1 I. STRUCTURE OF SUBSTANCES I.2. Electronic configuration of the atoms Louis de Broglie (France)...

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I. STRUCTURE OF SUBSTANCESI.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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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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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 K L M N O P QPrincipal quantum number n

n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

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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 l = 0

p l = 1

d l = 2

f l = 3

g l = 4

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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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s orbital – has a spherical symmetry and it is characterized by the

magnetic quantum number m = 0.

z

x

y

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There are 3 p orbitals, oriented along the coordinate axis x-y-z.

The magnetic quantum number takes 3 values (m = -1 ; 0 ; +1)

z

x

y

z

x

y

z

x

y

z

x

yz

x

yz

x

y

px orbital py orbital pz orbital

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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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The d orbitals

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The f orbitals

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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)one f sublevel (l = 3) containing seven f orbitals f (m = ±3,±2,±1,0)


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Shell Principal quantum nr

Azimuthal quantum nr.

Magnetic quantum nr.

K n = 1 l = 0 m = 0

L n = 2 l = 0l = 1

m = 0m = -1 ; 0 ; +1

M n = 3 l = 0l = 1l = 2

m = 0m = -1 ; 0 ; +1m = -2 ; -1 ; 0 ; +1 ; +2

N n = 4 l = 0l = 1l = 2l = 3

m = 0m = -1 ; 0 ; +1m = -2 ; -1 ; 0 ; +1 ; +2m = -3 ; -2 ; -1 ; 0 ; +1 ; +2 ; +3

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I. STRUCTURE OF SUBSTANCESI.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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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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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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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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b) GOLDANSKI’S

chessboard

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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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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.

1 I. STRUCTURE OF SUBSTANCES I.2. Electronic configuration of the atoms Louis de Broglie (France)...

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