AP Physics B 2013 problem 7: Misconceptions about atomic energy levels

Not at all verbatim, but the general gist of a student's complaint:

"The introductory physics curriculum is so backward-looking.  Everything we cover was developed in the 16th-19th century.  You'd think physics just stopped with Maxwell and Faraday.  I mean, what the heck, why don't we study any 20th century ideas?  I would love to learn some quantum physics, but no, this stupid AP curriculum is stuck in the way past."

In a paean to the Goddess of Irony,* the rant above was written on problem 7 of the 2013 AP B exam -- the problem about atomic energy levels and quantized electron transitions.

* Alanis Morissette

So how did everyone else do?  Those who had some idea of how to approach atomic energy level questions did, I think, no better or worse than clueful students on other exam problems.  My impression is that the "students don't do well on modern physics problems" meme is way overblown.  The topic is tough because it's abstract; but the real reasons for low scores are (a) it's often put at the end of the year, so teachers don't get to it; (b) teachers are themselves uncomfortable with the material; (3) It's too often taught as a set of equations into which uncomfortably big and small numbers must be crammed.

The AP Physics 2 course will expand the atomic and subatomic physics offerings.  Not only will students have to deal with energy level diagrams, nuclear decay, the photoelectric effect, and de Broglie wavelengths; but add in the Bohr model, and the probabilistic interpretation of the wave function.  And as on all Physics 1/2 topics, the students will be expected to do far, far more than merely calculate.

So how could you turn this AP Physics B question into an AP physics 2 question?  As with any question you're adapting for the new exams, start with student misconceptions, and force the test taker to articulate his understanding in words.

For example, part (a) asks the student to draw possible transitions.  Great question -- now justify in words why those are the allowed transitions.  Otherwise the answer might be a guess, or mimicry of a remembered in-class example.

Part (b) asks for a calculation of the longest wavelength of emitted photons.  The big deal here isn't whether the student can plug into ΔE=hc/λ.  The better AP Physics 2 style question would be to explain which transition would produce the longest photon wavelength, and why; and, perhaps, an explanation of what value for ΔE should be used with hc = 1240 ev*nm.

Parts (d) and (e) are pretty wonderful for AP Physics 2 as-is.  They probe a student's ability to describe what's happening to the electron in words.  When a student doesn't understand, his use of language betrays him.  

These parts ask for a justification of what happens to the electrons in the ground state when they encounter photons of energy 11 eV and 14 eV.  The biggest mistake here was misuse of the terms "excited" and "infinity."  Even of the clueful students, many just said something like "the electron would be excited, it would go to infinity."  No, no, no, don't use those words... it was so rare and wonderful to see a student say "the energy of the 14 eV photon is greater than the ionization energy, so the electron will be ejected from the atom with a kinetic energy of 14-12 = 2 eV."  Infinity isn't a place -- the only reason the infinity symbol appears on the diagram is that the states are numbered by convention, and the top state is something like state number three billion.  And an electron can never "be excited."*  The common terminology for levels above the ground state is "excited states."  

*In your laboratory, the school's internet porn filter works well.  So the electron has heard, anyway.

As for the 11 eV photon, it can't cause the electron to jump, because it's not equal to the difference between the ground state and any other state.  Most clueful students incorrectly stated that the electron would jump to "between the n=2 and n=3 state."  That's an easy misconception to fix, with practice.

If you plan on teaching AP Physics 2 in the next few years, try focusing more than usual this year on AP B atomic and nuclear physics.  You'll find that the conceptual, verbal, and experimental understanding required in AP Physics 2 will actually help you teach the Physics B material.