What General Chemistry Students Know (and Don

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What General Chemistry Students Know (and Dont
Know) About Quantum Concepts in Chemistry
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Quantum Concepts in ChemistryThe TeamPeter
Garik (presenting), Boston University (garik_at_bu.e
du)

• Haim Eshach,
• Ben Gurion University, Israel
• Luciana Garbayo, BU
• Alexander Golger, BU
• Morton Z. Hoffman, BU

• Peter Carr, BU
• Alan Crosby, BU
• Dan Dill, BU
• Yehudit Judy Dori,
• Technion, Israel

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Quantum Concepts in Chemistry

• This project is funded by the U.S Department of
  Educations Fund for the Improvement of Post
  Secondary Education (FIPSE).

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Quantum Concepts in Chemistry

• The objectives of our FIPSE project are
• to find ways to introduce quantum concepts into
  the chemistry curriculum
• to design software that will support the teaching
  of quantum concepts and,
• to evaluate the success of our software and
  curricular activities in supporting student
  learning of quantum concepts.

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Quantum Concepts in Chemistry

• Why teach quantum concepts at an early stage in
  the chemistry curriculum?
• The epistemology of a mature science relies upon
  foundational models for its research program.
• Such models provide a unifying perspective on the
  physical world and support the best insights and
  reasoning that we can currently achieve.

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Quantum Concepts in Chemistry

• For cosmology, it is the inflationary theory of
  the universe.
• For geology, it is plate tectonics.
• For biology, it is Darwinian evolution.

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Quantum Concepts in Chemistry

• For chemistry, one of the foundational models is
  unarguably the quantum theory of atomic structure
  and electronic behavior.
• The pedagogical issue is where does it belong in
  the curriculum?
• Quantum concepts appear burdened with additional
  abstractions (including mathematics) that make
  them first appear forbidding to teach.

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Quantum Concepts in Chemistry

• We argue that the unifying power of quantum
  concepts is so great, and their utilization for
  modern chemistry so extensive, that finding ways
  to successfully introduce them at an early point
  in chemistry education is our obligation to the
  students.

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Quantum Concepts in Chemistry

• What are quantum concepts in chemistry?
• The principal quantum topics in chemistry are
• 1) The description of electrons and how they
  behave in the presence of other charges.
• 2) The description of the interaction of
  radiation with matter, and primarily with
  electrons.

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Quantum Concepts in Chemistry

• Historically quantum concepts grew out of
  analogies to electromagnetic theory. Since the
  interaction of radiation with matter is a key
  concept in chemistry (spectroscopy), it is
  traditionally taught.
• The properties of electromagnetic waves provide
  an early access point for what we refer to as
  Quantum Readiness.

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Quantum Concepts in Chemistry

• What is a wave?
• What is an electromagnetic wave?
• Is there an associated electric field
• Is there an associated magnetic field
• What is the relationship between amplitude and
  intensity?
• What is constructive and destructive interference?

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Quantum Concepts in Chemistry

• How does the phase of a wave vary with time and
  space?
• How does a light wave interact with a charged
  particle?
• What is a photon?
• How do charged particles interact?
• Students prepared with these concepts should have
  analogies for understanding quantum phenomena.

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Quantum Concepts in Chemistry

• What are the quantum concepts that we would like
  students to master?
• The delocalization of the electron and its
  description by a probability amplitude.
• The quantization of energy levels.
• The pairing of a wave function with an energy.
• Constructive and destructive interference.
• The Pauli Exclusion Principle.

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Quantum Concepts in Chemistry

• The transition in energy levels associated with
  absorption and emission of radiation.
• The geometry of atomic and molecular orbitals.
• The atomic structure that arises from the Aufbau
  Principle.
• The molecular structure that arises from bonding
  orbitals and hybridization.

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Evaluating Students Conceptual Understanding of
Quantum Concepts

• As a first step to determining how students learn
  quantum concepts, we engaged in a qualitative
  research project.

