quantum concepts in chemistry () 1 students’ understanding of quantum concepts during their first...

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

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Students’ Understanding of Quantum Concepts During

Their First Introduction in a General Chemistry Course


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Exploring Quantum Concepts in Chemistry:The Team

Peter Garik (presenting), Boston University([email protected])

Luciana GarbayoSchool of Education

Alan Crosby, Dan Dill, Alexander Golger, Morton Hoffman

Department of Chemistry

Peter CarrScience and Mathematics Education Center

Boston University

mailto:[email protected]


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Exploring 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)

(Award No. P116B020856.)


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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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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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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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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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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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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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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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• 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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• 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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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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• 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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Design and Procedures

1) We interviewed students during the outset of their instruction on quantum concepts.

2) Students were selected from a pool of volunteers taking the honors general chemistry course at a research university.


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• 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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• 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.


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• 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 early in the students’ instruction, an assumption was made that students would have had exposure to quantum concepts in their high school chemistry courses.


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What is waving?

We asked students to answer the questions:

1. What is light?

2. It is said that light propagates as a wave. What is it that is waving?


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What is waving?

Student2’s response: It’s energy.

• S: Light, as far as I know, is made up of photons, and photons are little packets of energy without mass. That's the key part about photons. They move in waves, defined by wave functions. They're just perceptions of light you and I are seeing now is what our eyes are perceiving and then transferring into what our brain can tell us what we're seeing. That’s why, people who are colorblind, their perception is different than yours and mine.

• P: What is electric and what is magnetic about electromagnetic radiation?

• S: Well, anything that moves in a wave produces a magnetic field, I want to say. What is electric? It's just energy that’s moving, and as the energy moves it creates a corresponding magnetic wave.


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What is waving?

Student3’s response: The sinusoidal wave is a trajectory.P: Now you say that light can be either considered as

particles or waves. How does the particle of light travel?S: In a sinusoidal curve.P: Could you, perhaps, draw for me what you mean by

that?S: Sure. …Something, I guess you'd say… I mean, I

guess, on an xy axis, I assume starts off and it just keeps traveling like that.

P: Okay, could you label the axes?S: Sure.P: Okay, so y and x and, so, this is, then, a trajectory?S: This is the amplitude.


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What is waving? (Student3 continues)

P: Oh, amplitude, okay.S: This is the amplitude, so I guess I could just label that

amplitude.P: Amplitude of what?S: Amplitude of the wave… Of the particle in space,

traveling up and down.P: The amplitude of the particle traveling up and down.

Can you draw for me the particle on this? Or…S: I mean, this would be basically like the trajectory of it, I

would assume. So it would just start off here, I guess, at the zero, at the origin, and just travel along this path.


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What is waving?Student5: Packet of energy with wave trajectoryP: Okay. You drew a packet of energy. How does that

packet of energy travel?S: Like a wave does in a transverse version. Like a science

of the wave does. P: So could you draw for me a trajectory or how this packet

of energy is traveling?S: So, I mean, if this was the energy, it would travel in…

This is very abstract, I don’t… I can’t think of light traveling, per se. I only know the diagrams that I was taught, that I've seen before, and this is how I've seen it. Like, there's a little packet of energy, and it’s going along to a source, and you see it. This is the eye. (In the drawing, the student has drawn an eye at which the waving trajectory terminates.)


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What is waving?Student5 continues

P: Okay, so this is the trajectory, then?S: I think so.P: Of the packet of energy?S: Yeah.P: Is there a name for this packet of energy?S: Photon.P: Okay. So this is, then, a photon?S: Yeah, a packet of energy, this packet of energy

is a photon, and the photon travels in a wave-like motion through space.


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What’s waving?Student5 continued

• Later, in the context of discussing interference of waves, Student5 said:

• S: I think I should look at the book more closely. Energy. It has to be energy. I don’t know why, but I think it’s energy.

• P: And what's along this axis?• S: Distance.• P: Distance.• S: No, no, no. Yeah, it has to be, because this is

wavelength, and wavelength is measured in meters, so this is distance. Yeah.


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What’s waving?Student6: Confused by amplitude.P: What are photons? S: They're particles with light. And transfer momentum like

a particle. P: Could you perhaps draw for me what you mean by a

wave-like motion? S: Yeah. A classic sine wave. P: And this represents the light wave? S: Mm-hmm. P: What's on the y-axis and what's on the x-axis?S: X-axis is position… I think it would be position over here,

too. The real fundamental questions are the ones that mess you up, but you can solve if you have your amplitude.


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What is waving?Student6 continues.

P: So this is an amplitude of what? S: Of distance from the y-axis…or…x-axis, I'm

sorry. And that's squared when there's an interference. I think we just learned that. I'm not sure if that's right or not. But…

P: Now this is the wave-like motion of light, but you said something about photons.

S: Mm-hmm. Let's see, how do I explain that. I'm not sure if I could really put that into words. No, I don’t think I know how to answer that.


