TAP 507-1: Standing waves - for electrons?
Electrons have a frequency too
Electrons can be modelled as having a frequency. In another context you have seen how
superposition of waves in the laboratory produces standing waves. Here it is useful to put
these two together, describing electrons with standing waves, with their wavelength described
by de Broglie’s relationship:
  h / mv .
Here you look at some consequences of this step.
You will need:

vibration generator

signal generator

rubber cord

G-clamp

wooden blocks
Vibrating a rubber cord
Frequency Adjust
5
3
7
8
2
1
10Hz
100H z
1kHz
10kHz
9
100kH z
Frequency range
1000
100
10
1
1000
10
100
Frequency
Wave
Outputs
10 Hz
A
power
Make sure that you can get clear patterns with this apparatus. Note that only whole numbers
of half wavelengths fit onto the cord.
Electrons trapped in an atom are also constrained. Describing them as waves, where the
amplitude tells you the chance of find them in any one place, constrains you to draw the
waves in a similar way.
Making links
Putting relationships together with these results allows you to predict that electrons will have
certain allowed energy levels only.
simplest pattern
next simplest pattern
L
L

2
from diagrams
from de Broglie
from kinetic energy
= h
mv
Ek =
1
mv2
2

2
 = 2L
=L
h
mv = 
Ek =
mv =
h
2L
Ek =
h2
8mL2
mv =
h
L
p2
2m
p = mv
Ek =
h2
2mL2
2 ?  and 4 ? Ek
See if you can continue the series for the next two standing wave patterns that will fit onto the
cord.
You have
1. Reminded yourself about standing waves.
2. Seen some of the consequences of using standing waves to model electrons in
atoms.
External reference
This activity is taken from Advancing Physics chapter 17, 140E