H133: 1094 Session 4
Write your name and answers on this sheet and hand it in at the
end.
After the indicated time, move on to the next activity,
even if you are not finished!
1. Quanton in a Box [12 min.]
Start up the PhET applet "Quantum Bound States".
(Start>Programs>PhET, choose "Quantum Phenomena" from the left menu,
and click on the Quantum Bound States icon).
This applet shows energy levels and the corresponding
wavefunctions and probability densities for the energy
eigenvectors of different potentials.
The "square well" potential that comes up initially
is a finitedepth version of the "quanton in a box" potential.
 What force would a
Newtonian (i.e., classical)
particle feel at each x position?
Note that the wavefunctions don't go to zero at the "walls"
of the well; could this happen classically? Explain.
 For what energies would a quanton be "unbound"
(i.e., not confined to the well)?
 Roughly predict the energy of the n=2 state (secondlowest energy)
by estimating its wavelength from the simulation
and using this to find the
momentum and then the kinetic energy.
(To show the wave function, click on the 2nd level,
switch the Display to "Wave Function", and press "Pause"
to stop time.)
Compare to the value given by the simulation.
 Predict (and explain)
what will happen to the energy levels if you make
the box shallower.
[Hint: Does the wave function penetrate the walls more or less?]
Check your prediction by selecting "Configure
Potential" and reducing the "Height". Try a new explanation
if you were wrong the first time.
 Do twominute problem Q8T.3. [See Equation (Q8.5b) for
reference.]
2. Harmonic Oscillator [12 minutes]
Change the Potential Well using the pulldown menu on the upper
right to Harmonic Oscillator. This has the potential energy
k*x^{2}/2, which is the same as a spring.
 For what energies would a quanton be "unbound"
(i.e., not confined to the harmonic oscillator)?
 Vibrational levels of molecules are described by a harmonic
oscillator potential. Do problem Q8B.4.
 Time dependence I.
Based on Rule 6, what is the time dependence of
the probability density for the state with E2?
(Find the time dependence of the wave function
psi2(x,t) for a state composed only of eigenvector E2>
and then calculate the probability density.)
Does this agree with the simulation?
 Time dependence II.
Now use "Superposition State" to make a state with equal
parts E0 and E2 (so c0 and c2 should be equal).
Choose "Normalize" and then "Apply".
Measure the period of the probability density using the
clock in the lower left. Bonus: How is the result related to
the energies E0 and E2?
3. Models of the Hydrogen Atom [10 minutes]
Start up the PhET applet "Models of the Hydrogen Atom".
This applet simulates an experiment in which you shoot photons
of many different wavelengths ("White") or a single
wavelength ("Monochromatic") at a box with hydrogen gas.
With the switch on "Experiment", you can see what actually
happens outside
the box. With the switch on "Prediction", you can compare various
models ranging from more classical to more quantum mechanical
to see what they predict.

Turn on the electron gun and "Show Spectrometer".
Take a look first at "Experiment", then switch to "Prediction".
Try each of the models. Note that some are in clear
contradiction to the experiment (e.g., the Billiard Ball model
predicts many photons bouncing backwards).
For the last three,
"Show electron energy diagram".

For the "Classical Solar System" model, there is quickly
a "kaboom". What is happening and why? (Click on the icon
again to replay it.) How is this avoided in quantum mechanical
models?
 How does the deBroglie model compare to the Bohr model?
(E.g., similarities and differences.)
 Which of the models will (approximately)
reproduce the known hydrogen spectrum?
4. Discharge Lamps [12 minutes]
Start up the PhET applet "Neon Lights and Other Discharge Lamps".
This simulates the type of light we saw in class. You can
show "One Atom" of gas or "Multiple Atoms".
Start with "One Atom".
 Switch from "Single" Electron Production to "Continuous"
and click on the Spectrometer. What is the source of
energy to move an atom from the ground state to an excited
state?
 The Spectrometer shows only one wavelength of light. Why?
What do you need to change to get more wavelengths? (Try it!)
What if the energy of collision is less than the n=2
level (marked with a circled number 1)?
 Switch to "Multiple Atoms" and click on the Spectrometer again.
Identify
the wavelength of the red line and
show that the Bohr model quantitatively predicts it.
[Hint: see Q8X.5 on pg.156.]
 Take a look at other atoms besides hydrogen. Why do they
have more visible lines in their spectra?
H133: 1094 Session 4.
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