Quantum Mechanics

QUANTUM NUMBERS OF ELECTRONS OF ATOMS
There are four quantum numbers describe the location of electrons
The Principle Quantum Number: (n)
It represents the shell of orbitals in the atom, n is any integers (1,2,3,4,5,...)
The Second Quantum Number: (l) 
l=n-1
It describes the shape of the orbitals
s orbitals: spherical
p orbitals: dumbbell-shaped

The Third Quantum Number: (m_l)
-l <m_l <l
It represents the orientation of the e-pair in space.
m_l=-3,-2,-1,0,1,2,3 or -2, -1, 0, 1 , 2 (Depends on the element)

The Fourth Quantum Number: (m_s)
It represents the spinning direction of the electrons
m_s=1/2 or -1/2 only

Example: 
Question: What are the quantum numbers of the Element with Atomic number 31?
Answer: From periodic table, we know that Galium (Ga) has Atomic Number= 31 and the electron configuration (EC) is 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p¹

From the EC, we can see Ga has 4 orbitals of electrons: n=4 
The outer layer of Ga is p so l=1
The outer layer is p which has 3 orbitals: ml= -1, 0, 1
Since there is only 1 electron in the outer layer, it must be spinning up so m_s=1/2