quantum numbers and atomic orbitals

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I- quantum numbers :

L & rsquo; d & rsquo state, an electron in an atom, c & rsquo; is to say, : its energy, its movements around the core, the shape of the & rsquo; Orbital, is defined by 4 parameters called quantum numbers.

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

  • quantifies & rsquo; s Energy & rsquo; electron,
  • defines an electronic layer or level of & rsquo; 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” orbital; it defines an electronic sublayer, or a sub-level of & rsquo; 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 the & rsquo; orientation of & rsquo; 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 & rsquo; 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- d & rsquo function; wave ψ :

ψ is a purely mathematical function:

  • it n & rsquo; no physical meaning,
  • it is function of the coordinates of the & rsquo; electron,
  • it is defined by the 3 quantum numbers : n, / and M : yn,l,m

Example : l & rsquo; 2s orbital is represented by the function & rsquo; wave : y2,0,0

b- Description of the & rsquo; Orbital 's " :

C & rsquo; is an orbital of spherical symmetry, corresponding to I = 0, m = 0 These functions & rsquo; s wave & rsquo; writing : yn,0,0 or ψns

Example : Orbital “1s”

Note : the sign + indicated in & rsquo; inside the sphere is the sign of the function & rsquo; wave 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 & rsquo; is, the d orbital and f, the geometric representation is complex.

Course of Dr Tayeb Benmachiche Akila – Faculty of Constantine