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AP Physics Featured Question: Atomic Energy Levels

by Greg Jacobs
Woodberry Forest School
Woodberry, Virginia

Oh boy, atomic energy levels -- I know, it's a long year, and there's a lot of material to cover in AP Physics B. When time is short, atomic physics tends to take a backseat to other topics. It's listed last in the Course Description and in most textbooks, it's less than 10 percent of the AP Exam, and dadgummit, it sure is hard.

Isn't it?

Students tend to throw up their hands when they see all those numbers with 10-34 in them, and many of us threw up our own hands at the Bohr model when we tried to understand it in college.

But the Bohr model is no longer part of the AP Physics B Exam. And the mathematics necessary for atomic physics isn't even algebra; it's stuff we learned in sixth grade, for the most part.

One difficulty in atomic physics is the abstract nature of the subject. Your students most likely don't have any personal experience with the physical effects of atomic energy levels; they almost certainly have no experience calculating photon energies or stopping voltages. But perhaps the biggest obstacle for students in studying atomic physics in this course is that they believe the subject to be outrageously difficult. When the teacher provides simple analogies, simple computational methods, and straightforward problem solutions, the student thinks, "This is too easy! I must have missed something." I believe that it is a major part of the teacher's job in this unit to convince the class that most problems are not complicated.

One secret I've discovered in teaching atomic physics is the powerful imagery inherent in the energy level diagram. Even at the end of the year, many students don't think they're doing real computational physics unless they're using some seriously dense equations. Yet in atomic physics, equations are usually superfluous: reasoning from a diagram leads more easily to a correct answer.

Consider the example of finding the kinetic energy of electrons ejected from a photoelectric surface. Let's say the work function of the surface is 2.2 eV, and that 100 nm radiation is incident on the surface (as in part (d) of this featured question). An equation on the equation sheet is relevant to this situation:  . A student in equation mode might be fortunate enough to recognize that   represents the 2.2 eV work function. He might recognize that he can find the frequency, f, of the photons by plugging into  ; then, if he chooses the correct version of h from the constants sheet (h is listed in both J•s and eV•s), and if he properly converts 2.2 eV to joules, he'll get the correct kinetic energy. Of course, with so many opportunities to make a mistake, or to misidentify a numerical quantity, the chances for complete success are reduced.

Now think about doing the same calculation with only one equation, but with a very simple energy level diagram, even one not to scale. The only equation necessary is the conversion between a photon's wavelength and the energy the photon carries:  . On the equation sheet, hc is given as 1,240 eV×nm, making the calculation of this photon's energy doable without a calculator:

Now draw an energy level diagram:

We can now see graphically that, if the photon gives 12.4 eV of energy to the electron, and 2.2 eV are used to get out of the atom, the remaining 10.2 eV must be the kinetic energy of the ejected electron.

If you can get students to draw or at least picture an energy level diagram on every problem, they may switch from pounding on their calculators to really thinking about the conceptual implications of the atomic transitions involved.

Correlation to the Topic Outline
V.A. Atomic physics and quantum effects:
  1. Photons, the photoelectric effect
  2. Atomic energy levels
Featured Question

The diagram above shows three energy levels of a hypothetical atom. The lowest available energy level is

  1. Draw arrows on the above diagram showing all possible photon emissions for electrons that begin in the –2.2 eV state.
  2. What wavelength(s) of visible light can electrons emit that begin in the –2.2 eV state?
Now visible light is incident upon a photoelectric surface with work function 2.2 eV.
  1. On the axes below, sketch a graph of the maximum kinetic energy   of ejected electrons as a function of the wavelength   of the incident light for the range of wavelengths indicated. Label the vertical axis with an appropriate scale and units.

  1. What is the stopping potential for electrons ejected from this surface by 100 nm radiation?

Greg Jacobs teaches AP Physics B and C at Woodberry Forest School in central Virginia. He is a graduate of Haverford College, and has a master's degree in engineering from Northwestern University. When he is not teaching, Greg broadcasts Woodberry Forest varsity baseball games over the Internet; he is a reporter for STATS, Inc., covering baseball, basketball, and football; and he is a Reader and consultant for the College Board's AP Physics program. Greg lives on campus at Woodberry with his wife Shari and their son Milo Cebu.

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