Transcript s orbital

I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
Louis de Broglie (France) and Werner Schrödinger (Austria) in the
mid 1920s, suggested that like a light, the electron has both wave and
particle properties.
When Schrödinger carried out a mathematical analysis based on
this idea, he obtained a new model for the atom: wave model.
In this model the electron has not a well defined orbit. The motion
of the electron seems to be rather a vibration. The three-dimensional
region of space around the nucleus where we can find the electron is
called orbital. In fact, it is a region of probability where the electron is
likely to be found.
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
The electronic configuration represents the distribution of electrons
of an atom in shells, subshells and orbitals. All the electrons which have the
same mean path from the nucleus form a main energetic level or main
electronic shell.
The state of an electron in an atom is completely described by
four quantum numbers:
• principal quantum number, n – correspond to the main energetic shells
• azimuthal quantum number, l – correspond to the sublevels
• magnetic quantum number, m – describes the shape of the orbitals
• spin quantum number, s – describes the rotation of the electron around
its own axis. It can take two values: +1/2 or -1/2.
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
There are 7 main shells. The first main shell is the closest to the
nucleus and it has a minimum energy. It is denoted by K and has the
principal quantum number n = 1.
Energetic level
Principal quantum
number n
K
L
M
N
O
P
Q
n=1 n=2 n=3 n=4 n=5 n=6 n=7
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
Each electronic level is made up of one or more subshells or
sublevels, which in turn contain one or more orbitals. There are the
following subshells:
Subshell
Azimuthal quantum number
s
p
d
f
g
l
l
l
l
l
=
=
=
=
=
0
1
2
3
4
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
The orbital is a region of space around the nucleus where there is
more likely to found the electrons.
There are several types of orbitals:
Orbital
Shape
Magnetic quantum number
s orbital
spherical shape
m=0
p orbital
two lobes
m = -1; 0; +1
d orbital
four lobes
m = -2; -1; 0; +1; +2
f orbital
complex shape and symmetry m = -3; -2; -1; 0; +1; +2; +3
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
s orbital – has a spherical symmetry and it is characterized by the
magnetic quantum number m = 0.
y
z
x
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
There are 3 p orbitals, oriented along the coordinate axis x-y-z.
The magnetic quantum number takes 3 values (m = -1 ; 0 ; +1)
y
y
y
y
z
z
z
z
x
x
px orbital
y
y
z
z
x
x
py orbital
x
x
pz orbital
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
There are 5 d orbitals, with the shape of four lobes oriented
differently in space. The magnetic quantum number can take 5
values (m = -2 ; -1 ; 0 ; +1 ; +2).
There are 7 f orbitals, with complex shape and geometry. The
magnetic quantum number can take 7 values (m = -3; -2 ; -1 ; 0 ;
+1 ; +2; +3).
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
The d orbitals
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
The f orbitals
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I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
K shell (n = 1) consists of 1 sublevel:
one s sublevel (l = 0) containing one single s orbital (m = 0)
L shell (n = 2) consists of 2 sublevels:
one s sublevel (l = 0) containing one single s orbital and (m = 0)
one p sublevel (l = 1) containing three p orbitals (m = -1, 0, +1)
M shell (n = 3) consists of 3 sublevels:
one s sublevel (l = 0) containing one single s orbital and (m = 0)
one p sublevel (l = 1) containing three p orbitals (m = -1, 0, +1)
one d sublevel (l = 2) containing five d orbitals (m = ±2, ±1, 0)
N shel (n = 4) consists of 4 sublevels:
one s sublevel (l = 0) containing one single s orbital and (m = 0)
one p sublevel (l = 1) containing three p orbitals (m = -1, 0, +1)
one d sublevel (l = 2) containing five d orbitals (m = ±2, ±1, 0)
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one f sublevel (l = 3) containing seven f orbitals f (m = ±3,±2,±1,0)
I. STRUCTURE OF SUBSTANCES
I.2. Electronic configuration of the atoms
Shell
Principal
quantum nr
Azimuthal
quantum nr.
Magnetic quantum nr.
K
n=1
l=0
m=0
L
n=2
l=0
l=1
m=0
m = -1 ; 0 ; +1
M
n=3
l=0
l=1
l=2
m=0
m = -1 ; 0 ; +1
m = -2 ; -1 ; 0 ; +1 ; +2
N
n=4
l
l
l
l
m
m
m
m
=
=
=
=
0
1
2
3
=
=
=
=
0
-1 ; 0 ; +1
-2 ; -1 ; 0 ; +1 ; +2
-3 ; -2 ; -1 ; 0 ; +1 ; +2 ; +3
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
An orbital can be empty or it can contain one or maximum two
electrons. If two electrons occupy the same orbital, they must have
opposite spins, associated with spin quantum number s, which may be
±1/2.
The electron configuration is the arrangement of electrons on
shells, subshells and orbitals. Electrons fill low energy orbitals, closer to
the nucleus, before they fill higher energy ones.
The order of energy levels is not identical to the principal
quantum number, due to the interaction between electrons and nucleus.
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
The electron configuration is the arrangement of electrons on shells,
subshells and orbitals.
The electron configuration of an atom can be established according to
the following rules:
1) The principle of increasing energy
2) Pauli’s exclusion principle
3) Hund’s rule
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
1) The principle of increasing energy
Electrons fill low energy orbitals, closer to the nucleus, before they fill
higher energy ones.
The order of energy levels is not identical to the principal quantum
number, due to the interaction between electrons and nucleus.
1s 2s2p 3s3p3d 4s4p4d4f...............
The order in which electrons occupy orbitals can be established using the
minimum (n+l) rule or GOLDANSKI’S chessboard.
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
a) Minimum (n+l) rule: the electronic levels and sublevels will
be filled in the increasing order of the sum of the principal
quantum number and the orbital one. For the same n + l, the low
energy corresponds to the orbital with the lower n.
The order is:
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p
n
1
2
3
4
5
6
l
0
0
1
0
1
2
0
1
2
3
0
1
2
3
4
0
1
2
3
4
5
s
s
p
s
p
d
s
p
d
f
s
p
d
f
g
s
p
d
f
g
h
n+l 1
2
3
3
4
5
4
5
6
7
5
6
7
8
9
6
7
8
9
10
11
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
b) GOLDANSKI’S
chessboard
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
2. Pauli’s exclusion principle
Two electrons in an atom cannot have all four quantum
numbers identical.
If two electrons exist in the same orbital (they have
identical principal number, orbital and magnetic ones) these
electrons must have opposite spins (different spin numbers).
Maximum number of electrons in an electronic shell with
principal number n is 2.
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I. STRUCTURE OF SUBSTANCES
I.3. The order of filling orbitals
3. Hund’s rule
When orbital of identical energy are available,
electrons occupy these singly, rather than in pairs. As a
result, an atom tends to have as many unpaired electrons
as possible.
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