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МюУхCOMPILATION: atomic models (Bohr, probability)
[Editor's note: Read the closely related compilations entitled "Models-Outdated?04" and "Teaching Atomic Models" (2004) in the general concerns section. More recent compilations are on the chemistry modeling listserv webpage.]
Date: Tue, 6 Dec 2005
From: Don Yost
Subject: atomic models
On another list serve, we are involved in a discussion of atomic models. Most of the people do not realize that Bohr's model is a quantum model, but besides that, there is the belief that students who believe in the planetary model of the atom are ignorant and should be taught the "probability" model (the one in chem books with fuzzy bulbs sticking out which is starting to show up in middle school texts).
I understand how Bohr's model can grow from the planetary model, and explain all sorts of things about atoms, but I can't understand how the "probability" model would help a student understand anything about an atom. My background, here, may be weak, but I can't think of a single calculation a student to do using this model. I can't see any prediction or phenomenon which this model makes clear for students. Can some of you chem people out there help me out?? Other than being a factoid, how is the probability model useful? (I know it can help with chem bonds and all that stuff, but I'm talking students here.)
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Date: Wed, 7 Dec 2005
From: James Vesenka
The key to the Bohr model is that only "discrete" orbitals are allowed. To my understanding, the Bohr model says nothing about fuzzy probability distributions. Rather, unlike the planetary model which allows any orbit of radius r around a center of mass, the Bohr model allows only certain orbits in which the wavelength of the electron is a discrete integer of the radius of the orbit r.
And here is the experiment, with predictions you can have the students make. Have them predict the spectra of a hydrogen discharge tube using the classical model. The spectra should look like a rainbow of colors in the classical picture. But it doesn't have a rainbow; it only has discrete wavelengths corresponding to allowed electron orbital transitions.
The fuzzy orbital picture requires quantum mechanical probability distributions. These models are probably misleading to the teachers (if they don't understand them) and thus to their students. They probably leave the impression that the fuzzy ball is a region of electrons, rather than the region in which up to a pair of electrons MIGHT exist. I agree with Don, I don't see a way in which the probability model can help K-12 students, and might even hurt them unless the teacher understands and knows how to communicate the nature of the probability model. And even then, as Don says, how does one make a useful prediction from this model? Without the math, it is a concept without simple predictive abilities.
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Date: Wed, 7 Dec 2005
From: DAVID HURWITZ
In reply to Don Yost's cry for help, I shall put in my two cents' worth. This has brought back memories of my course in physical chemistry taken as an undergrad chemical engineer in 1964-5. The supporting math was challenging, but my professor used simple examples to deliver the concepts.
Bohr's model is the next logical step from the planetary model. If you are willing to discuss Heisenberg's Uncertainty Principle in real terms, it may be OK to move on to the Probability model. You also may get trapped into explaining Schroedinger's paradox. This is also useful.
The models in the books are usually terrible, so I don't get very upset. [Remember, this is the same crowd that renamed reciprocals as "multiplicative inverses."] I usually do a real life example, i.e., asking the kids to tell me what color a car is in the parking lot. I follow this with, "Are you sure that the color is the same on the other side?" I lead this into a discussion of accuracy versus precision. When the kids buy in to that discussion, we can go back to the probability model. Quantum physics isn't as hard or as arcane as the non-math, non-science types think. (Careful Socratic questioning can elicit the understanding in most kids, regardless of age. It's their teachers and their parents that are the biggest problem.)
I applaud the textbook writers for trying to improve the critical thinking skills of elementary school kids. Unfortunately, most K-5 teachers need some professional development to present this particular topic in a meaningful manner. (I still chuckle at complaints from an articulation meeting in which elementary school teachers couldn't solve a simple rate equation problem. ... Scary, but true!)
Dave Hurwitz
Modeler and Math Teacher
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Date: Wed, 7 Dec 2005
From: Traci Maxted
To respond to Don Yost about atom models in HS texts:
I discussed this with the AP chem teacher and he was not aware of the probability model being used in HS texts, other than to show students that the atom doesn't look like "hula hoops". Primarily the Bohr model is shown, for the reasons given, simplification, usefulness in showing quantum and other properties of atoms. His concern was the statement he heard from some newer teachers at a conference that we have not ever seen atoms and that it was impossible to view them. We have photos of atoms on our walls because we think they are cool. There may be a problem with understanding more than with texts. I use the Bohr model in my discussion of "scientific models" since it is such a classic example.
