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.  

Using the AP Physics 1 Curriculum Framework -- it's a reference work, not a novel.

What will an AP Physics 1 test look like?  Neither you nor I has much guidance from sample questions published by the AP Physics 1 test development committee.  You can find what has been released by downloading the curriculum framework and looking toward the back -- you'll see about 10 sample questions.

But that tome of a curriculum framework includes all these hyper-specific "learning objectives."  Many in College Board leadership positions contend that teachers should carefully read all 150+ pages.  I disagree.  Read one small section to get a feel for the curriculum framework.  Read the "Science Practice" skills students will be expected to demonstrate.  You should look at the "concepts at a glance" that start on page 152, and you should get a copy of the topic checklists that are being distributed at AP Summer Institutes and workshops.*  Use these checklists along with the sample problems that have been and will be provided in order to plan your AP course.  As you actually start your course, refer to the learning objectives and the "essential knowledge" statements as necessary to adjust your focus.  After a few years of teaching AP Physics 1, you'll develop a good sense of what is and isn't important.

* I can't link a copy, because I don't believe these documents have been released except in the materials provided to APSI participants.

Most importantly, don't stress about possibly missing a detail that might be buried in this tome.  Let's say you miss the Physics 2 sentence that says electric and magnetic field "lines" will be replaced by vector field notation.  That's a change from standard textbook coverage, from what most of us learned in college, and from the AP Physics B exam.  But so what, say you teach field lines the old way.  What happens?  Your students possibly struggle with one point somewhere on the Physics 2 exam this year.  And you figure out a year or two down the road that you've been doing it wrong.  And you change.

[Personal story:  I attended my AP Summer Institute in 1997, right after special relativity had been taken off the exam.  Based on the instructor's suggestion, I wrote a huge note: "NO SPECIAL REL!"  Then in March I went and taught special relativity, thinking it was on the exam.  No, no one fired me, and my students did quite well.  Relax, and take a minimum three-year long-term focus.]

When I created my best attempt at a practice test, I simply entered every learning objective from the AP Physics 1 curriculum into random.org, and wrote a multiple choice question to test each of the first 50 LOs that showed up.  Randomizing and using the LOs is a good exercise if you have the time and creativity to use them as review, or to write questions toward them (or even to ask students to write questions toward them).

Is that generally how the actual AP Physics 1 test will be developed?  Almost definitely not.  Hopefully, in summer 2014 when the official course description comes out, we'll see some further guidance about how much of the test will be devoted to each topic.  For now, I'm doing my best to represent the nature of this brand new test.  I will be wrong in many places.  I will fail to emphasize some part of the exam that shows up significantly; that could be a topic, or a skill, or just a simple approach to a complex idea.  After the first test in 2015, I will evaluate my teaching, and improve.  By 2017, I'll have figured most of it out.

And you do the same.  Don't listen to the education professor types who expect you to read, remember, and use every word of the framework.  Think of the framework like a dictionary -- you should have a good idea what's in there, but you don't read it front to back.  You look things up when you need them, with the goal of becoming fluent in the language, not of being able to parrot the contents.

"Because V=IR"

My first laboratory exercise with circuits shows the students a circuit with a battery and two resistors in series.  Part (a) asks which resistor takes the larger current through it -- that's easy, because they see the fact of physics that says "current through series resistors is the same through each and equal to the total."

Part (b) is slightly more complicated.  It asks which resistor takes the larger voltage across it.  Everyone recognizes that the 70 ohm resistor is the one with larger voltage.  But how should that statement be justified?

Incomplete justification:  "The larger resistor must take the larger voltage."  Says who?  All justifications in physics must begin with a fact, an equation, or a calculation.  We have no fact of physics in our textbook or our fact sheet that says larger resistors take larger voltages.  So try again.

Incomplete justification:  "The larger resistor takes the larger voltage because V=IR."  Not good enough.  Everything in circuits can, in some sense, be justified with the phrase "Because V=IR."  Just citing an equation isn't enough -- I need to see how the equation is used to justify the answer.

Incomplete justification:  "The larger resistor takes the larger voltage because in V=IR, when resistance increases so does voltage."  Almost there... but missing an important element.  This equation contains more than just resistance and voltage.  Mathematically, a slightly larger R with a much smaller I would produce a smaller V!  

When justifying an answer with an equation, always start with the variable(s) that don't change:

Complete justification:  "The larger resistor takes the larger voltage because in V=IR, each resistor takes the same I because they are series resistors.  Then mathematically a larger R gives a larger V."  I need to see the statement about constant current for both resistors before I accept the justification.

