# 3.4 quantum numbers

```SCH 4U1
THE ORGANIZATION OF ELECTRONS: Quantum Numbers
Electrons can be organized by four quantum numbers. This combination of numbers are
unique for any given element. The first three numbers were created by Erwin Schr&ouml;dinger
and the last number was created by Wolfgang Pauli.
The principal quantum number (n), introduced by Bohr is a whole number (1,2,3...) that
specifies the energy level of an atomic orbital and its relative size. The greatest number of
electrons allowed at any energy level is 2n2.
The secondary quantum (l), describes an orbital’s shape. The numbers range from 0 to n-1.
An s sublevel = 0, a p sublevel = 1, a d sublevel = 2, an f = 3, g = 4, h = 5...etc. The number n
will give the number of sublevels. The number n2 will give the number of orbitals at that
energy level.
The magnetic quantum number, ml, indicates the number of orientations a sublevel may have.
They are numbers from –l to +l.
Sublevel
Secondary quantum
number, l
Number of
orientations
Magnetic quantum
number, ml
s
p
d
f
g
The fourth and last number is the spin quantum number, ms, and it describes the spin of an
electron. In order to get two electrons into the same orbital the electrons must have
opposite spin. There are only two values: -1/2 and +1/2.
With all four quantum numbers any electron is unique and can be described.
Identify the electron qualities of the following quantum numbers:
n=4
l=1
ml = -1
ms = +1/2
n=2
l=0
ml = 0
ms = -1/2
```