3.4 Quantum Numbers

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