• Quantum-Mechanical Model of the Atom– Describes the probability that the electron will be in a

certain region of space at a given instant. – Orbitals are regions of different energies where the

electrons can be found.

• The quantum-mechanical model uses 3 quantum numbers to describe an orbital: – The principal quantum number (n)

• Can be any positive integer (n=1, n=2, n=3, etc.)• Describes the energy level

– The angular momentum quantum number (l)Lowercase cursive L

• Can have values from 0 to (n–1)• Defines the shape of the orbital

– The magnetic quantum number (ml)• Can have integer values between – l and + l • Describes the orientation of the orbital in space

Value of l 0 1 2 3

Orbital shape s p d f

n Possible values of l

Subshell possible values of ml

# of orbitals in subshell

Total # of

orbitals

1

2

3

4

s orbitals

• Have a spherical shape.

• There is one orbital in each s subshell.

p orbitals• Dumbbell shaped orbitals• Each p subshell contains 3 orbitals.• Each of the 3 orbitals is oriented along a different

axis (x, y, or z)

d orbitals• Each d sublevel contains 5 orbitals.• 4 of the 5 orbitals have a four-leaf clover

shape. The dz2 orbital has lobes on the z

axis and a “doughnut” shape in the x-y plane.

f orbitals• An f sublevel will contain 7 orbitals

• All orbitals in the same subshell are said to be degenerate, meaning that they have the same energy. (i.e. the 3 orbitals in the 2p sublevel each have the same energy).

• A maximum of 2 electrons can be located in a given orbital.

Type of Sublevel

# of orbitals # of electrons

spdf

SubshellsSubshell Number of

OrbitalsMax # of Electrons

s 1 2

p 3 6

d 5 10

f 7 14

• The fourth quantum number– The magnetic spin quantum number (ms)– Can have a value of either + ½ or – ½ – Represents the electron’s spin about its axis, which

can generate a magnetic field in two possible directions.

• The Pauli Exclusion Principle– No two electrons in an atom can have the same

quantum numbers. – Therefore two electrons found in the same orbital will

have opposite spins (+ ½ and – ½)

• Rules for writing electron configurations: – Aufbau Principle: orbitals are filled in order of

increasing energy (lowest energy orbitals filled first).– Pauli Exclusion Principle: no more than two

electrons can be found in a single orbital. Two electrons in the same orbital have opposite spins.

– Hund’s Rule: for degenerate orbitals, the lowest energy is obtained when the number of electrons with the same spin is maximized.

• Valence Electrons – outer-shell electrons – Include s and p electrons in the highest energy level– Electrons that are involved in chemical bonding

• Core Electrons = inner-shell electrons• For example, a phosphorus atom has 15 total electrons

– Phosphorus has 5 valence electrons (the electrons in the 3s and 3 p orbitals)

– Phosphorus has 10 core electrons (found in the first and second energy levels)

• The octet rule atoms tend to form chemical bonds to reach a full outer-shell of 8 valence electrons.

• For example, the phosphorus atom on the previous slide would gain three electrons to reach a full outer shell. This P3- ion would have the same electron configuration as the element argon.

• When an atom and an ion have the same electron configuration, they are said to be isoelectronic.

• Transition metal ions– d and f electrons are not considered valence

electrons.– Outer shell s and p electrons will be lost first.

• For example:

Fe

Fe2+

Fe3+