What General Chemistry Students Know (and Don’t Know) About Quantum Concepts in Chemistry

What General Chemistry Students Know (and Don’t Know) About Quantum Concepts in Chemistry Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Peter Carr, BU Alan Crosby, BU Dan Dill, BU Yehudit Judy Dori, Technion, Israel Haim Eshach, Ben Gurion University, Israel Luciana Garbayo, BU Alexander Golger, BU Morton Z. Hoffman, BU Quantum Concepts in Chemistry:The TeamPeter Garik (presenting), Boston University (garik@bu.edu) Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Quantum Concepts in Chemistry This project is funded by the U.S Department of Education’s Fund for the Improvement of Post Secondary Education (FIPSE). Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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.” Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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? Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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). Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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). Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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 student’s responses to elicit deeply held convictions. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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). Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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). Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings A key quantum concept is that atomic orbitals are stationary quantum states characterized by two quantities: a wave function and an energy (ψ, E). As we see from the following responses, students wrestle mightily with this apparently simple idea. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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 it’s 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, that’s 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 that’s in that energy level. P: So, what is the connection between an energy level and an orbital? S: Orbitals are at specific energy levels. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings: Orbital/Energy Level S2.112.post S: Energy level. This is word, this is the phrase that I just really don’t like. An energy level represents the difference between two orbitals as far one electron moves from one orbital to another. I can’t 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 don’t 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 couldn’t come up with a phrase that accurately described it. And, it’s, I think, energy state is better because it describes the state of the electron, the electron is in the excited state, it’s not where it is normally at. But then when you start saying state, students start thinking ‘is it a solid, liquid, or gas?’ and there’s 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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings: Orbital/Energy Level S3.112.post S: An orbital is… It’s 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 there’s, in the first energy level there’s the s orbital, which is spherically shaped, and that’s, there’s a probability of finding it there, and then if you go into the second orbital, in the middle there’s a node, a region where is just doesn’t, you wont, you will not find the electron, when you get into higher more complex atoms with more electrons. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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 it’s no…[pause] Every orbital, that, like the different orbitals, have different possible energy configurations…no, that’s not what…I am not really sure how to explain it. Umm…I know that they’re related, I just can’t 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 can’t really think of any other way to say it. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings Another example of student confusion emerged in discussions of what electromagnetic radiation and photons are. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings: Nature of Light S1.112.post P: Okay. When you say that it’s electromagnetic radiation, can you elaborate on that? What is electromagnetic? S: It’s oscillating in energy, and that induces some sort of magnetic oscillation with it, but electromagnetic radiation would be the, like, wave that’s 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 it’s the energy. Yeah. Well, it’s 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 is…We 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 function…Or 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 I’m pretty sure psi is unitless. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings: Nature of Light 3.112 P: What is light? S: It’s electromagnetic radiation. P: What do you mean by electromagnetic, when you say electromagnetic radiation? S: Well, it’s… In wave form it’s 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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings: Nature of Light S3.112.post What’s waving? S: It’s… It’s not really anything that’s in particular waving, that’s just… Cause it’s… It’s actually found to be… There’s the wave and particle duality, so it’s not really waving necessarily. I mean, there’s 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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Findings: Nature of Light S4.112.post P: Okay, can you tell me what light is? S: Nope, still really don’t 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 doesn’t really have a distinct form or shape. It’s just the wave that they say is just a general, just a representation of…of what it could be. Not technically the actual movement itself, it’s just a theoretical representation of what it could be, not technically the actual movement itself. It is just a theoretical representation because we can’t 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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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 electron’s wave function and the wave function of radiation. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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 Findings Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

Example: H-spectrum chunk H-spectrum chunk S: There’s…I don’t 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 be…The 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 you’d 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 jumps…This 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 there’s a certain energy that it emits, and energy is equal to Plank’s 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 that’s within the visible range, or visible light range. So that’s what we just saw, was electrons going down an energy level, and the atoms emitting light. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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 there’s 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… That’s 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, you’d 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 you’d 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: I’m 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 don’t believe there is. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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). Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

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. Quantum Concepts in Chemistry (http://quantumconcepts.bu.edu)

What General Chemistry Students Know (and Don’t Know) About Quantum Concepts in Chemistry