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Thursday, June 20, 2019

Waves and Nodes


When we think about electrons as waves, we need to be sure that we are thinking about the “right kind” of waves. Waves can travel (like light or sound waves). These are often depicted in images like this:
Make sure you understand the basics of waves, which are covered here.

When we think about electrons in an atom, however, we need to be thinking about standing waves. The easiest example of a standing wave is the plucked string on a guitar or other stringed instrument.In this case the string vibrates back and forth but remains in the same place. 

For those who know something about stringed instruments, you may have heard of harmonics. Harmonics are created when the string is forced to remain motionless in the middle and the vibration continues on BOTH sides of that point. This will cut the wavelength in half. Other harmonics create third, fourth and more parts of the wave. 


What matters for us, in this discussion is the points where the string is NOT vibrating. These points are called nodes. If you look carefully at this image, you will see that there is a dark red line and a paler line. If this were a guitar string, the dark red line is where the string will be at one moment, and then, as it vibrates, the string will occupy the paler line. 

The points where the red lines cross the black center line are nodes. As the string vibrates, this point never moves. In fact, if you could touch the string at that point (and not anywhere else) you would not be able to tell if the string was vibrating. A node, then, is a place where the wave has no measurable value.

In the first diagram (top left) there are no nodes. In the second diagram (top right), there is one node. Note that as the number of nodes increases the wavelength decreases.

Remember that wavelength is related to energy. Specifically, the higher the energy of the wave, the shorter the wavelength. Since shorter wavelengths (in the same string) means more nodes, we can say that as energy increases, so does the number of nodes. We should also note that the lowest energy wave has 0 nodes.

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