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Theoretical Background and Methodology

• We base our qualitative research approach of
  using interviews on the empirical result from
  misconceptions research that, in assessing a
  population of students understanding of a
  scientific phenomenon, the number of different
  conceptions observed saturates quickly
  (Wandersse, Mintzes and Novak 1994).

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Theoretical Background and Methodology

• For our interpretive work reading the interviews,
  we adopted a perspective based on a dynamics
  systems approach proposed by Smith, diSessa and
  Roschelle (1993), diSessa and Sherin (1998), and
  by Petri and Niedderer (1998).

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Theoretical Background and Methodology

• We look for phenomenological primitives or
  cognitive elements/tools that students employ in
  order to construct their understanding.
• We expect to find cognitive attractors
  recurring misconceptions expressed by the
  students.
• We further expect to find stable cognitive
  elements, the deep seated convictions upon which
  students rely for their interpretations.

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Theoretical Background and Methodology

• To further understand students reasoning, we
  adopt a modified ontological categorization
  scheme following Chi and Slotta (1993). They
  categorize entities as matter (objects),
  processes, and mental states. This can be useful.
  For example, if a student thinks that a photon is
  an object, then with it comes a host of
  associations such as the photon energy object
  collides with an electron and knocks it to
  another orbital.

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Theoretical Background and Methodology

• We add to these ontological categories the field
  category in order to have a sensible ontology for
  quantum entities.
• Finally, we follow Lawson (1993) by including
  chunking as an important component in explaining
  the way that our minds organize what we learn.

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Design and Procedures

• We interviewed students prior to, and subsequent
  to, instruction on quantum concepts.
• Students were selected from a pool of volunteers
  taking the honors general chemistry course at a
  research university.

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Design and Procedures

• The students were all freshman in their second
  semester.
• This was an elite group of students they had
  passed a placement test to enroll in the honors
  course for science majors.
• Most students were chemistry or science
  concentrators.

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Design and Procedures

• Students were selected for the interviews to
  produce an even grade distribution.
• Each interview was conducted based on the same
  set of questions (an interview guide approach).
• To the extent possible, the interviews were
  clinical in nature in a Piagetian fashion. The
  interviewers flexibly probed the individual
  students responses to elicit deeply held
  convictions.

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Design and Procedures

• As an aid to better elicit explanations from the
  participants, experiments were done during the
  interview (double slit interference pattern,
  hydrodgen discharge tube with grating, strong
  magnets).
• In conducting the interviews prior to
  instruction, an assumption was made that students
  would have had exposure to quantum concepts in
  their high school chemistry courses.

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Findings

• Our findings in our pre-instruction interviews
  are confirmatory of prior physics education
  research, and some echo our earlier findings with
  high school students (Eshach and Garik 2001).
• 1) In describing the structure of the hydrogen
  atom, most students began with descriptors
  reminiscent of the Bohr model (orbit, circular
  region) but in further conversation they
  described and drew pictures with elements of an
  electron cloud model, albeit one frequently
  characterized by a rapidly moving particle. Such
  transitional descriptions of the H-atom agree
  with the reports of Petri and Niedderer (1998),
  Müller and Wiesner (2002), Mashhadi (1996), and
  Ireson (2000).

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Findings

• 2) Students knew that both light and electrons
  possessed wave-like properties. However, some
  believed that this referred to the trajectory of
  these as particles in space, a previously
  described cognitive attractor (Ireson 2000
  Müller and Wiesner 2002 Olsen 2002).
• 3) In discussing interference of light waves,
  students referred to waves as if they were
  objects, as opposed to being dynamic events
  (Wittmann 2001).

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Findings

• 4) The confusion of students about the properties
  of electromagnetic waves is apparent from the
  fact that they were unaware that there is an
  electric field component to radiation. This was
  uniformly true in our pre-instruction interviews.

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Findings (and Disclaimer)

• Many topics were covered in the pre-interviews.
  The post-interviews tended to be more focused as
  learning of specific items were investigated.
• At the risk of mischaracterizing what these very
  bright and very well taught students
  accomplished, we will now focus on two areas in
  which they encountered difficulty.

