Quantum Numbers and Electron Configurations

Quantum Numbers, Atomic Orbitals, and Electron Configurations

• Each electron in an atom is described by four quantum numbers
• The first three quantum numbers (n, l, ml) specify the particular orbital of interest
• The fourth quantum number (ms) specifies how many electrons can occupy that orbital

Principal Quantum Number (n)

• n = 1, 2, ..., 8
• Describes the average distance of an electron from the nucleus (like the innermost electron shell)
• n indicates the energy level and the size of the orbital
• Higher values of n correspond to higher energy levels and larger orbitals
• All orbitals with the same value of n are in the same shell (level)
• For a hydrogen atom, n=1 is its ground state
• Higher values of n represent excited states

Angular or Orbital Quantum Number (l)

• l = 0, 1, ..., (n-1)
• Specifies the shape of an orbital with a particular principal quantum number
• Divides shells into smaller groups of orbitals called subshells (sublevels)
• Letter codes (s, p, d, f, g, h...) are used to denote different subshells, where:
  • l=0 is an s subshell
  • l=1 is a p subshell
  • l=2 is a d subshell
  • l=3 is an f subshell
• The value of l also has a slight effect on the energy of the subshell, increasing with l (s<p<d<f)

Magnetic Quantum Number (ml)

• ml = -l, ..., 0, ..., +l
• Specifies the orientation in space of an orbital with a given energy (n) and shape (l)
• ml divides the subshell into individual orbitals that hold the electrons
• There are 2l+1 orbitals in each subshell
  • s subshell has only one orbital
  • p subshell has three orbitals
  • d subshell has five orbitals

Spin Quantum Number (ms)

• ms = +½ or -½
• Specifies the orientation of the spin axis of an electron
• An electron can spin in only one of two directions (sometimes called up and down)
• The Pauli exclusion principle states that no two electrons in the same atom can have identical values for all four of their quantum numbers.
• This means that no more than two electrons can occupy the same orbital, and those two must have opposite spins (paired)
• For two electrons in the same orbital, the spins must be opposite

Aufbau Principle

• Describes the filling order of atomic orbitals in a multi-electron atom.
• It begins with the atom’s lowest energy level and works up
• The electronic configuration of an atom describes how electrons are distributed among various atomic orbitals
• Inner shells begin filling first, then outer shells.

Electron Configurations of elements (example)

• Hydrogen (Z=1): 1s¹

• Helium (Z=2): 1s²

• Lithium (Z=3): 1s²2s¹

• Beryllium (Z=4): 1s²2s²

• ... and so on.

• Each element's electron configuration follows specific rules and patterns. The configurations demonstrated in the diagrams (e.g., 2,8,1 for Sodium) indicate the number of electrons in each electron shell. The shells corresponding to a particular value of the principal quantum number (e.g., n=1, n=2, n=3)