[عاطف خليفة]

Quantum numbers

They define the orbital, energy, shape and the direction of orbital

* I) The principal quantum number (n)

1- It is used to define the order of the principal energy level

2- The number of electrons required to fill an energy level= ( 2n2 )
It is limited to any whole number value
e.g. 1,2,3,…,7.

Ex
The 1st shell is filled with (2×12)=2electrons
The 2nd shell is filled with (2×22)=8electrons

* II) The subsidiary quantum number (l)

1. It indicates the number of energy sublevels within each principal energy level

2. Each principal energy level consists of a number of energy sublevels equal to its principal quantum number

3. Sublevels are designated as s.p.d and f.

4. sublevels are arranged according to increasing energy as following order :
S< P < d< f.


Note
Sommerfield found that each one spectral line was made of some spectral lines.

* Ill) The magnetic quantum number (m)

1. It represents the number of orbitals within a certain energy sublevel

2. Sublevel(s) has one orbital of spherical symmetrical

3. Sublevel (p) has three orbitals their axises take the three spatial formations(px - py - pz )
The electron cloud of each orbital is dumb-bell shaped

4. Sublevel (d) has 5 orbitals

5.Sublevel (f) has 7 orbitals

* IV) The spin quantum number (ms)

- It defines the type of spin motion of the electron around its axis

- The electron spins in clock-wise ↑ or anticlockwise ↓



* The relationship between n, I and m

Fig
1. The number of sublevels equals the number of the principal level (n)

2. The number of orbitals within a principal level equals (n2)

3. The maximum number of electrons can be found in a principal level equals 2 n2