The electron stays in the atom. Thus, its total energy will be negative (remember in Module B be defined "Binding Energy" to be negative). An energy diagram, such as Figure 2, represents both the electrons total and potential energies.
We will use this diagram to explore wave functions of electrons in atoms.
Start the Wave Function Sketcher program.
Create a potential energy similar to Figure 2. Follow the steps to sketch a wave function and attempt to draw a wave function for all three regions. Be certain to calculate the wavelength for each region and keep it fixed.
If you have difficulties sketching the wave function, describe the problems below.
Make a sketch of your best wave function even if it is not quite smooth at both boundaries.
You probably found making smooth connection at both boundaries difficult. Get one right and the other one is messed up.
What would you need to change to create an acceptable wave function?
To see that we can draw wave functions for this situation, set up the following parameters.
Potential Minimum = -4.3 eV Potential Width = 0.71 nm Total Energy = 1.3 eV
Make a sketch of your wave function, describe its shape below.
You probably found this wave function much easier to draw. That's because the parameters are "just right." You can see by looking at the wave function how it fits nicely into the available space. Other similar examples are shown in Figure 3.
Figure 3: Some wave functions which just fit in the potential energy with minimum = 4.3 eV and width = 0.71 nm.
Why do you think that it is easy to draw a wave function for certain potential and total energies and not for others?