Quantum Numbers, How to determine quantum numbers?

 Quantum numbers:

• These are numbers which determine the electronic configuration of atoms.
• There are four quantum numbers

 

(a)- Principle quantum number (n):

§  Describe the main energy states.

§  Related to the size of the atomic orbital (distance from the nucleus)

§  It takes integer numbers: 1, 2, 3, 4……

§  Larger value of (n) means higher energy

§  Larger value of (n) means that the electrons are less strongly bound to the nucleus

§  The numbers take the following letters:

1=K  ,   2= L   ,  3=M    , 4=N  ………………….

§  The number of electrons in a main energy level equal to2n²

 (b)- Angular quantum number (l):

ü Determine the number of sub-levels (the number of sublevels in a main energy level equal to its principal quantum number).

ü Describe the shape of the orbitals in the sublevel (or subshell).

ü Take integer numbers from 0 to (n-1).

ü The numbers take the following letters

0=s      ,    1=p    ,    2=d     ,     3=f     ,    4=g

 

(c)- Magnetic quantum number (m_l):

Ø Related to the orientation of orbitals in space

Ø Determine the number of orbitals in each sub-level (orbitals of the same sublevel differ in orientation but not in their energies).

Ø Take integer numbers from (-l) to (+l) including “0”.

Ø For example l =1 means that we have the sublevel p and the values of m_l are -1, 0, +1, and so we have three atomic orbitals

 

(d)- Spin quantum number (m_s):

·        Determine the magnetic field result from the spin of electron

·        Take the values + ½ or - ½.

Examples for quantum numbers (How to calculate n, l, m_l, and m_s for an atom)

Symbol of main level	n	l	m	Number of sub levels	Symbol of sub level	Number of orbitals
K	1	0	0	1	1s	1
L	2	0 1	0 +1,0,-1	2	2s, 2p	1 3
M	3	0 1 2	0 +1,0,-1 +2,+1,0,-1,-2	3	3s, 3p 3d	1 3 5
N	4	0 1 2 3	0 +1,0,-1 +2,+1,0,-1,-2 +3,+2,+1,0,-1,-2,-3	4	4s 4p 4d 4f	1 3 5 7

          

  Orbitals:

The electron capacity of each orbital is two electrons.

The shapes of the  orbitals in each sub level are given as follow:

 

(a)- S sublevel:

       Consist of one orbital with spherical shape as illustrated in the figure:

(b)- P sublevel:

        Consist of three orbitals P_x , P_y , and P_z.  and their shapes are as follow:

(c )- d  sublevel:

             Consist of five orbitals  d_xy , d_yz , d_xz  , dx²-y²  , and  dz² 

(d)- f sublevel:

             Consist of seven orbitals with very complicated shapes.