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