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Findings

• A key quantum concept is that atomic orbitals are
  stationary quantum states characterized by two
  quantities a wave function and an energy (?, E).
  
• As we see from the following responses, students
  wrestle mightily with this apparently simple idea.

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Findings Orbital/Energy Level

• S1.112.post
• P What is an orbital?
• S An orbital is the space where the electron is
  probably going to be, and its defined by a wave
  that fits with the Schrödinger... Or that meets
  the solution for the Schrödinger Equation.
• P You say the space that an electron is going
  to be. That is an orbital?
• S Well, okay, let me rephrase this, hopefully
  clearer. An orbital is an area of space that
  satisfies the Schrödinger Equation, and has a
  specific energy that satisfies that equation, and
  within that area in space, each point in space
  has a probability that the electron may be at
  that point in space, and an orbital is all the
  points in space that satisfy that energy.
• P What is an energy level?
• S An energy level is a specific energy that
  satisfies the Schrödinger equation, thats a
  possible solution for that equation, and you can
  have many points in space that will satisfy that
  energy, and all the points that satisfy that
  energy make up the orbital thats in that energy
  level.
• P So, what is the connection between an energy
  level and an orbital?
• S Orbitals are at specific energy levels.

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Findings Orbital/Energy Level

• S2.112.post
• S Energy level. This is word, this is the phrase
  that I just really dont like. An energy level
  represents the difference between two orbitals as
  far one electron moves from one orbital to
  another. I cant say this still. The electron
  moves from one orbital to another that difference
  is known as a quote, unquote, energy level. I
  left you saying last time saying that I dont
  think that is good word for it, but I never, I
  thought about it for a long time actually. I
  spent most of the day thinking about it, and I
  couldnt come up with a phrase that accurately
  described it. And, its, I think, energy state is
  better because it describes the state of the
  electron, the electron is in the excited state,
  its not where it is normally at. But then when
  you start saying state, students start thinking
  is it a solid, liquid, or gas? and theres too
  many overlapping words in chemistry. It makes
  things very confusing. But, an energy level is
  just the difference between two orbitals of an
  atom.

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Findings Orbital/Energy Level

• S3.112.post
• S An orbital is Its actually just another name
  for the wave function, which is the probability
  of finding an electron in a certain shape and
  area, distance away from the nucleus.
• P What is an energy level?
• S An energy level is the radius, a certain set
  radius away from the nucleus where electrons are
  found to be.
• P What is the relationship between an orbital
  and an energy level?
• S Orbitals are found in certain energy levels,
  so if theres, in the first energy level theres
  the s orbital, which is spherically shaped, and
  thats, theres a probability of finding it
  there, and then if you go into the second
  orbital, in the middle theres a node, a region
  where is just doesnt, you wont, you will not
  find the electron, when you get into higher more
  complex atoms with more electrons.

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Findings Orbital/Energy Level

• S4.112.post
• P What is the relationship between an orbital
  and an energy level?
• S The energy level dictates, no actually not,
  actually its nopause Every orbital, that,
  like the different orbitals, have different
  possible energy configurationsno, thats not
  whatI am not really sure how to explain it.
  UmmI know that theyre related, I just cant
  really explain how. Like, ah, as energy
  increases, the radius of the electron, or the
  distance of the electron away form the nucleus
  increases and generally speaking, the different,
  the more complex, um orbital shapes also increase
  complexity as energy does. I guess that the only
  way I can explain, I cant really think of any
  other way to say it.

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Findings

• Another example of student confusion emerged in
  discussions of what electromagnetic radiation and
  photons are.