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What is waving?Superficial Comments

• The students were baffled by how to resolve the particle-like nature of light with its presumptive wave-like property.

• They were uniformly unaware that it is the electric and magnetic fields’ oscillations that give rise to the wave-like character of light.

• Not a single student could properly label the y-axis of their graph as a field strength.

• Our subsequent studies with junior physical chemistry students have found this same pattern of ignorance (pardon, but it’s true) about radiation.


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How does light interact with matter?

The researchers asked the participants:

If an H-atom is exposed to radiation, what may happen to the electron?

During the interview, the researcher also took care to find an opportunity to ask what the interaction is tetween a charged particle and radiation.


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Student2:P: Would light interact with a charged particle? S: In theory, yes, because it's energy reacting with energy.

Well, energy reacting with something that's charged. Since light creates a magnetic field on its own, something that would have a charged particle would, in some way, be affected by it.

Student5:P: Okay. What would happen if that light or that packet of

energy were to go by a charged particle?S: I don’t know. If it was negatively charged, I assume that it

would be attracted, or repelled. I mean, the charge would… It would depend on the charge. It would probably go to it or not go to it, I think. I don’t know.


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Student3:Well, from what we just went over lately, which we just started a light

and electromagnetic waves and stuff, I would say it's electromagnetic radiation. You know, it’s in a wave, and according to what we've read in our chem books so far, it's actually …Also consists of…It has particle-like and wave-like characteristics. When it's alone, it's more particle-like, and when it's a whole group of photons, it's more wave based, and so it's basically electromagnetic radiation in space.

P: What is electromagnetic radiation?S: It's a… It's a…In a sinusoidal curve, just electric, and a magnetic

field.P: An electric…And what would happen if electromagnetic radiation

was to pass by a charged particle?S: It would actually…Depending on the particle's behavior to it, it

would…It might actually knock up an electron to a higher energy level and make it, let it emit a photon, which is a charged particle.


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Student6:P: Okay, suppose that I had a charged particle and a light

wave came by my charged particle. What would happen to the charged particle?

S: …it would transfer momentum to the charged particle. P: Can you explain to me the mechanism by which this

momentum is transferred? S: Okay…I'd say that the photon, the photon is a particle

that, without mass, can't transfer momentum and so it transfers momentum to the charged particle.


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Student6 continuesP: Photon is without mass, did you say? S: Mm-hmm, yeah . P: And so it transfers momentum to the particle. S: Which is odd, because momentum is mass times

velocity. So that's why quantum is so confusing. P: So how does the photon then transfer the momentum? S: I don't really know, actually. I think I understand the

mechanics of what happens. That's what we've been studying lately. But how it actually transfers it, I don’t think I really know.


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Student8: Momentum transfer.P: When a photon interacts with an electron can you tell me

a little bit more about how it interacts.S: There is a transfer of energy from the photon packet,

which is the packet of energy, and the light strikes the electron, the electron gains energy and this energy is transferred into kinetic energy, or energy of motion. And in doing so, the electron gains a certain momentum. And so, in a way when the light hits it, it hits it with a certain momentum that is transferred into the electron and the electron behaves with a certain kinetic energy and this explains the particle-like theory.


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Superficial Comments

Students do not know the force relationship between a charged particle and the electric and magnetic fields of a light wave.

The object view of a photon has completely occluded the field nature of the light wave.

In the absence of an understanding of the electromagnetic nature of light, the mechanism for exchange of energy is reduced to a contact problem.


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Reconciling particle- and wave-like characters of an electron orbital

We asked the students: “Describe in your own words what a hydrogen atom is. Please draw a picture that you feel assists with your description.”

We have conducted interviews with high school students in the past and categorized their response to this question (Eshach & Garik 2001). This cohort of students was an elite group and their responses tended to be more uniform and restrained. Little remained of the Bohr planetary model in the descriptions provided by the students; there was more of an attempt to integrate particles with a probability density interpretation.


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Student2: The speedy electron.S: It would be, like, nucleus which we knew where it was and it would sort of

be, like, a mess around it, and in that scribbled mess would be where you find the electron, somewhere in there.

P: Mm-hmm. When you say where we would find it, what do you mean? I mean, is there a difficulty with finding the electron?

S: Again, to measure the exact location of an electron, I would imagine it would require something like stopping it from moving, because they're moving at extremely high speeds and it's…I can't think of a way… There may be, that I don't know, but I can't think of a simple way to pinpoint the exact location of an electron over any given period of time. We can't necessarily tag them and attract them. We can't slow them down enough because I don’t think… Again, if you stop an electron, I want to say that part of the reason an atom stays the way it is and keeps its structure is because electrons are moving. And that if you stop that electron then, you know, what's to keep it from rushing towards the nucleus, because it's a positive nucleus and negative electron? What's to stop them from coming together?