The protest:  "But Mr. Jacobs, I already told you that the current was the same for both resistors in part (a)."  You did, and I appreciate it.  I nevertheless need you to say it again in part (b), or at least to refer me back to part (a).  Without the explicit statement about constant current, Ohm's Law doesn't lead to the conclusion you think it does.*

*  In the very rare situation when the student gets huffy with me, I remind him firmly that I'm asking him to write just four extra words; if he wants to ask the headmaster to replace the physics teacher because I require four more words than he personally wants to write, he's welcome.  Until he has that conversation with the headmaster, he may stop whining and do the work like I asked him to.

Why I'm picky here:  In general, the key to justifying an answer directly from an equation without calculation relies on identify the constant variables.  So I'm emphasizing the technique that will help students be successful beyond this single problem, or even this single exercise.

Beyond that, I've established how this sort of justification should look throughout this circuit exercise. When the students come to the combination parallel-series circuit, they see quickly that current is not the same for each resistor; so the reasoning "R2 takes the largest voltage because it is the larges resistor" is never even written down for me to criticize.  The class may groan at my pedantry, but they gain the benefits.  There's a method to my madness, even when my students don't see the method right away.

Justify the distractors when writing multiple choice items

Before I get into the meat of this post, a caveat:  Don't actively WRITE multiple-choice items for your classes unless you have no other option.  If you're teaching at the AP or Regents level -- even if you're not technically teaching a course labeled "AP" or "Regents" -- multiple-choice questions are more plentiful than Tribbles in an unpredated colony.  Use them.  I still, after 17 years of teaching, don't ever use multiple-choice questions of my own design on tests in these classes.  That said, good multiple-choice for conceptual physics, and (currently) for the new AP Physics 1 course, are more comparable to American Bison.  They're out there, the population is slowly increasing, but they're tough to find outside of Yellowstone National Park.

Multiple-choice questions must be carefully constructed if they are to test physics knowledge rather than general test-performance instincts.  Just as we don't want a free-response question to be game-able by anticipating the rubric, a multiple-choice item should not be game-able by eliminating choices for reasons unrelated to physics.  If a distractor* in an item is so silly as to be instantly eliminated without physics reasoning, the question is poor.  For example, a calculational question in which only one choice could be obtained by any possible algebraic manipulation of the given values; a question with three short, poorly-phrased phrases and one long, clearly written sentence; or a verbal question in which one or more choices doesn't even refer to physics principles.  

* "Distractor" in ETS-speak means "wrong yet plausible choice"

Questions for the new AP Physics 1 and 2 exams will have only four, not five, choices.  Why?  At the meeting for AP consultants last April, we were told that in their research, ETS could find no statistical difference in performance between four-choice and five-choice questions.  Furthermore, it was contended that the fifth choice increases the reading comprehension burden on the student, to the extent that students in studies were often not reading all the way through the fifth choice.*  And finally, the committee's perception was that, all too often, test authors grasp at straws in coming up with a fifth plausible distractor.  

* This should surprise no one who sends class emails beyond one sentence in length.  Try burying an offer of extra credit in the middle of an email's second paragraph, and you'll see.

In order to make the question authors focus more on the reasonability of the distractors, ETS now asks authors of each item to justify each distractor.  We of course mark the correct answer, perhaps with the reasoning that we hope will lead the student to choose that answer.  But then for each of the three incorrect options, we fill in a box to say why we think a student might plausibly, if incorrectly, choose that wrong answer.

The process of justifying distractors makes writing questions more time consuming, in that the expected incorrect reasoning must be articulated in words.  But the questions become of such higher quality.  Plenty of times I've improved the language in a distractor, or changed it entirely, because of a disconnect between what the problem stated and my justification for a student's thought process.  The item review process can be more efficient, not only because the justifications for each choice are spelled out, but because fewer poor-quality items are submitted to begin with.  (In previous years I've reviewed questions in which the author seemed to just make up random crap for a couple distractors.  With the requirement for written justification, many of these questions will be weeded out before the review stage.  It's not likely that even a less-skilled test author will submit a justification that says "No student would ever pick this choice unless he's a total dipstick.  I'm out of ideas.")

And writing justification for each potential wrong answer forces the writer to consider common misconceptions.  One of my favorite sources of inspiration in writing multiple-choice is to think about open response problems that I've given to my class, or that I've graded at the AP exam reading.  On such problems I generally have an intimate familiarity of the myriad ways in which students can be wrong.  So I rephrase the problem as a multiple-choice item, sometimes with distractors nearly verbatim from actual incorrect student answers.

If you have written multiple choice items for your own test, look at some with an eye to justifying the distractors.  Why would an intelligent student with an incomplete or incorrect knowledge of physics choose each one?  If you can't say, then eliminate the choice.  (If you're not teaching AP or Regents, who says every multiple-choice item has to have the same number of choices?  A three-choice question, with answers like "greater than, less than, or equal to" can be just fine.)  Mercilessly cull any question that  can easily be answered without physics knowledge.  Have a trusted and knowledgeable colleague review the items you've written.  The quality of your tests will skyrocket; and your students' understanding of physics will improve as well.

