Atomic Orbitals

1
Atomic Orbitals

• And Quantum Numbers

2
Quantum Numbers

• A series of 4 numbers (and/or letters) that
  specify the properties of an electron in its
  orbit
• The first 3 come from the Schrödinger equation
  solutions (energy level, shape and orientation of
  the orbital)
• The last one describes the electron occupying the
  orbital

3
Principal Quantum Number

• Symbol is n
• Indicates the energy level (or shell)
• As n increases, so does distance from the nucleus
• Total number of orbitals (each can hold 2
  electrons) in an energy level is n2

4
Angular Momentum Quantum Number

• Shape of the orbital
• Symbol is l
• Number of possible shapes for an energy level is
  equal to n
• Values possible for l are zero and positive
  integers up to n-1
• Values for l also have letter designations

5
Letter Designations for l

• l0
• l1
• l2
• l3

• s (shape is spherical)?
• p (shape is dumbbell)?
• d (shape is multiple dumbbell)?
• f (shape is complex)?

6
To Designate Electrons

• Electrons in the s sublevel of shell 2 would be
  2s
• Electrons in the p sublevel of shell 3 would be
  3p

7
Magnetic Quantum Number

• Indicates the orientation around x, y and z axes
• Symbol is m
• Values range from -l to l
• For example, for l2, there are 5 orientations
  -2, -1, 0, 1, 2

8
Spin Quantum Number

• Only two possible values, 1/2 or -1/2
• Single orbital (such as 3px) can only hold 2
  electrons, each of which has opposite spin