Download Brown_PPT_Tark_Ch05_part2

PowerPoint to accompany
Chapter 5
Electronic
Structure
of Atoms
Part-2
Heisenberg Uncertainty Principle

Heisenberg showed that the more
precisely the momentum of a particle is
known, the less precisely its position is
known.

In many cases, our uncertainty of the
whereabouts of an electron is greater
than the size of the atom itself!
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Quantum Mechanics



Erwin Schrödinger developed a
mathematical treatment into which both the
wave and particle nature of matter could be
incorporated.
It is known as quantum mechanics.
The Energy, Momentum and Position of
each electron around an atom can be
expressed as the solution to a wave
equation.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Quantum Numbers

Solving the wave equation gives a set of
wave functions, or orbitals, and their
corresponding energies.

Each orbital is a probability function which
describes a spatial distribution of electron
density.

An orbital is described by a set of three
quantum numbers.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Quantum Mechanics

The wave equation is
designated with a lower case
Greek psi ().

The square of the wave
equation, 2, gives a
probability density map of
where an electron has a
certain statistical likelihood of
being at any given instant in
time.

2 = ▼H 2
Figure 5.14
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Principal Quantum Number, n

The principal quantum number, n,
describes the energy level on which the
orbital resides.

The values of n are integers ≥ 0.

n determines the size of an atom
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Azimuthal Quantum Number, l

This azimuthal quantum number defines
the shape or direction of the orbital.

Allowed values of l are integers ranging
from 0 to n − 1.

We use letter designations to
communicate the different values of l and,
therefore, the shapes and types of
orbitals.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Azimuthal Quantum Number, l
Value of l
0
1
2
3
Type of orbital
s
p
d
f
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Magnetic Quantum Number,
ml

Describes the three-dimensional
orientation of the orbital.

Values are integers ranging from -l to l:
−l ≤ ml ≤ l.

Therefore, on any given energy level,
there can be up to 1 s orbital, 3 p
orbitals, 5 d orbitals, 7 f orbitals, etc.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Magnetic Quantum Number,
ml

Orbitals with the same value of n form a shell.

Different orbital types within a shell are
subshells.
Table 5.2
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Electron Probability Functions
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
s Orbitals

Value of l = 0

Spherical in shape

Radius of sphere
increases with
increasing value of n
Figure 5.17
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
s Orbitals
Figure 5.16
Figure 5.20
Observing a graph of
probabilities of
finding an electron
versus distance from
the nucleus, we see
that s orbitals
possess n−1 nodes,
or regions where
there is 0 probability
of finding an
electron.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
p Orbitals

Value of l = 1

Have two lobes with a node between
them
Figure 5.18
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
d Orbitals
Figure 5.21

Value of l is 2

Four of the five
orbitals have 4
lobes; the other
resembles a
longer p orbital
with a doughnut
around the centre
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Energies of Orbitals

For a one-electron hydrogen atom,
orbitals on the same energy level have
the same energy, i.e. they are
degenerate.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Energies of Orbitals
Figure 5.22

As the number of
electrons increases,
so does the repulsion
between them.

Therefore, in manyelectron atoms,
orbitals on the same
energy level are no
longer degenerate.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Spin Quantum Number, ms

In the 1920s, it was discovered that
two electrons in the same orbital do
not have exactly the same energy.

The “spin” of an electron describes its
magnetic field, which affects its
energy.

This led to a fourth quantum number,
the spin quantum number, ms.

The spin quantum number has only 2
allowed values: +½ and −½.
Figure 5.23
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Spin Quantum Number, ms
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Electron Configurations


Distribution of all electrons in an atom.
Consist of:



Number denoting the energy level.
Letter denoting the type of orbital.
Superscript denoting the number of
electrons in those orbitals.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Orbital Diagrams

Each box represents one
orbital.

Half-arrows represent the
electrons.

The direction of the arrow
represents the spin of the
electron: +½  or -½ ↓
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Hund’s Rule
“For degenerate orbitals, the lowest energy
is attained when the number of electrons
with the same spin is maximized.”
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Periodic Table

Atoms fill orbitals
in increasing
order of energy.

Different blocks
on the periodic
table correspond
to different types
of orbitals.
Figure 5.25
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Some Anomalies
Some
irregularities
occur when
there are
enough
electrons to
half-fill s and d
orbitals on a
given row.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Some Anomalies

For instance, the electron configuration
for Iron is: [Ar] 4s1 3d5 rather than
the expected: [Ar] 4s2 3d4.

This occurs because the 4s and 3d
orbitals are very close in energy.

Hund’s rule for degenerate (half filled)
orbitals is to half fill each box.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Some Anomalies

For instance, the electron configuration
for Copper is: [Ar] 4s1 3d10 rather than
the expected: [Ar] 4s2 3d9.

This occurs because the 4s and 3d
orbitals are very close in energy.

Symmetry and similar energies for
electrons fills the 3d-block first
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
Some Anomalies

For instance, the electron configuration
for Iron is: [Ar] 4s1 3d5 rather than
the expected: [Ar] 4s2 3d4.

This occurs because the 4s and 3d
orbitals are very close in energy.

These types of anomalies occur in fblock atoms, as well.
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
End of Chapter 5 part 2
Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia