Generalities on the atomic structure

Generalities

The atom is composed of three types of particles: protons, neutrons and electrons.

Electrons have an electric charge of \(-1.6 \times10^{-19}\) Coulombs (C) and a mass of \(9.8 \times 10^{-28}\) grams. Protons have an electric charge of \(+1.6 \times 10^{-19}\) Coulombs and a mass of \(1.67 \times 10^{-24}\) grams. Neutrons have no electric charge and a mass of \(1.675 \times 10^{-24}\) grams.

The nucleus is made up of N particles:

\(Z\) protons and \((N - Z)\) neutrons. The mass number A corresponds to the total of neutrons and protons. The relation between the radius of the atom \(R\) and the radius of the nucleus \(r\) is given by \(R/r =10^5\).

Note that for a given chemical element, characterized by its atomic number \(Z\), several isotopes can exist, each containing the same number of protons but a different number of neutrons.

Electrons in atoms

Revolving around the nucleus, \(Z\) electrons occupy discrete orbitals, characterized by four quantum numbers. It is impossible to simultaneously define the position and momentum of an electron. We therefore define the probability of presence of the electron in an orbital which can be represented by an ellipse with the nucleus as base point. An orbital can be defined by:

  • the principal quantum number which characterizes the large axis of the ellipse or shell: shell \(K\) \((n=1)\), shell \(L\) \((n=2)\), ....., shell \(Q\) \((n=7)\);

  • the azimuthal quantum number \(l\) that characterizes the small axis of the ellipse \((0 ≤ l ≤ n-1)\) or sub-shell: sub-shell \(s\) \((l=0)\), sub-shell \(p\) \((l=1)\), subshell \(d\) \((l=2)\) and sub-shell \(f\) \((l=3)\);

  • the magnetic quantum number \(m\) which characterizes the inclination of the orbital plane in relation to the magnetic moment of the nucleus \((-l ≤ m ≤ +l)\);

  • the spin quantum number which characterizes the two possibilities of the electron's rotation around itself (spin down\(- 1/2\) or spin up \(+ 1/2\)).

Shell and sub-shell filling principle

According to the Pauli exclusion principle, electron states cannot hold more than two electrons, which must have opposite spin. In other words, no pair of electrons can have the same quantic numbers. The order of filling the electron states by \(Z\) electrons is related to the principle of occupying the lowest energy states (see following table).

Each shell contains a maximum of \(n\) contient au maximum \(2n^2\) electrons. For example, in shell \(K\) \((n=1)\),, two electrons with opposite spin can be present; they are in sub-shell \(s\) \((l=0)\). In shell \(L\) \((n=2)\), two electrons are present in sub-shell s \((l=0)\) and a maximum six electrons are present in sub-shell \(p\) \((l=1)\), etc.

Electron configurations for elements of the periodic table

Z

element

1

s

1

H

1

2

He

2

Z

element

1

2

s

s p

3

Li

2

1   

4

Be

2

2   

5

B

2

2 1

6

C

2

2 2

7

N

2

2 3

8

O

2

2 4

9

F

2

2 5

10

Ne

2

2 6

Z

element

1

2

3

s

s p

s p d

11

Na

2

2 6

1   

12

Mg

2

2 6

2   

13

Al

2

2 6

2 1

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

18

Ar

2

2 6

2 6

Z

element

1

2

3

4

s

s p

s p d

s p d f

19

K

2

2 6

2 6   

1         

20

Ca

2

2 6

2 6   

2         

21

Sc

2

2 6

2 6 1

2         

22

Ti

2

2 6

2 6 2

2         

23

V

2

2 6

2 6 3

2         

24

Cr

2

2 6

2 6 5

1         

25

Mn

2

2 6

2 6 6

2         

26

Fe

2

2 6

2 6 7

2         

27

Co

2

2 6

2 6 8

2         

28

Ni

2

2 6

2 6 9

2         

29

Cu

2

2 6

2 6 10

1         

30

Zn

2

2 6

2 6 10

2         

31

Ga

2

2 6

2 6 10

2 1      

32

Ge

2

2 6

2 6 10

2 2      

33

As

2

2 6

2 6 10

2 3      

34

Se

2

2 6

2 6 10

2 4      

35

Br

2

2 6

2 6 10

2 5      

36

Kr

2

2 6

2 6 10

2 6      

Z

element

1

2

3

4

5

s

s p

s p d

s p d f

s p d f

37

Rb

2

2 6

2 6 10

2 6      

1         

38

Sr

2

2 6

2 6 10

2 6      

2         

39

Y

2

2 6

2 6 10

2 6 1   

2         

40

Zr

2

2 6

2 6 10

2 6 2   

2         

41

Nb

2

2 6

2 6 10

2 6 3   

1         

42

Mo

2

2 6

2 6 10

2 6 5   

1         

43

Tc

2

2 6

2 6 10

2 6 6   

1         

44

Ru

2

2 6

2 6 10

2 6 7   

1         

45

Rh

2

2 6

2 6 10

2 6 8   

1         

46

Pd

2

2 6

2 6 10

2 6 10   

47

Ag

2

2 6

2 6 10

2 6 10   

1         

48

Cd

2

2 6

2 6 10

2 6 10   

2         

49

In

2

2 6

2 6 10

2 6 10   

2 1      

50

Sn

2

2 6

2 6 10

2 6 10   

2 2      

51

Sb

2

2 6

2 6 10

2 6 10   

2 3      

52

Te

2

2 6

2 6 10

2 6 10   

2 4      

53

I

2

2 6

2 6 10

2 6 10   

2 5      

54

Xe

2

2 6

2 6 10

2 6 10   

2 6      

Z

element

1

2

3

4

5

6

s

s p

s p d

s p d f

s p d f

s p d f

55

Cs

2

2 6

2 6 10

2 6 10   

2 6      

1         

56

Ba

2

2 6

2 6 10

2 6 10   

2 6      

2         

57

La

2

2 6

2 6 10

2 6 10   

2 6 1   

2         

58

Ce

2

2 6

2 6 10

2 6 10 2

2 6      

2         

59

Pr

2

2 6

2 6 10

2 6 10 3

2 6      

2         

60

Nd

2

2 6

2 6 10

2 6 10 4

2 6      

2         

61

Pm

2

2 6

2 6 10

2 6 10 5

2 6      

2         

62

Sm

2

2 6

2 6 10

2 6 10 6

2 6      

2         

63

Eu

2

2 6

2 6 10

2 6 10 7

2 6      

2         

64

Gd

2

2 6

2 6 10

2 6 10 7

2 6 1   

2         

65

Tb

2

2 6

2 6 10

2 6 10 9

2 6      

2         

66

Dy

2

2 6

2 6 10

2 6 10 10

2 6      

2         

67

Ho

2

2 6

2 6 10

2 6 10 11

2 6      

2         

68

Er

2

2 6

2 6 10

2 6 10 12

2 6      

2         

69

Tm

2

2 6

2 6 10

2 6 10 13

2 6      

2         

70

yb

2

2 6

2 6 10

2 6 10 14

2 6      

2         

71

Lu

2

2 6

2 6 10

2 6 10 14

2 6      

2         

72

Hf

2

2 6

2 6 10

2 6 10 14

2 6 1   

2         

73

Ta

2

2 6

2 6 10

2 6 10 14

2 6 2   

2         

74

W

2

2 6

2 6 10

2 6 10 14

2 6 3   

2         

75

Re

2

2 6

2 6 10

2 6 10 14

2 6 4   

2         

76

Os

2

2 6

2 6 10

2 6 10 14

2 6 5   

2         

77

Ir

2

2 6

2 6 10

2 6 10 14

2 6 5   

2         

78

Pt

2

2 6

2 6 10

2 6 10 14

2 6 6   

1         

79

Au

2

2 6

2 6 10

2 6 10 14

2 6 7   

1         

80

Hg

2

2 6

2 6 10

2 6 10 14

2 6 9   

2         

81

Tl

2

2 6

2 6 10

2 6 10 14

2 6 10 

2 1      

82

Pb

2

2 6

2 6 10

2 6 10 14

2 6 10 

2 2      

83

Bi

2

2 6

2 6 10

2 6 10 14

2 6 10 

2 3      

84

Po

2

2 6

2 6 10

2 6 10 14

2 6 10 

2 4      

85

At

2

2 6

2 6 10

2 6 10 14

2 6 10 

2 5      

86

Rn

2

2 6

2 6 10

2 6 10 14

2 6 10 

2 6      

Z

element

1

2

3

4

5

6

7

s

s p

s p d

s p d f

s p d f

s p d f

s

87

Fr

2

2 6

2 6 10

2 6 10 14

2 6 10   

2 6      

1

88

Ra

2

2 6

2 6 10

2 6 10 14

2 6 10   

2 6      

2

89

Ac

2

2 6

2 6 10

2 6 10 14

2 6 10   

2 6 1   

2

90

Th

2

2 6

2 6 10

2 6 10 14

2 6 10   

2 6 2   

2

91

Pa

2

2 6

2 6 10

2 6 10 14

2 6 10 2

2 6 1   

2

92

U

2

2 6

2 6 10

2 6 10 14

2 6 10 3

2 6 1   

2

93

Np

2

2 6

2 6 10

2 6 10 14

2 6 10 4

2 6 1   

2

94

Pu

2

2 6

2 6 10

2 6 10 14

2 6 10 5

2 6 1   

2

95

Am

2

2 6

2 6 10

2 6 10 14

2 6 10 7

2 6 1   

2

96

Cm

2

2 6

2 6 10

2 6 10 14

2 6 10 7

2 6 1   

2

97

Bk

2

2 6

2 6 10

2 6 10 14

2 6 10 8

2 6 1   

2

98

Cf

2

2 6

2 6 10

2 6 10 14

2 6 10 9

2 6 1   

2

99

Es

2

2 6

2 6 10

2 6 10 14

2 6 10 10

2 6 1   

2

100

Fm

2

2 6

2 6 10

2 6 10 14

2 6 10 11

2 6 1   

2

101

Md

2

2 6

2 6 10

2 6 10 14

2 6 10 12

2 6 1   

2

102

No

2

2 6

2 6 10

2 6 10 14

2 6 10 13

2 6 1   

2

103

Lr

2

2 6

2 6 10

2 6 10 14

2 6 10 14

2 6 1   

2