The document discusses the four quantum numbers - n, l, ml, and ms - that are used to describe an electron orbital. The principal quantum number n refers to the main energy level, the azimuthal quantum number l describes the sublevel shape, the magnetic quantum number ml gives the orientation in space, and the spin quantum number ms has two possible orientations of +1/2 or -1/2. Together the four quantum numbers uniquely specify an electron orbital in an atom.

1. Quantum Numbers

2. •According to Heisenberg’s UNCERTAINTY
PRINCIPLE, it is not possible to give the
exact position of an electron and its energy at
the same time. But the probability of finding
the electron in an orbital of given energy can
be determined
•An orbital can be described by the four
quantum numbers n, l, 𝒎𝒍, 𝒎 𝒔

3. Principal Quantum Number, n
•Refers to the main energy
level of an orbital
• n = 1, 2, 3, 4, …

4. Azimuthal Quantum Number, l
• Also called angular momentum number or subsidiary
number
l Sublevel
0 s
1 p
2 d
3 f

5. Magnetic Quantum Number, 𝒎𝒍
•Describes the orientation of the orbital in
space and can have an integral value
from –l to +l, including 0.

6. sublevel l 𝒎𝒍
s 0 0
p 1 -1 , 0, or +1
d 2 -2, -1 , 0, +1, or + 2
f 3 -3, -2, -1 , 0, +1, + 2, or +3

8. Spin Quantum Number, 𝒎 𝒔
• Experiments show that if an electron is placed in a magnetic field,
only two orientations are possible for the electron spin.
• Two orientation:
• +1/2 = an arrow pointing up ( ↑ ) = clockwise direction
• -1/2 = an arrow pinting down ( ↓) = counterclockwise direction

9. sample
n = 4 3𝒅 𝟑
l = 2
𝒎𝒍 = 0
𝒎 𝒔 = +1/2
Note: d = n-1
f = n-2
↑ ↑ ↑

10. • electron configuration 1s22s22p63s23p64s23d3
• atomic number = 23
• period =4
• group = VB
• valence = 2
• type = metal
• magnetic property = paramagnetic

11. Did you know?
•The letters s, p, d, f were taken from the
words sharp, principal, diffuse and
fundamental, which are related to the spectra
of the photons emitted when certain elements
were heated or otherwise energized