Teacher’s Guide
Quantum Phenomena
Overview
Students are introduced to the concept of electron waves and probability distributions.
Students explore electron interference and diffraction and how electrons differ from
particles when encountering barrier with slits in it. Students learn how the wave nature
of an electron allows electrons to tunnel through barriers, how two nuclei can share an
electron in a covalent bond, and how electron waves and energy levels in an atom are
related.
Learning Objectives
Students will be able to:
 Define a probability distribution and explain how it relates to an electron wave
 Compare how particles interact with slits to how electrons interact with slits
 Describe how an electron can appear on the other side of a barrier
 Use the concept of electron waves to explain the sharing of electrons in a
covalent bond
Student Prerequisite Knowledge
Students should already have a basic understanding of:
 probability
 atoms, ions, and chemical bonding
 quantized energy levels in an atom
 interference and diffraction as it relates to waves
Background and resources
http://www.colorado.edu/physics/2000/schroedinger/index.html - Experiments on
Wave Interference
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html - More
information about the probability density of an electron around a hydrogen atom
Approximate time for lesson completion: 60 minutes
Activity Answer Guide
Page 1:
The electron wave behaves like water waves
bending around a barrier. (diffraction of waves)
1. Can you think of a rule of the dartboard
game that will result in a different probability
distribution than the one shown above?
According to your new rule, how would the
new probability distribution look like?
One example might be to say that you get the
most points for hitting the yellow triangles. This
would cause the pattern to change in a way that
would have more dots concentrated on the
yellow areas and less on the red areas.
2. Give an example of probability distribution
and describe how you may visualize it.
You could record on a map where people have
the flu and the areas with higher concentrations
of dots indicate where you are more likely to
catch the flu.
Page 2:
1. The motion of the electron wave is most
like:
(b) A water ripple bouncing off a rock
2. Observe the two simulations above
carefully. The motion of the ball and the
motion of the electron wave have one thing
in common. What is it?
The motion is symmetrical about one axis.
Page 3:
1. Based on your observation from the above
simulations, which of the following must be
true?
(b) Electrons behave more like water waves in
the single-slit experiments.
2. If you click one of the rectangular
obstacles in the above quantum model and
type DELETE to remove it, what will you
observe when you run the simulation? Try to
explain your observation using the concept
of electron wave.
Page 4:
1. Based on your observations from the
above simulations, which of the following
must be true?
(b) Electrons behave more like water waves in
the single-slit experiments.
2. If you click one of the rectangular barriers
and resize it so that one of the slits is closed,
what will you observe when you run the
simulation?
It will behave like the single slit experiment. You
will stop the interference pattern and only see
diffraction.
Page 5:
1. Use the "Step through" button to run the
tunneling model on the right step by step.
Take a snapshot that shows the tunneling of
the electron.
2. How does the snapshot you took in the
window to the left show quantum tunneling
of an electron?
3. Take a snapshot that shows the formation
of a proton and a hydrogen anion and add
some annotations to explain it.
It shows how the chance of finding the electron
occurs on both sides of the barrier.
Page 6:
1.Why does the electron wave always tend to
surround a proton?
The electron wave represents the probable
position of the electron. The electron has a
negative charge, so it will be attracted to the
positive charge of the nucleus. The electron
wave shows the close proximity of the electron
and the nucleus by surrounding the nucleus.
2. Take a snapshot that shows the formation
of a hydrogen molecule and add some
annotations to explain it.
4. Take a snapshot that shows the formation
of two hydrogen atoms and add some
annotations to explain it.
Page 7:
1. Which of the following readings of the
frequency slider did you find capable of
exciting the electron?
(b) 1
2. Describe how you determined the answer
to the question to the left based on the
observation from the above simulation.
When I set the oscillation frequency to 1, I get a
stable electron distribution with two peaks (at
least temporarily), indicating the shape of the
electron probability distribution is now in a
“stable” excited state.
3. What frequencies other than the one you
have selected for the above question can
excite the electron? Explain your answer
based on your observation.
If you wait a long time at frequency 3 a new
stable electron distribution occurs that shows
four peaks.
4. What trend about the change of the shape
of the electron wave did you observe when
you moved the mouse from the lowest
energy level to the highest one? Explain your
observation.
As the energy level increases, the number of
peaks in the electron wave increases.
A ball moves smoothly from on place to another
in a straight line. An electron wave spreads out
to describe the locations an electron is likely to
be found. When a ball hits a wall it rebounds, but
when an electron hits a barrier is causes the
electron wave to “ripple” and sometimes the
electron can tunnel through the wall.
4. The three images below show the motion
of the electron wave in a container similar to
what you saw on Page 2 but with a different
condition. Explain what this sequence of
images shows.
This sequence of images shows an electron
tunneling through the side of its container.
5. The pictures below are the results of two
experiments. One shows the results of a
machine gun shooting at a barrier with two
slits the other an electron gun shooting at a
barrier with two slits. In both images, a bright
spot represents a hit. Can you tell which one
is which? Explain your answer.
The machine gun bullets will act like bouncy
balls. The bullets will be found in two clusters,
one behind each slit. Thus, the picture on the
right represents the results of machine gun
bullets hitting the barrier.
The electrons will diffract and interfere as they
pass through the slits, creating several regions
where electrons will hit the screen. The picture
on the left represents the results of electrons
striking a barrier with two slits.
Page 8
1. What phenomenon is shown in the image
to the left?
(b) Diffraction
2. Which of the following does an electron
wave NOT represent?
(d) The energy of an electron.
3. Describe the difference between the
motion of a bouncy ball and the motion of an
electron wave.
6. When a quantum leap happens to an
electron in an atom, what has NOT changed?
(b) The ground state.
7. When an electron wave becomes shared
equally by two nuclei the result is
(c) a covalent bond
Further Extensions
 Discuss the Davisson-Germer
experiment, which proved that electrons
diffracted when they interact with
crystals.
 Explore electron microscopy, which is
used to view objects on the atomic scale
using electrons and analyze the
structure of materials using electron
diffraction
 Discuss how electrons in a hydrogen
atom can have different quantum
numbers, and how those quantum
numbers result in different probability
distributions.