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Date: Wed, 7 Dec 2005
From: "R. McDermott"
It may be worthwhile to note that the "probability model (the one in chem books with fuzzy bulbs sticking out which is starting to show up in middle school texts)" is only one of the possible solutions stemming from the wave equation(s) for an electron. This solution is based upon "like" energy values. You could get an equally valid solution that had identical probability shapes but differing energies (or so I'm told). We tend to think of the "s", "p", etc solution as the only correct solution to the wave equation, and it isn't. Wave equations typically produce a SET of solutions and the solver chooses the one s/he wants (the one that best suits what one is trying to achieve). This specific choice has the virtue of accounting for the multiplicity of spectral lines (for atoms with more than one electron) that the Bohr model does not predict, so I guess that one could argue that evaluating the energies associated with the various sublevels and orbitals would allow for calculation of the spectral pairs, triplets, etc of multiple electron atoms. I doubt the evaluations and subsequent calculations would be as simple as the equation Bohr's used to find shell energies, however.
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Date: Thu, 8 Dec 2005
From: Tim Burgess
Don,
There has been quite a response concerning the atomic model. Wow.
Why would a probability model be pushed?
The Bohr model predicted a precise radius using the idea of matter-waves. In fact due to the limitations of orbits being defined as "standing waves" there were only particular locations where the orbits could be. When his calculations using electrostatics and waves yielded predictions that precisely matched actual estimations, the Bohr "quantum atom" became a model that would, with modifications, become the accepted "model" of how we thought about the atom. No treatment of the atom in three-dimensional space was included.
The modification of the Bohr model provided for "probability distributions". These distributions were applied to three-dimensional space. I understand that the fact that atoms are three-dimensional in fact does help explain a lot of "reaction probabilities" in kinetic chemistry (the shapes of those standing waves are not always spheres, right?)
So I think that is the underlying purpose of teaching the "probability" model. I think, as you do though, that understanding the underlying Bohr atom is a true prerequisite and is reachable by the end of a good high school physics course. Knowing about the probability model is not the same as understanding the probability model. SO the argument fires up!
The REAL Question: Is "knowing" (rather than "understanding") a model useful at all? Some would say knowing is as much a goal as understanding in the school. So it appears that the underlying issue is related to teaching to understand rather than teaching to recall. If you are a modeler then I think I know where you fall on that question, eh?
One more item. In the very strictest interpretation we will NEVER "see" an atom with our eyes (which have much too limited a range of sensitive wavelengths that are much too long for useful reflection and resolution of the atom). If you consider spectral/optical techniques involving high frequencies that "reflect" and "define" the boundaries of the electron "clouds" that are then represented on an image able to be seen by our "eyes" as seeing, then you may have a looser definition of "seeing" in that conversation. Despite the definition differences, there is no doubt that an atom does in fact exist, right?
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Date: Fri, 9 Dec 2005
From: Andy Edington
Subject: Pictures of Atoms and Atomic Models
The "pictures of atoms" on our classroom walls and in our textbooks were made by measuring electric fields near the surfaces of various substances. Those measurements are then used as data by a computer program to create the images. The computer program algorithms for coloration, shadows, and other imaging are based on an underlying physical model: the little round ball model of atoms. The images come out looking like little round balls because that is the physical model that we have chosen to use when interpreting our data. For more on this, a good starting point would be a book from the early days of scanning tunneling micrography titled "Taming the Atom: The Emergence of the Visible Microworld", by Hans Christian von Baeyer, Random House, 1992. ISBN 0-679-40039-7. I use this book with a handful of interested high school students each year.
