3.4 Quantum Numbers

principle quantum number (n)

the quantum number that describes the size and energy of an atomic orbital.

 

• The first and most important quantum number

• Introduced by Bohr and sometimes called the shell number

n tells us 2 main things:

1. Energy level of the electron

2. The size of the orbital (how far it is from the nucleus)

a bigger n means…

• The electron is in a higher energy level

• The orbital is larger

• The electron is farther from the nucleus

subshells

orbitals of different shapes and energies, as given by the secondary quantum number; often referred to as s, p, d, and f

secondary quantum number (l)

This quantum number describes the shape of an atomic orbital.

• It has whole number values from 0 to n-1 for each value of n.

• Also describes the energy of atomic orbitals

  • When n = 1, l = 0

  • When n = 3, l = 0, 1, and 2

magnetic quantum number (m_l)

• Describes the orientation of an atomic orbital in space, relative to the other orbitals in the atom

• In other words, it tells you which direction the orbital is pointing relative to the other orbitals.

value of m_l depends on

• The values of mₗ depend on the value of the secondary quantum number l.

• For a given l, the possible values of mₗ range from: –l to +l, including 0

So the number of possible mₗ values = number of orbitals in that subshell.

nodes

Nodes are regions where the probability of finding an electron is zero.

spin quantum number (m_s)

the quantum number that relates to the spin of the electron, limited to +1/2 or -1/2

Pauli exclusion principle

"In a given atom, no two electrons can have the same set of four quantum numbers (n, l, m_l, and m_s)."

aufbau principle

Electrons are placed into orbitals by filling the lowest energy orbitals first

hund’s rule

When several orbitals at the same level of energy, one electron is placed into each of the orbitals, before a second electron is added.