Modern Atomic Theory
Electron Atomic Orbitals
Part I: Quantum Mechanical Model
• The Bohr model’s prediction of electron energies
and locations was limited in accuracy to the
Hydrogen atom.
• Scientists DeBroglie and Schrödinger proposed
that the electrons is acting as a wave as well as
a particle.
• Schrödinger developed an equation which
predicts the location of an electron based upon
probabilities.
• Electrons in this model are located in Orbitals
not orbits, despite sounding similar, they are
vastly different.
• The location of the electron is given by four
numbers called Quantum Numbers
• These quantum numbers act like your
street address that give you homes
location.
– Zip code
– State
– City
– Street
– Number
– Suite
Quantum Numbers [n, l, ml, ms]
• n is the principle energy level. Limited to
integers starting at 1. [n = 1, 2, 3….]
• l is the orbital quantum number. Its values
are limited to all integer values up to n-1.
• ml is the magnetic quantum number. Its
values are limited to integers from -l to +l.
• ms is the electron spin designation. It is
either +½ for spin up or -½ for spin down.
Shapes of Orbitals
• The shape of the orbital is given by the second
and third quantum numbers.
• Instead of using a number for the second
quantum number, l, a letter designation is used.
–
–
–
–
–
–
0 is s (sharp)
1 is p (principle)
2 is d (diffuse)
3 is f (fundamental)
4 is g
and so on down the alphabet
• The third quantum number ml, determines the
number of possible orientations of the orbital
based on the second quantum number.
• If l = 0 then ml can only be 0 and there is only
one orientation of the orbital.
• If l = 1 then ml can be [-1, 0, +1] and there are
three orientations of a “p” orbital.
• If l = 2 then ml can be [-2, -1, 0, +1, +2] so there
are five orientations for a “d” orbital.
• If l = 3 then ml can be [-3, -2, -1, 0, +1, +2, +3]
so there are seven orientations for a “f” orbital.
s Orbitals [l = 0]
• The s orbital is spherically
shaped.
• There is only one possible
orientation for the s orbital.
• Each energy level has an s
orbital and they get
concentrically larger.
• Two electrons fill each s orbital
p Orbital [l = 1]
• The p orbital is “dumbbell” shaped.
• There are three possible orientations for
the p orbital.
• Each energy level n=2 and beyond has a p
orbital and they get concentrically larger.
• Two electrons fill each orientation of the p
orbital for a total of 6 electrons per energy
level.
p Orbitals – three orientations
d Orbital [l = 2]
• The d orbitals are uniquely shaped.
• There are five possible orientations for the
d orbital.
• Each energy level n=3 and beyond has a d
orbital and they get concentrically larger.
• Two electrons fill each orientation of the d
orbital for a total of 10 electrons per
energy level.
d Orbitals
f Orbital [l = 3]
• The f orbitals are uniquely shaped.
• There are seven possible orientations for
the f orbital.
• Each energy level n=4 and beyond has an
f orbital and they get concentrically larger.
• Two electrons fill each orientation of the f
orbital for a total of 14 electrons per
energy level.
f Orbitals
The location of electrons is a superposition
of all of the individual orbitals.