Instruction with models includes physical models as well as mathematical models and graphical models. In chemistry, the focus is more on physical models. The most common molecular physical models taught in high school distinguish between pairs of electrons localized between adjacent nuclei, "lone" pairs of localized electrons, and de-localized electrons that are involved in resonance stabilization and conduction. For example, when we draw a structural formula on paper, we use a single line to represent a localized pair of electrons between adjacent nuclei, represented by letters. (e.g. H-H for a hydrogen molecule) Attempts to reconcile the physical Bohr model of the atom with observed molecular shapes and interactions are unsuccessful, except for the simplest molecules. In my experience, a "probability model" or "fuzzy model" usually means the teacher is trying to get the students to visualize a physical model that allows electrons to be grouped in ways that correspond to observed molecular shapes and interactions. I suspect some people, when hearing the words "Bohr model" think of the mathematical model, not the physical model. Likewise, when hearing the words "probability model", they think of the Schroedinger wave equation. When I teach "the Bohr model" and the "probability model", it is as physical models, and I use it as a bridging activity to relate experimental observations of spectral lines and ionization energy patterns to the experimental observations used to group atoms on the periodic table and then to the physical models used to help organize, analyze, and communicate about experimental observations of various substances, such as molecular, ionic, and metallic substances.
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Date: Fri, 9 Dec 2005
From: Carmela Minaya
Subject: A Different Mathematical Atomic Model?
I just wanted to put in my two cents challenge regarding the atomic model discussion.
Some of us this summer were privileged to attend Dr. Hestenes' workshop on Geometric Algebra. He invested much effort and thought into modifying Clifford Algebra and applying it to physics. GA is an effective tool to model physical phenomena mathematically and to create a picture of what is happening within the mind's eye. It fosters a new way to think about and mentally model the world around us (the world we can see and the world we cannot see, but can theorize about). A GA equation lends itself to a geometric model. Some of the properties work a little differently than in regular algebra.
I see the potential for using this tool in the area of atomic modeling. Hestenes has written a paper on quantum mechanics using GA:
There are several obstacles. The old saying: "You can't teach an old dog new tricks." There is current resistance because many of the problems can be solved using trigonometry and calculus. However, those solutions are pages long whereas the GA solution could be broken down into something as simple as a parallelogram. Teachers would have to learn and master this language. Then we would have to teach it to our chemistry students. We would then need to guide them as they apply the tool to quantum mechanics and the atomic model. Though the obstacles are many, I believe that the rewards of seeing with new eyes and thinking new with new ideas will far outweigh the struggle.
There are already a few within the modeling community who know GA fairly well, who have helped several of us last summer understand some of the simpler concepts. If enough of us within the next five to ten years invest in learning this, then in twenty years or so we could revolutionize the way the atomic model is viewed and thought of.
Anyone up for the challenge? Hestenes received an AAPT award (the Oersted Medal in 2002) for his work in the area of GA. Hestenes has written several papers and books on the application of GA in a variety of settings which could serve as a good starting point.
I have recruited a math colleague and a student to learn it with me at my school. We will commence over the Christmas break. Why not get a group together at your school and learn it together?
------------------------------
Date: Fri, 9 Dec 2005
From: Jane Jackson
[I posted Don Yost's query about atomic models to the chemmod listserv. Dr. Guy Ashkenazi, a young professor in Chemistry Education, replied. Guy visits ASU each summer to work with Larry Dukerich and other chemistry modelers. -- Jane J]
Date: Fri, 09 Dec 2005
From: Guy Ashkenazi
Reply-to: chemMod - chemistry modeling teachers
> I can't see any prediction or phenomenon which this model makes clear for students. Can some
> of you chem people out there help me out?? Other than being a factoid, how is the probability model useful? (I know it can help with chem bonds and all that stuff, but I'm talking students here.)
At the general chemistry level, I totally agree. I taught a general chemistry course for three years without mentioning the term "orbital". I only discussed Lewis's model for bonding. This year, however, I was specifically requested by the organic chemistry instructor to talk about orbitals, because he thinks organic chemistry cannot be taught without orbitals. When I asked him where does he use orbitals, his answer was: "We use orbitals mainly to describe chemical bonding and reactivity: what are sigma and pi bonds, what are alkenes and why is there cis-trans isomers, addition to alkenes, sp3 vs. sp2 and the 3D structure of compounds based on orbital theory, cycloadditions etc." Except for the last one (cycloadditions), I see no reason to use orbitals to describe the bonding, reactivity and 3D structure of organic molecules. Most of his list consists of names derived from quantum theory (sigma vs. pi bond, sp2 vs. sp3 hybridization), but which can be easily replaced by other names (single vs. double bond, planar vs. tetrahedral geometry). But who am I to argue with the great quantum chemical insights of organic chemists?