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Findings Nature of Light

• S1.112.post
• P Okay. When you say that its electromagnetic
  radiation, can you elaborate on that? What is
  electromagnetic?
• S Its oscillating in energy, and that induces
  some sort of magnetic oscillation with it, but
  electromagnetic radiation would be the, like,
  wave thats oscillating in energy, I think.
• P It is said that light propagates as a wave.
  What is it that is waving?
• S Oh, I think its the energy. Yeah. Well,
  its the value of the wave function, and that is
  related to energy.
• P And what is it that is oscillating?
• S The value of the wave function. So
• P Could you put a Could you label what your
  axis, or what your axes are?
• S Okay, well, if this an axis that isWe can
  label it x, we can label it anything, then where
  it crosses this other axis is zero and the value
  of the function along that axis equals to psi of
  the function, whatever the functionOr psi of the
  variable, whatever you chose to call that axis,
  x, or r, or d.
• P Okay, what are the units for x, and what are
  the units for psi?
• S the units for x would be distance, so
  probably meters, or centimeters, however you
  chose to measure it, and Im pretty sure psi is
  unitless.

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Findings Nature of Light

• 3.112
• P What is light?
• S Its electromagnetic radiation.
• P What do you mean by electromagnetic, when you
  say electromagnetic radiation?
• S Well, its In wave form its electricity
  perpendicular to magnetic waves.
• P Okay, but when you say electricity, what do
  you mean by electricity?
• S Just the charge of the electron.
• P Charge of the electron?
• S Uh huh.
• P So are there electrons present within an
  electromagnetic wave or radiation?
• S Yes.

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Findings Nature of Light

• S3.112.post
• Whats waving?
• S Its Its not really anything thats in
  particular waving, thats just Cause its Its
  actually found to be Theres the wave and
  particle duality, so its not really waving
  necessarily. I mean, theres a sine curve so I
  guess it would be energy, if anything.
• P So you said the sine curve, and now you say
  energy. How do you relate the sine curve to
  energy?
• S As it As the wave propagates up and down its
  different states, or different amounts of energy.

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Findings Nature of Light

• S4.112.post
• P Okay, can you tell me what light is?
• S Nope, still really dont know. Just pretty
  much, packets of , well not packets of energy,
  just straight up energy. Quantized energy. There.
• (skip)
• P It is said that light propagates as a wave.
  Can you tell me what it is that is waving or
  oscillating for a light wave?
• S The way it moves. It just goes in a wavelike
  fashion. And so, the traditional thought that
  light is just a straight beam, the individual,
  well, theoretical, the quantity that they
  quantify as a particle is moving in a wavelike
  fashion, not just straight.
• (skip. What follows demonstrates that the above
  is a liberated conviction, and not deeply held
  conviction.)
• S Light doesnt really have a distinct form or
  shape. Its just the wave that they say is just a
  general, just a representation ofof what it
  could be. Not technically the actual movement
  itself, its just a theoretical representation of
  what it could be, not technically the actual
  movement itself. It is just a theoretical
  representation because we cant measure what it
  looks like or what it does. So, we just have to
  give some mathematical computation to that to
  represent some sort of quantification of light
  itself.
• During the course of the interview, this student
  interpreted the two-slit experiment done in his
  presence with a HeNe-laser as showing a pattern
  of electron density.

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Findings

• These two examples of misconceptions both revolve
  around a common problem the understanding of a
  wave function. In one case it is the wave
  function for a particle with mass. In the other
  it is for a massless particle, a photon.
• The difficulties revealed suggest that a common
  solution might be in order that emphasizes the
  field nature of both the electrons wave function
  and the wave function of radiation.

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Findings Chunks

• Chemistry education relies heavily on students
  acquiring chunks of knowledge that can be drawn
  upon quickly. There is chunked knowledge that
  students need to learn about atomic structure
  (principal quantum number, s, p, d, f), about the
  Periodic Table (groups of elements, periodic
  trends), and spectroscopy.
• Here we provide an example of a successful chunk,
  and then one that is less well founded.