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Student2 continuesS: I know there's a strong force and a weak force. We

glazed over that in high school. We really never talked about what it was or about what it did. That's what kept the atom from collapsing on itself. But I can’t… Back to the original question, I can't think of a way that you could possibly measure exactly where the electron would be. You can make… You can measure it, the area, because you would be able to see a charge moving around. I don't know how to describe this. If you looked at it long enough, like if you put it on something that would detect a charge, a change in charge, you would see… You know, there's obviously a dark spot in the center, where the positive charge is, and then you would see sort of a haze around it, because it's moving so fast. You couldn't take a picture fast enough to see exactly where the electron is.


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There is much to be commended in the causal reasoning of Student2. Indeed, the electron does have substantial kinetic energy.

A product of the student’s reasoning is the liberated conviction that there must be a reason why the electron does not collapse into the nucleus. Even expert quantum chemists can baffled by this (Eshach & Garik 2002).


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Student3P: So you say the electron is whizzing around the

proton?S: Yes. There's mostly empty space between the

nucleus and the trajectory of the electron.P: Do you think you could show me what trajectory,

roughly, the electron is following?S: … I couldn't tell you what trajectory it really follows,

but I know it's not circular, per say.P: Uh-huh. But you said there was empty space…S: Uh-huh. The probability of finding the electron is,

you know, somewhere in a circular pattern around the nucleus, there's a probability of finding it there. There’s… You can't really pinpoint the location of the electron.


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• P: Okay.• S: But there's a probability of, you know,

finding, like, a 90% probability of finding it in a certain area around the nucleus.

• P: You're referring to a circular area.• S: Yes.• P: It is a two-dimensional?• S: No. It's a three-dimensional.• P: Three, so do you mean circular, or would

you…?• S: Spherical.


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From this response we can truly conclude that we have met the enemy, and it us (Kelly, comic communication).

The 1s orbital has spherical symmetry. But like all the other orbitals, it has no shape. We impose shape upon the orbitals in our diagrams by emphasizing regions of higher density and their symmetry. Despite the potential causal pitfalls (bouncing around inside a sphere), Student3 has done an admirable job of avoiding arriving at the worst of the misconceptions that can be imagined.


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FindingsOur 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 treated the sinusoidal representations of the waves as if they were objects, as opposed to being processes (Wittmann 2001). Ironically, it would be correct to treat the field as an object, as opposed to graph representing the value of the field at a single instant of time.


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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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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 (Wanderse, Mintzes and Novak 1994).


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• 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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– 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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To further understand students’ reasoning, we adopt a modified ontological categorization scheme following Chi, Slotta and de Leeuw (1994). 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 can collide with an electron and knocks it to another orbital.


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Extending Chi et al’s Ontological Categories

The ontological categories proposed by Chi for analyzing science learning are broad and general.

The underlying epistemology subscribes to specific scientific model.

But (!), an epistemology must be specified prior to discussing ontology.


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Extending Chi et al’s Ontological Categories

As written by diSessa and Sherin (1998)

“…the comment is often made that every observation is theoretically based, as well as empirical. The notion of pure and indubitable ‘data’ is no longer regarded as a serious possibility in the philosophy of science, nor is it commonly used in the avowed warrants of professional science.”


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Models of the Physical Universe

Biblical basis

Classical Dynamics

Newton/Maxwell

Aristotelian

Quantum Mechanics/ Einsteinian Special

and General Relativities

As realized

byAs

realized by

As realized

by

As realized

by

Matter Divine Matter

Processes Divine Processes

Figure 1: Epistemology determines ontological categories and subsequent trees modeled after Chi et al (1994). (N.B.: The States of Mind ontological category is missing due to lack of space.)

Matter Fields/Energy

Processes


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Quantum and Relativistic

Model

Energy/Matter Processes

Macroscopic Mesoscopic Elementary

Level

Macroscopic Mesoscopic Elementary

Level

Elementary

Particles

Elementary

Fields/Excitations

Figure 2: Beginning of ontological tree for modern quantum and relativistic science. Note the lateral separation of elementary particles and elementary field excitations. (N.B.: The States of Mind ontological category is missing due to lack of space.)


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Ontological Categories, Trees, and Wave-Particle Duality

In order to adequately describe the ontological categories of classical and modern physics, we have added the field ontology to a branch on Chi’s trees.

In terms of these ontological categories, we can say that students have great difficulty with quantum concepts because of the ontological blur between particles and fields.


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Duality and Crossing TreesIn Creativity: Shifting Across Ontological

Categories Flexibly, Chi (1997) writes that:“…it is possible to cognitively change the

representation of a concept through cognitive operations if the changes do not require the concept to be re-represented across branches or trees…”

Wave-Particle duality explicitly requires the student to move between branches, and when considering processes, between trees.


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Conclusions

1. Currently, the field ontological category is not adequately recognized, taught or explained. It must be added to the curriculum in the form of an explanation of electric and magnetic fields. It must be recognized as an object that can be strictly imaginary and unobservable as for an orbital.

2. After all this analysis, we return to the wave-particle oxymoron with a new insight into Born’s creativity and the realization that students must be informed of the integration task they face.

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