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## 13 April 2011

### Atomic Energy Levels Exercise

Okay, I'll admit my prejudice right off the bat:  I hate teaching atomic physics.  What I love most about teaching physics, rather than math, history, or (gasp) English, is that the answer to most questions can be demonstrated unambiguously with an experiment.  We have no truck with opinions in introductory physics:  I routinely provoke an argument in class, then settle the argument with a quantitative demonstration.

With atomic physics, though, I generally cannot show a demonstration.  Even those demonstrations that I can do -- like passing light from a mercury vapor lamp through a diffraction grating to see the discrete wavelengths of light emitted -- still require multiple leaps of abstraction in order to connect the problem solving to the phenomenon.  This isn't calculating the speed of a cart.

Nevertheless, the AP curriculum requires that I teach atomic physics.  The approach I take is to avoid exposition as much as possible.  I've found analogies and cutsey trick methods of imagining "what's really happening" in an atom are useless.  Instead, I take my inspiration from Richard Feynman:  "Shut up and calculate."

I provide each student with a set of two or three energy levels from an imaginary "atom," as shown in the picture.  The energy levels in these atoms are randomly determined, and all between -0.1 eV and -6.0 eV -- each student has a different set of energy levels.  I show very briefly the equation E = hc/λ, how the energy of the photon is determined by the difference between two energy levels, and the shortcut that hc takes the value 1240 ev*nm.  From there, I let the class work through a set of questions that could be asked about such an atom:

1. Photons of what energy can be absorbed by your atom?

2. Photons of what energy can be emitted by your atom?

3. What wavelengths of electromagnetic radiation are absorbed by your atom?

4. What wavelengths of electromagnetic radiation are emitted by your atom?

5. If an electron with no initial kinetic energy is captured by your atom, what wavelengths of EM radiation will be emitted?

6. The “Work Function” is defined as the minimum amount of energy necessary to kick an electron out of the atom from the ground state. What is the work function of your atom?

7. 7.0-eV photons are incident upon your atom. An electron in the ground state should be ejected from the atom. What will be
a. the ejected electron’s kinetic energy
b. the ejected electron’s speed
c. the incident photon’s speed

8. Assume all electrons in your atom start in the ground state. Your atom is illuminated with monochromatic 1300 nm IR radiation. What happens? (Describe any transitions that occur; if electrons are ejected from the atom, give their kinetic energy.)

9. Assume all electrons in your atom start in the ground state. Your atom is illuminated with monochromatic 620 nm red light. What happens?

10. Assume all electrons in your atom start in the ground state. Your atom is illuminated with monochromatic 200 nm UV radiation. What happens?

11. Your atom is illuminated with white light (visible wavelengths only, no IR or UV). What happens?

12. Your atom is illuminated with monochromatic 200 nm UV radiation, as in problem 10; this time, though, the radiation is more intense, i.e. the laser beam is brighter. What happens?

13. What minimum wavelength of incident light is necessary to ionize your atom?

14. Assume all electrons are initially in the ground state. 100 nm UV radiation is incident upon your atom. Electrons may be ejected from your atom. If so, they will have some kinetic energy.
a. What KE will these ejected electrons have?
b. I want to bring these electrons to rest using a potential difference. What “stopping voltage” is necessary to bring these electrons to rest?

I let the students use their texts and the 5 Steps book to try to figure these out.  I tend to help one person with each question; after that, I direct questions back to a student who has already been helped, so they teach each other.

This exercise sure ain't perfect.  Usually, students who "get" atomic physics learn plenty from this exercise.  Those who don't "get" atomic physics from this exercise also don't "get" it through lectures or reading.

GCJ