some definitions:
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collection of orbitals with same n: “electron shell”;
shells named K,L,M,N,..
one or more orbitals with same n and l : “subshell”;
spectroscopic notation for orbitals:
orbitals denoted by value of n and a letter code
for the value of l :
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l
l = 0: s
l = 1: p
l = 2: d
l = 3: f
l = 4: g
and alphabetic after that;
e.g.: “2s” refers to the subshell n=2, =0;
number of electrons in the subshell is added as
a superscript;
e.g.: “2p6 means a configuration where 6 electrons are
in the subshell 2p, i.e the subshell with n = 2 and l = 1.
PAULI EXCLUSION PRINCIPLE  :
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No two electrons in the same atom can have the same set
of four quantum numbers
 the number of electrons in a given subshell is limited to
2x(2l + 1) (factor of 2 is due to orientation of spin),
number of electrons in a given shell is limited to 2n2 .
 in multi-electron atom, electrons cannot all sit in
the lowest energy levels.
Electron configurations of the elements
Periods 1,2,

1s
1
2
3
4
5
6
7
8
9
10
H
He
Li
Be
B
C
N
O
F
Ne
2s
1
2
2
2
2
2
2
2
2
2
3,
4
1s 2s 2p 3s 3p
2p
11 Na 2 2 6 1
1
2
2
2
2
2
2
2
12 Mg 2 2 6 2
13 Al 2 2 6 2 1
1
2
3
4
5
6
14 Si 2 2 6 2 2
15 P
2 2 6 2 3
16 S
2 2 6 2 4
17 Cl 2 2 6 2 5

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
period 5
18 Ar 2 2 6 2 6
1s
2s
2p 3s
3p 4s
3d
4p 5s
4d
5p
Rb 2
Sr 2
Y 2
Zr 2
Nb 2
Mo 2
Tc 2
Ru 2
Rh 2
Pd 2
Ag 2
Cd 2
In 2
Sn 2
Sb 2
Te 2
I 2
Xe 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
1
2
4
5
5
7
8
10
10
10
10
10
10
10
10
10
1
2
3
4
5
6
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
1
1
2
1
1
1
2
2
2
2
2
2
2
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
1s
2s
2p 3s
3p 4s
3d
4p
K 2
Ca 2
Sc 2
Ti 2
V 2
Cr 2
Mn 2
Fe 2
Co 2
Ni 2
Cu 2
Zn 2
Ga 2
Ge 2
As 2
Se 2
Br 2
Kr 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
1
2
3
5
5
6
7
8
10
10
10
10
10
10
10
10
1
2
3
4
5
6
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
2
2
2
2
Electron configuration,
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cont’d
Period 6
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
1s
2s
2p 3s
3p 4s
3d
4p 5s
4d
5p 6s
Cs 2
Ba 2
La 2
Ce 2
Pr 2
Nd 2
Pm 2
Sm 2
Eu 2
Gd 2
Tb 2
Dy 2
Ho 2
Er 2
Tm 2
Yb 2
Lu 2
Hf 2
Ta 2
W 2
Re 2
Os 2
Ir 2
Pt 2
Au 2
Hg 2
Tl 2
Pb 2
Bi 2
Po 2
At 2
Rn 2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
2
2
2
2
2
2
2
4f
1
3
4
5
6
7
7
9
10
11
12
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
5d
6p
1
1
1
1
2
3
4
5
6
7
9
10
10
10
10
10
10
10
10
1
2
3
4
5
6
Electron configuration,
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cont’d
Period 7
1s 2s
87 Fr 2
88 Ra 2
89 Ac 2
90 Th 2
91 Pa 2
92 U 2
93 Np 2
94 Pu 2
95 Am 2
96 Cm 2
97 Bk 2
98 Cf 2
99 Es 2
100Fm 2
101Md 2
102No 2
103Lr 2
104Rf
105Db
106Sg
107Bh
108Hs
109Mt
110Uun
111Uuu
112Uub
113Uut
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1s 2s
2p 3s
3p 4s
3d
4p 5s
4d
5p 6s
4f
5d
6p 7s
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
3d
4p 5s
4d
5p 6s
4f
5d
6p 7s
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2p 3s
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3p 4s
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
2
2
5f
2
3
4
6
7
7
9
10
11
12
13
14
14
14
14
14
14
14
14
14
14
14
14
5f
6d 7p
1
2
1
1
1
1
1
2
3
4
5
6
7
9
10
10
10 1
6d 7p