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

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• 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.

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• 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

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