Orbitals:
What? Why?
The Bohr theory of the atom did not
account for all the properties of
electrons and atoms.
The Bohr theory of the atom did not
account for all the properties of
electrons and atoms.
Einstein proposed that light had the
properties of particles (“photons”) as
well as waves.
The Bohr theory of the atom did not
account for all the properties of
electrons and atoms.
Einstein proposed that light had the
properties of particles (“photons”) as
well as waves.
De Broglie proposed that some
things usually thought of as
particles, such as electrons, also
have wave properties!
For light:
hc
E = h 

For matter:
E = mc
2
For light:
For matter:
hc
E = h 

What if:
hc

 mc
E = mc
2
then
h

2
 mc
For light:
For matter:
hc
E = h 

What if:
hc
h
or  
mc

 mc
E = mc
2
then
h

2
 mc
h
or for matter ,  
mu
h

mu
Would imply that anything with mass and
speed has a wavelength!
For canceling units, J =
kg  m2
s2
h

mu
speed
Would imply that anything with mass and
speed has a wavelength!
For canceling units, J =
kg  m2
s2
Sample Problem 7.3 Calculating the de Broglie Wavelength of an Electron
PROBLEM: Find the deBroglie wavelength of an electron with a speed of
1.00x106m/s (electron mass = 9.11x10-31kg; h = 6.626x10-34
kg*m2/s).
PLAN:
Knowing the mass and the speed of the electron allows to use the
equation  = h/mu to find the wavelength.
SOLUTION:
=
6.626x10-34kg*m2/s
9.11x10-31kg x 1.00x106m/s
= 7.27x10-10m
For larger objects, wavelength is much too
small to measure.
Electrons do have wave-like properties and
this can be shown by experiment: for
example, they can be diffracted.
Figure 7.14
Comparing the diffraction patterns of x-rays and electrons.
x-ray diffraction of aluminum foil
electron diffraction of aluminum foil
Figure 7.13
Wave motion in
restricted systems.
The Heisenberg Uncertainty Principle
h
x   (mv ) 
4
The Heisenberg Uncertainty Principle
h
x   (mv ) 
4
Uncertainty
in position
The Heisenberg Uncertainty Principle
h
x   (mv ) 
4
Uncertainty
in position
Uncertainty
in velocity
The Heisenberg Uncertainty Principle
h
x   (mv ) 
4
Uncertainty
in position
Uncertainty
in velocity
(A very
small
number)
The Heisenberg Uncertainty Principle
h
x   (mv ) 
4
Uncertainty
in position
Uncertainty
in velocity
(A very
small
number)
This equation puts a limit on how precisely we can know the
position and the velocity of a particle at the same time.
A full theory is called “Quantum Mechanics.”
Instead of telling us where an electron is at any point
in time, it gives probabilities of finding an electron at
a given point in space.
The equations that give the probabilities are known
as wavefunctions.
The wavefunctions contain the quantum
numbers that determine what kind of orbital the
electron is in.
Instead of describing electrons
in orbits like this:
Instead of describing electrons
in orbits like this:
We must describe them as “clouds” of electron density,
with a volume of changing probability around the nucleus.
• https://undergrad-ed.chemistry.ohiostate.edu/H-AOs/
Figure 7.16
Electron probability in the
ground-state H atom.
Figure 7.12: (a) Probability Distribution for
Hydrogen 1s Orbital in 3D Space (b) Probability
of Finding the Electron at Points Along a Line
Figure 7.13: (a) Cross Section of Hydrogen
1s Orbital; (b) Radial Probability Distribution
Figure 7.14: (a) Representations of
Hydrogen 1s, 2s, and 3s Orbitals (b) Surface
Containing 90% of the Total Electron Probability
Figure 7.15: (b) Boundary Surface
Representations of all Three 2p Orbitals
Figure 7.15: (b) Boundary Surface
Representations of all Three 2p Orbitals
Boundary surfaces (at right) enclose, say, 90% of the
electron’s position.
Figure 7.19
The 2p orbitals.
Figure 7.17: (b) Boundary
Surfaces of Five 3d Orbitals