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# I- quantum numbers :

L’state of’an electron in an atom, c’that is to say : its energy, its movements around the core, the shape of the’orbital, is defined by 4 parameters called quantum numbers.

a- You name n, principal quantum number : n = 1, 2,…. ∞

• quantify l’l energy’electron,
• defines an electron shell or a level d’energy.

n = 1 => layer K ; n = 2 => The layer ; n = 3 => layer M ; etc…

b- You name /, azimuthal quantum number, with : 0 ≤ I ≤ n-1

characterizes the « form » of the’orbital; it defines an electronic sublayer, or a sublevel d’energy.

/ = 0 => underlay s / = 1 => sublayer p
/ = 2 => underlay d / = 3 => underlay ƒ

c- The number m, magnetic quantum number : with : -1 ≤ m ≤ +1 => m can take (21 + 1) values. IT defines l’orientation of the’orbital :

/ = 0=>m = 0=>the only direction => 1 Orbital s => 1 quantum box / = 1 => m = -1; 0 ; 1 => 3 orientations => 3 p orbitals of the same energy => 3 quantum boxes

d- You name s, spin quantum number s, defines the rotation of the’electron on itself. Two orientations are possible : s = +1/2 (T) et s = -1/2 {-l).

Remarks :

– Les names n, I, m define an atomic orbital (quantum box) m = 0 – The four quantum numbers n, I, m, s define an electron.

Ex : 1 electron on the underlayer s : # II- Orbital and descriptions :

### a- Function d’onde ψ :

ψ is a purely mathematical function:

• she n’has no physical meaning,
• it is a function of the coordinates of the’electron,
• it is defined by the 3 quantum numbers : n, / and M : yn,l,m

Example : l’orbital 2s is represented by the function d’Where : y2,0,0

### b- Description of the’orbital "s" : C’is an orbital of spherical symmetry, corresponding to I = 0, m = 0 These functions d’where s’write : yn,0,0 or ψns

Example : Orbital « 1s »

Note : the sign + indicated at’interior of the sphere is the sign of the function d’onde ψ1s

### c- Description orbital "p" :

The p orbitals (/ = 1) can be represented by two lobes nearly spherical, contiguous, whose axes of symmetry x-, y and z of the reference trihedron.

So we call them « n px », « n py » and « n pz » according to the value of m (n > 2). They are called lateral or axial symmetry. Note :

for orbital I = 2 a I = 3 c’i.e. the d and f orbitals, the geometric representation is complex.

Course of Dr Tayeb Benmachiche Akila – Faculty of Constantine