From Waves to Orbitals

Submitted by jshorb on Fri, 02/04/2011 - 02:01

If you have already gone through our Wave Tutorial, then you've learned about wavelengthThe distance between the crests of adjacent waves (or between any adjacent corresponding points in waves); used in the context of electromagnetic radiation., frequencyThe rate at which a periodic event occurs; specifically, the rate at which the waves of electromagnetic radiation pass a point., and standing waves within a circular boundary. That tutorial concluded with a video of the Chladni Plate in use. To the left you can see this video once again. As the sound waves create a standing wave pattern within the circular plate, the grains of sand get shaken into a discernible pattern.

As the frequency increases, you'll notice that the sound gets to be a higher pitch (if you have the sound turned on), and that the circular rings of sand get more closely spaced - and indeed you'll notice that there are more of them in the same area! 

The area where the sand collects is the area where the plate is vibrating the least. Thus, as can be seen in the next video, the standing waves create stationary nodes where there is little motion. This wave demonstrator shows a standing wave patter in only 1 dimension (as opposed to the 2 dimensions in the Chladni plate).

On the Chladni plate sand collects in the places where there is a stationary region between two vibrating regions. Such a place is called a node. Nodes in the wave demonstrator have the same property. How many nodes does this wave demonstrator have?

Suppose that the waves in the wave demonstrator were associated with an electronA negatively charged, sub-atomic particle with charge of 1.602 x 10-19 coulombs and mass of9.109 x 1023 kilograms; electrons have both wave and particle properties; electrons occupy most of the volume of an atom but represent only a tiny fraction of an atom's mass. in a confined space. In order to create a standing wave with 4 nodes, would you have to increases or decrease the energyA system's capacity to do work. of the electron?