The four quantum numbers describe the distribution and behavior of electrons in atoms. They are derived from the Schrodinger equation for the hydrogen atom. The four quantum numbers are the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The principal quantum number determines the electron's energy level. The azimuthal quantum number indicates the subshell and possible shapes of an orbital. The magnetic quantum number describes the orientation of an orbital. The spin quantum number indicates the spin of an electron.

1. The Four Quantum
Numbers

2. Quantum mechanics
•It requires of 4 quantum numbers to describe to theIt requires of 4 quantum numbers to describe to the
distribution and behavior of electrons in atoms.distribution and behavior of electrons in atoms.
• They derive from the Equation of Schrödinger forThey derive from the Equation of Schrödinger for
the hydrogen atom.the hydrogen atom.
•The Quantum Numbers are :: n l m sn l m s

3. Quantum Numbers
n = Level of Energy, main quantum number.
values = 1, 2, 3……7
l = Sublevel of Energy, secondary quantum number.
If n = 1 then l = 0. If n = 2 then l = 0 y 1
m = Direction of the orbital ones, quantum number
magnetic.
If l = 0 then m = 0. If l= 1…. m = -1, 0 y 1
s = spin or turn of electrons, quantum number of spin
electronic. Their values are + ½ up and right and
- ½ down and left.

4. The Four Quantum Numbers
Quantum
Number
Name Relation Values
n Principal Quantum Number Determines the level of Energy
of an orbital
1, 2, 3, 4,.......7
l Secondary Quantum Number
Azimutal
Sublevel: it indicates Form of
the orbital.
s (sharp), p (principal),
d (difuses) y f (fundamental)
Depend on the value of n
If n = 1, l = 0
If n = 2, l = 0 y 1
If n = 3, l = 0, 1 y 2
m Quantum Number Magnetic It describes the Orientation of
the orbitals in the space,
by effect of a magnetic
external field
Depend on the value of m
If l = 0, m = 0
If l = 1, m = -1 0 1
If l = 2, m = -2 –1 0 1 2
s Quantum Number:
electronic spin
It indicates spin of electrons + ½ - ½
up down
favor of mr against mr

5. Atomic Orbitals: s, p, d, f

6. Representations of the
cloud of orbitals “s”

7. Representations of
the orbitals “p”

8. Group of 3 orbitals “P”
on their 3 axis: Px, Py, Pz

9. Number of electrons by
Energy level
n No. de
Subniveles
Tipo de Orbital No. de Orbitales No. Máx. de
electrones
por subnivel
No. Máx. Total de electrones
por nivel
1 1 1s 1 2 2
2 2 2s 1 2 8
2p 3 6
3 3 3s 1 2 18
3p 3 6
3d 5 10
4 4 4s 1 2 32
4p 3 6
4d 5 10
4f 7 14

10. Bibliography
Burns, R. (2003) Fundamentos de Química. 4ª Ed. Pearson,
Prentice-Hall. México, D. F.