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Findings

• Based on our interviews, some of the chunks we
  heard were
• light
• interference
• energy level
• orbital
• spectrum

• atomic structure
• H atom
• He atom
• Li atom
• H2
• molecular bonding

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Example H-spectrum chunk

• H-spectrum chunk
• S TheresI dont think I could draw it as
  electrons jumping within an atom, just because
  all the It would be hard to draw all the
  different shapes of the orbitals, and everything,
  but if you wanted to draw, you could draw, like,
  lines here, and this would beThe scale that this
  was on would be increasing energy, and the first
  energy level would be down here, very low energy,
  and that would be the n equals one energy level,
  and then youd somewhat further up have n equals
  two, and as you increase, the energy levels get
  closer together, until eventually they blend into
  a solid line up here, and when an electron
  jumpsThis would be n equals five. When an
  electron jumps down, if you put energy in it,
  into an atom, to get an electron all the way up
  to a higher energy level, and then it goes and
  falls back down into the n equals two energy
  level, then theres a certain energy that it
  emits, and energy is equal to Planks constant
  times a certain frequency, and so, if you find
  the frequency and convert that to a wavelength,
  you can find out that these jumps, where an
  electron goes down from n equals five to two, n
  equals four to n equals two, or n equals three to
  n equals two, all emit energy thats within the
  visible range, or visible light range. So thats
  what we just saw, was electrons going down an
  energy level, and the atoms emitting light.

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Example Interference Chunk

• P Do you think you could sketch for me what you
  mean by this destructive interference?
• S So just like in the experiment theres two
  slits, the light passes through there, and then
  you just go on from here and here, and it would
  meet at a central point, which is the wall, so
  right here, and when it Thats just one section
  of the sine curve. When it meets this way, you
  get constructive interference, and if the
  amplitude of it was, say, plus one, plus one,
  plus one, minus one, minus one, youd get
  amplitude added up to a plus two, and minus two.
  You have to get the intensity, which is square of
  that result and plus two equals And This
  would result in zero, with a flat line, and that
  would result in the square root of that and youd
  get nothing. So that would be a dark region and
  that would be a bright region.
• P Why would the interference between the two
  waves be different at different positions?
• S Im not sure I understand it.
• (skip)
• P Is there something that determines whether
  they meet and result in destructive interference
  as opposed to meeting and resulting in
  constructive interference?
• S No. I dont believe there is.

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Discussion

• The honors students that we interviewed showed a
  remarkably stronger understanding of the Born
  interpretation of orbitals than we have found in
  the past. Our prior experience, with high school
  students and medical students (Eshach Garik
  2001 and 2002), matched other reports in the
  literature that students describe atomic
  structure as a composite of Bohr, de Broglie, and
  electron cloud concepts.
• Moreover, on the whole the students we
  interviewed grasped the fundamental spectroscopic
  fact that the energy of emitted radiation is the
  difference between energy levels, as opposed to
  the energy of a level (Zollman 2002).

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Discussion

• Nevertheless, these students exhibited a series
  of misconceptions that are enlightening for an
  education researcher.
• Specifically, we observe that the lack of a
  careful introduction to the properties of an
  electromagnetic wave, specifically the fact that
  there is an electric field, eventually led to
  students confusion.

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Discussion

• We further suggest that the confusion that
  students evidenced about photons as objects, and
  the relationship between energy levels and
  orbitals, is a result of not understanding the
  field nature of both electromagnetic radiation
  and wave states of matter.

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Discussion

• Such incomplete conceptions can later manifest
  themselves when chunks of knowledge are put to
  the test. For example, the interference chunk
  previously related at first sounds plausible.
  However, it proves inoperative when tested for
  predictions. The student apparently has
  constructed the chunk with waves behaving as
  objects. As such, he cannot predict where maxima
  and minima should occur in an interference
  pattern.

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Conclusion

• Given the central nature of quantum concepts to
  modern chemistry, the dearth of education
  research in how to teach this subject is
  surprising. Many papers have appeared in J. Chem.
  Ed. discussing methods of instruction that rely
  on quantum principles, but evaluation of these
  methods is seemingly missing.
• It is our conviction that if properly approached,
  quantum concepts are teachable from an early
  stage in the undergraduate chemistry curriculum.
  We hope to follow-up this current research with
  future work that supports the design of
  successful curriculum.