Based on complex mathematical calculations and interpretations.

Elaborately described in Quantum Mechanics by the German physicist

Werner Karl Heisenberg.

This model is also called the “Electron Cloud Model”

The electron is found inside a blurry “electron cloud”, also called the “probability region”.

“The more precisely the position of a particle is determined, the less precisely the momentum is known in this instant; and vice versa.”

Describes the region of space where the electron is most likely to be found.

Provides information on the energy of the electron.

Energy is quantized,meaning: can be subdivided into small but measurable increments.

An orbital is not a circular path, rather it is an energy state that can be described by the four quantum numbers.

Principal Quantum Number (n or shell)- the main energy level of an orbital- related to the total energy of the

electron in an atom- represents physically the radial distance

that the probability region extends out from the nucleus

- values: positive integer beginning with 1- 2n2 rule: maximum number of electrons

that can occupy a main energy level

Azimuthal Quantum Number (l)- energy sublevels- defines the shape of the orbital- values: 0 until the integer n-1

lSublev

elOrbital Shape

0 S Spherical1 P Dumbbell-shaped

2 D4 cloverleaf-shaped; 1 dumbbell-shaped w/

ring3 F (too complex to describe)

Magnetic Quantum Number (ml)- describes the orientation of the orbital in

space- values: integral value from –l to +l, including 0- formula: 2l + 1 = number of ml values per

sublevel

Sublevel l ml

S 0 0

P 1 -1, 0, 1

D 2 -2, -1, 0, 1, 2

Spin Quantum Number (ms)

- represents the electron spin- describes the direction of the spin of

one electron in reaction to the magnetic field generated by another electron nearby.

- values: +½ ( ) – clockwise spin and -½ ( ) – counterclockwise spin

Describes how the electrons are distributed among the orbitals.

Ground state – lowest energy state of the atom;most stable arrangement of the electrons

“The electrons fill the orbitals, one at a time, starting with the lower energy orbital then proceeding to the one

with higher energy.”

n+l rule

- used to identify which orbital has lower energy and is filled up first as electrons are added to the atom.

- the lower the (n+l), the lower the energy

- if (n+l) values are equal, the one with lower n value has the lower energy.

“No two electrons in the same atom can have the same set of four

quantum numbers.”

Consequently, it means: Only two electrons may occupy an orbital, and they must have different spins.

Sublevel # of orbitalMaximum # of electrons

S 1 2

P 3 6

D 5 10

F 7 14

“When electrons occupy orbitals of equal energy, they don’t pair up unless all the orbitals have been filled up by a single electron.”

Degenerate orbitals – orbitals or energy levels with the same energy

Paramagnetic Element– has one or more unpaired electrons in its orbital– can be attracted to a magnet

Diamagnetic Element- only paired electrons in its orbitals- slightly repelled by a magnet

Padolina et al. Conceptual and Functional Chemistry. QC: Vibal Publishing House, Inc., 2004.

Brescia et al. Fundamentals of Chemistry. NY: Academic Press, Inc. 1983