Quantum Mechanical Model of
the Atom
Problem with Bohr’s Model
• Bohr’s model of the atom could not explain
why the spectra of other elements had too
many lines. What appeared to be a single line
in a spectrum was actually several lines closely
grouped together.
Modified Bohr Model
• By breaking Bohr’s energy levels into
sublevels, it was possible to explain these
spectra. Therefore, an energy level is actually
made up of many energy states that are
closely grouped together.
• Bohr’s levels were broken into the following
sublevels:
Sharp Principle Diffuse Fundamental
Each sublevel holds a different number
of electrons
Sublevel
Maximum # of Electrons
Pairs of Electrons
S
2
1
P
6
3
D
10
5
F
14
7
Orbitals
• The space occupied by a pair of electrons is
called an orbital. Each orbital can hold one
pair of electrons. Orbital describe regions in
space where is electron is more likely to be
found.
Sublevels
Principle
Quantum #
Allowed
Subleves
Number of
sublevels
Number of
orbitals
Number of
electrons
1
S
1
1
2
2
S, P
2
4
8
3
S, P, D
3
9
18
4
S, P, D, F
4
16
32
n
n2
2n2
n
Energy levels and multi-electron atoms
• To construct a model of an atom, follow these
two rules:
(1) Aufbau Principle – Electrons always enter
orbitals of the lowest energy first.
(2) There is a maximum number of electrons for
each energy level. The number is given by 2n2
where n is the principle quantum number.
Pauli Exclusion Principle
• An atomic orbital may describe at most two
electrons. To occupy the same orbitals, two
electrons must have opposite spins. Spin is a
quantum property of electrons and may be
clockwise (represented by an upward pointing
arrow ↑) or counterclockwise (represented by
a downward pointing arrow ↓).
Hund’s Rule
• When electrons occupy orbitals of equal
energy, one electron enters each orbital until
all the orbitals contain one electron with spins
parallel (either all the spins are clockwise or all
the spins are counterclockwise). Second
electrons then add to each orbital so that
their spins are paired with the first electrons
in the orbital.
Steps to Writing the Electron
Configuration of an Atom
• Step 1
• Get a Periodic Table of Elements
• Find out how many electrons the atom has.
On the periodic table, the atomic number is
the number of protons of the atom, and thus
equals the number of electrons in an atom
with zero charge.
Step 2: Mnemonic for Filling Orbitals
Step 3
• Put one electron into the highest energy orbital available,
starting with 1s (holds a maximum of two electrons). Fill
the orbitals in this order (the number in superscript
following the sublevel is the maximum number of electrons
it can hold):
– 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2
5f14 6d10
– Note: Energy level changes as you go up. For example, when you
are about to go up to the 4th energy level, it becomes 4s first,
then 3d. After the fourth energy level, you'll move onto the 5th
where it follows the order once again. This only happens after
the 3rd energy level!
Step 4
• Once you've put every electron into an orbital
(according to the order), write the configuration
as shown at the end of step 3. Only write the
orbitals that contain electrons.
• So, an uncharged antimony atom's electron
configuration would be 1s2 2s2 2p6 3s2 3p6 4s2
3d10 4p6 5s2 4d10 5p3. Notice that the superscript
number following 5p is 3. That's because only
three electrons are in the 5p sublevel, so the
sublevel is not completely occupied (it lacks three
more electrons).
Practice
• Write the electron configuration for the first
20 elements.
• Write the electron configuration of Br, Ag, Ba,
Au, and U.
Energy Level Diagrams
• The electron configuration of atoms can also
be shown in energy level diagrams. In such
diagrams, individual orbital are represented
by spheres, boxes, or lines. Each orbital can
hold a maximum of 2 electrons containing
opposite spins. The height of each orbital is
representative of its energy. The higher the
orbital is in the diagrams, the higher is its
energy.
Example using spheres for orbitals
Examples
• I will use boxes to represent individual
orbitals. Examples
• Hydrogen
Oxygen
Potassium
Practice
• Draw the energy level diagram for the
following:
Lithium
Fluorine
Silver
Electron Orbital Shapes