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3.4 Quantum Numbers

4 quantum numbers, can be used to describe:

  • the spectrum lines emitted by excited electrons

  • the magnetic properties of electrons

  • the arrangement of electrons in their orbital

  • the relationship between the electron structure of the atom and its placement on the periodic table

  • The Principal Quantum Number (n)

    • energy levels in an atom may be called shells
    • Bohr identified the shell number as the principle quantum #
    • describes the size and energy of an orbital
    • only integers

  • The Secondary Quantum Number (l)

    • Arnold Sommerfield & Peter Debye (1951) to explain the results of high resolution line in spectra
    • Very small energy steps (sub levels) within the main energy level
    • Describe the shape of the electron orbital
    • The number of sub levels is equal to the value of n ( n = 3, then 3 sub levels)
    • n = 3, l = 0, 1, 2
      • s: l=0
      • p: l=1
      • d: l=2
      • f: l=3

  • The Magnetic Quantum Number (ml)

    • Explains the orientation of the electron orbital
    • Orbitals may have the same energy level and shape, but different orientation (exist at various angles)
    • Valued at integers from +l to -l, including 0
    • For example, if l = 1, then ml = +1, 0, -1
    • This means there are 3 different p orbitals.

  • The Spin Quantum Number (ms)

    • Wolfang Pauli (1925) to explain the Zeeman effect
    • Since charged particles create magnetic fields when vibrating, electrons must be spinning on axes
      • Limited to +1/2 or -1/2
    • An opposite pair of electrons spin in a stable way to produce no magnetic property (they cancel each other out), but an unpaired electron can be affected by a magnetic field.

Rules of Quantum Numbers

  • Pauli Exclusion Principle
    • No two electrons in an atom can have the same 4 quantum numbers
    • Each orbital may only hold 2 electrons, each with opposite spins!
  • Aufbau Principle
    • Electrons are placed into orbitals by filling the lowest energy orbitals first
  • Hund’s Rule
    • When several orbitals are at the same level of energy, one electron is placed into each of the orbitals, before a second electron is added