------------------------------
Date: Fri, 9 Dec 2005
From: Don Yost
Thanks for all the replies, private and public. Pretty much confirmed what I suspected. A nice summary from our friend in Chicago (Gregg Swackhamer):
"We do not use Excel to do fifth grade arithmetic, we do not use jackhammers to clean our dishes, and we do not use Schroedinger atoms to account for mixtures, substances, compounds, and elements. Oh, I suppose you could do all of these, but then you would lose your friends from trying to show off. Or from being committed. Unless, of course, you write school science textbooks!"
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Date: Wed, 14 Dec 2005
From: Charles Rhodes
Students can begin to understand the need for a probability model in the context of their study of the Bohr atom. Lab measurements of the hydrogen line spectrum lead directly to calculation of photon energies and the identification of the associated Bohr energy level transitions. Student estimates of the intensity of each spectral line lead to a rich discussion of the relative probability of each identified transition. The following prompts are useful to structure and lead the discussion.
* Ask a student to list the lines in the order of brightness he/she observed.
* Do we agree on the order of intensity of the hydrogen spectral lines in the Balmer series? Notice the move from brightness to intensity.
* Rank the spectral lines by estimated number of photons per second.
* Identify the Bohr atom energy level transitions corresponding to the observed photon energies.
* Consider the collection of atoms emitting the observed spectrum. Each of the atoms individually is capable of emitting the entire observed spectrum. Ask students to describe a process or cycle of excitation and emission leading to a single atom producing the spectrum.
* Suppose a single atom emits 1000 photons per second at the energies in the observed spectrum. Use the observed intensities to estimate the number of each energy photon emitted each second. The total of the estimates must equal 1000 in this example.
* What is the probability an atom will emit a "red" photon? Find the probability for the other observed photons.
* What is the probability of a transition from Bohr energy level 3 to level 2? Nothing in the Bohr model predicts this probability. Nevertheless, we see the probability in our observations of the spectrum.
* Observe that many atoms, each producing the spectrum, increases the total number of photons but not the energy of individual photons.
* Consider an alternative view. Perhaps an individual atom repeatedly emits only one energy photon while another atom emits a different energy photon. There is nothing in the Bohr model to support this idea. But if it were so, then what is the probability of an atom being of the type that emits only "red" photons?
* Summarize who probability is related to our observation and point out that the class has not yet studied a model that can predict these probabilities.
In the kinetic molecular theory we use statistical methods to deal with the very large number of particles. Newtonian mechanics applies to the interactions between individual particles and between the particles and the container. The discussion suggested above has much in common with the use of statistical concepts in the kinetic molecular theory. Quantum mechanics is anticipated by asking how one can predict the probabilities of a hydrogen atom emitting the observed relative intensities of spectral lines.
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Date: Thu, 15 Dec 2005
From: Tim Burgess
Charles Rhodes wrote:
"(1) Do we agree on the order of intensity of the hydrogen spectral lines in the Balmer series? Notice the move from brightness to intensity.
(2) Rank the spectral lines by estimated number of photons per second."
Estimating (by visual inspection) is problematic. Generally, my understanding is, that human eyes have a greater sensitivity to wavelengths corresponding to green (for example). Even more challenging is the significant variation between individuals in terms of color and intensity estimations. Estimated numbers of photons will be difficult (if not impossible) to rank without clear theoretical expectations. Like a house of cards that would make the line of questions you offer less fruitful than one would like.
I happen to have a spectral analyzer (kind of pricey) that can actually do the counting per second. Even at a resolution of 1.3 angstroms the samples fall off rapidly from the designated values. Using this device I'll try your line of questions this year.
COMPILATION: atomic models (Bohr, probability)
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Мт'ASU#aT Date: Tue, 6 Dec 2005 TitleDate: Tue, 6 Dec 2005
!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^ўџџџ`abcdefўџџџhijklmnўџџџpqrstuvўџџџ§џџџyўџџџўџџџўџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџ РF6нщЯШ{1Tableџџџџџџџџ_WordDocumentџџџџџџџџ%МSummaryInformation(џџџџgDocumentSummaryInformation8џџџџџџџџџџџџoCompObjџџџџџџџџџџџџXџџџџџџџџџџџџџџџџџџџџџџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџџџџџ РFMicrosoft Word DocumentўџџџNB6WWord.Document.8