Just with waves on a rope there are multiple possibilities for the wave function in the atom.
Below are pictures of four possible wave functions for an electron bound to an atom. For each wave function the electron have a different energy.
Which of the wave functions shows the electron with the LOWEST energy?
Which of the wave functions shows the electron with the HIGHEST energy? Explain your reasoning for this and the previous question.
In quantum mechanics we give the wave functions for bound states numbers - "quantum numbers" - to label them. The lowest energy wave function has the quantum number n = 1, the second lowest n = 2 etc.
Start the program Bound States. You should have downloaded this program to your hard drive in the previous module. If you can't find it you can download it by clicking here.
[Kim, Kevin will be able to give you the download location, he set it up for the previous tutorial that needed bound states last week]
Go to the Potential menu pull down and change the well depth to about -500 eV.
List the allowable energies for the well below.
For each allowable energy click on the energy level line (on the left side of the screen) to see the symmetric and anti-symmetric wave function solutions. Symmetric is in blue, anti-symmetric is in green. For each energy which is the acceptable wave function symmetric or anti-symmetric? Make a list below.
Remember the acceptable wave function will decay towards zero in classically forbidden regions.
How is all this related to the spectra of gases we observed way back in Module B?
Lets explore the answer to this rhetorical question by considering a hypothetical gas that has spectral lines at 2.0 eV, 2.4 eV and 3.0 eV. Sketch an energy diagram for this gas, showing the transitions which correspond to the spectral lines.
Describe the energy diagram you sketched (include numerical values) below.
How many energy states (as used in the Bound States program) will you need to describe this hypothetical gas?
Assume that the lowest energy state is an n = 1 state, sketch the wave functions for each of the energy state you have identified.
Describe your sketches for each energy state below.