Teach calculation, even in conceptual physics, even in AP Physics 1

Physics teaching, as a profession, has come a long way since the dark days of the 1970s and 80s.  Although many of the country's classes remain in a "shut up and calulate" mode, more and more physics teachers are recognizing the importance of verbal explanation and conceptual understanding.  Sure, the prevalence of Webassign encourages a plug-and-chug mentality.  But textbooks, teaching literature, and standardized exams (such as the SAT II, AP, and Regents) ever-increasingly prioritize questions that are not simply of the form, "calculate the acceleration."

I'm sure longtime readers recognize that I am a whole-hog supporter of this trend toward articulating physics concepts.  The new AP Physics 1 and 2 exams, especially, will reward knowledgeable physics students at the expense of those who merely search the equation sheet for something with a Q in it; and I am one of the loudest supporters of the new exams.

People are often surprised, then, when I reveal that I firmly believe in teaching calculation in all my classes -- including AP Physics 1, including conceptual physics.

Remember, we physics teachers approach our subject with a degree of sophistication and experience that is far beyond that of our padawans.  Our sophistication helps us recognize the True Meaning of Physics, which prioritizes conceptual understanding; but our students are many steps behind us.  We've got to deal with students as they are, not as we idealize that they should be.

True, deep understanding begins with the basics: memorization of facts.  I don't care how clever or insightful a student might be, if he can't tell me that momentum is conserved in a collision, or define acceleration as change in velocity in one second, he can't reason appropriately about physics.  Recall of facts is a precursor to advanced reasoning in any subject.

For the majority of physics students, though, calculation comes next.

Physics education research pooh-poohs calculative exercises in favor of ranking tasks, semi-quantitative reasoning*, and other "Tasks Inspired By Physics Education Research."  From Pearson education, promoting one of their TIPER workbooks: "[These books]...reinforce the sense that the ideas of science have coherence and power that extends beyond the facts and equations."

*i.e. "From how many times higher should a ball be dropped in order to double its time of descent?"

I object to the pooh-pooh on a couple of levels.  Firstly, such an attitude can be compared to those teachers of history who prioritize narrative over fact, or those proponents of teaching "whole language" as opposed to vocabulary and grammar.  Certainly they have a point, in that an excess of memorization and drill without payoff can demotivate promising students; nevertheless, if you're actually going to learn anything about history or language, then facts and vocabulary are non-negotiable precursors.

More practically and less philosophically, actually watch students over a year as they come to grips with physics concepts.  Our goal is for students to use equations as tools for understanding: 

"With no initial speed, the kinematics equation reduces to d=(1/2)at².  The acceleration is the same either way because the ball is in free-fall.  Since the time variable is squared and in the numerator, the distance for the ball drop must be multiplied by 2², or by a factor of four."

At the beginning of a student's first year of physics, such reasoning can be beyond even very capable students.  In fact, their instinctive approach is to "set up a proportion," coming to the conclusion that twice the time must mean twice the height -- logic, see?  Such a student is not ready for advanced verbal reasoning yet.

What's NOT beyond anyone is a calculation: Use the equation d=v₀t+(1/2)at² to calculate the distance the ball falls in, say, 1 s; then do another calculation for 2 s; and see that the ball falls four times as far.  This student is using calculation as a crutch, yes.  But (a) he's getting the answer right, (b) he's doing correct, if brute-force, physics, and (c) he is showing progress in his physics understanding, because he reasoned from a relevant equation rather than "logic."

As the year goes on, it's my job to guide such a student away from brute force and toward more subtle reasoning.  One easy idea is to award more or extra credit to those students who use a sophisticated, non-calculational approach.  Or, perhaps require students to make numerous calculations to answer a ranking task; then come back and ask them to describe a way to justify the ranking without doing any numerical calculations.

The point is, a non-insignificant subset of your class needs to use calculation as a first step toward  a deeper understanding of physics.  Even in conceptual physics, I'm pleased with students who make up simple values to plug into equations.*

* My freshmen have taken to calling this approach a "false calculation" -- if the acceleration isn't known, for example, just use 1 m/s per second.  This approach works for virtually any semi-quantitative question or ranking task.

When I teach AP Physics 1 in 2014-15, I intend to begin with material identical to that which I've used in AP Physics B: end-of chapter-style problems involving calculation, always mixed with some sort of descriptive prompt, and always including the requirement for presentation and communication.  Once we've become comfortable approaching this newfangled course called physics, then I'll cover the same material again, this time always going beyond mere calculation.