Category: teaching model

A new study reports a creative approach to modelling the atom motivated by a love story

Keith S. Taber

The science curriculum contains a good deal of abstract material that is both challenging, and – sadly – not always found intrinsically interesting, to many learners. The teacher has to find what can 'make the unfamiliar familiar', something I have written quite a lot about on this site.

Read about teaching as making the unfamiliar familiar

Modelling 'the' atom

One such abstract topic is the structure of 'the' atom ¹ – an area where learners will likely come across multiple models and diverse representations, and where what is being modelled and represented (as a quanticle – a quantum object) simply cannot be adequately represented concretely. Given that, it is hardly surprising that often even keen and capable learners show alternative conceptions in this topic (Taber, 2002 [Download paper]).

I was therefore intrigued by a recent research paper that described an approach to progressing learners' ideas about atomic structure by asking them to engage with a story. Narrative is a recognised way of helping make the unfamiliar familiar, and here a story was referenced that is familiar to many people: that of Shakespeare's 'star-crossed lovers': Romeo and Juliet.

So, in the storyline, electrons were named after characters from the tragic tale. It is common to relate abstract chemical ideas to social relations (chemistry uses such metaphors as 'sharing electrons', 'nucleus loving' species, reagent species that 'attack' other molecules, and substances that 'compete') – but this does risk the anthropomorphism (that is, treating non-human entities as if they have human qualities) actually confusing learners.

Read about anthropomorphism and science

That is, molecules and ions, and nuclei and electrons are not like people, and do not think or have desires, and so they do not act from motivations such as love or hate or jealousy…

Perhaps this seems SO OBVIOUS that only the weakest student could possibly get confused and think otherwise?

But I know from my own research (e.g., Taber & Watts, 1996 [download paper]) that actually even studious, intelligent learners can come to habitually use anthropomorphic language without noticing that they are explaining chemistry in terms that would only make sense if atoms and molecules and ions and electrons did have preferences, and could think for themselves, and did act accordingly!

Atoms can not care about anything – so they do not care about how many electrons they have, and they never deliberately do anything in order to obtain full shells or octets (as they cannot act under their own volition, of course). But many generally successful, hard-working, intelligent, learners in chemistry classes all over the world seem to think otherwise (Taber, 1998 [Download paper]).

Read about the octet framework – an alternative conceptual framework

Likewise, electrons do not care if they are in an atom or not, or whether they are spin-paired or not (and if so, which other, indistinguishable, electron they are paired with), or which energy level of a system they populate.

The authors of the recent paper (which is open access, so freely available for anyone who wishes to download/read it) claim that students found the story-related activity engaging (which certainly seems likely) and that it helped address some misconceptions about atomic structure. They note that:

• "Students do not clearly understand the concept of an orbital" (Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024)

This is a topic that has long interested me so I took a look at the activity the researchers had devised. The learners were

"10th-grade classes, with the participants' average age being between 15 and 16, attending a technical computer science high school ¹…[who] had already studied the atomic model in their chemistry classes during the first half of the year."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

I have taught a basic (planetary) model of atomic structure to students at this age, and also more advanced models to 16-19 year old learners (on A level courses), so I was keen to read about the activity. The authors did not include an explicit statement of the curriculum content which was being treated as target knowledge, although they did include a discussion of their rationale for the story, as well as comments on student work, from which some features could be deduced or inferred. (I would have found it useful to have read an explicit statement of just what the learners were expected to know – what the 'correct' model was meant to be – at the outset of the paper.)

I approached the paper thinking it was ambitious to teach an orbital model of the atom to students of this age. My reading of the story (reproduced below) reinforced that initial impression (I admit, I was challenged in places!) – although the authors certainly felt the students in their research coped well with the challenge.

Although I felt I struggled interpreting some features of the narrative,

A student with a specific learning disorder (SLD), mentioned, "The connection of a fairly complicated topic with such a simple story"

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

It is important to note that the teaching scheme adopted a dialogic approach, where class discussions were included at two points after the students had worked in groups on parts of the activity. The activity was also conceptualised as being part of an enquiry-based learning cycle. So, the material below should be read accordingly, as it does not reflect this wider classroom context.

Read about dialogic teaching

Read about enquiry-based science education

The story

The story is broken into four parts, each leading to a task for the learners (working in groups) to engage in.

Prologue

"Romeo is a bold and dynamic electron found in an atom with seven energy levels. He is at the 4s energy level, together with the faithful Mercutio, his companion on raids. Always upside down compared to him, but then there is no place for two equal electrons in their crew. The two are part of the Montague family, known for being particularly lively.

Juliet is an electron in 2s, she is more tied to her nucleus and in fact she is a Capulet, a rival family to that of the Montagues and decidedly more calm. Juliet is always accompanied by her nurse; they too are turned upside down with respect to each other.

There is a grand ball to which everyone is invited, and, to better organize their arrangement, there is a need to schematize their position."

[Instructions to learners: "Discuss with your classmates what should be the design of the atom where the two families «are» and build
a model"]

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Chapter 1 – part 1

"At one point during the dance, Romeo notices Juliet in her orbital, and, even if he occasionally gets close to her, he is unable to stay there permanently: quivering with love, he asks who knows her and what her tastes are in terms of radiations (electrons are well known to be romantics). He discovers that Juliet is obsessed with color harmony and that the color she prefers is purple "486 nm". To get noticed he wants to perform his famous photon–spectroscopic serenade and jump to emit a purple trail.

[Instructions to learners: "Discuss with your teammates to help Romeo understand how far he will have to jump and whether or not he would have gotten closer to Juliet in this way."]

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Chapter 1 – part 2

"The two are deeply in love and would like to spend the rest of their days together. But Juliet's family hinders them, crying scandal: a Montague cannot be so tied to the nucleus! What to do? The nurse offers Romeo the chance to take her place, but, for her, this would mean losing her place next to Juliet. Romeo and Juliet, very hesitant, then decide to move towards the orbitals occupied by the Montagues. But how to get up there?

While the couple is tormented by this problem, an enlightened friar, Lory, arrives to their rescue with two THz 457s, offering to give them a lift. Despite this help, Romeo and Juliet are unable to reach the Montague orbital, so they loudly invoke another friar, Enzo, asking for new help.

[Instructions to learners: Discuss with your teammates to understand how far they will jump thanks to the first photons and which photons Fra Enzo will have to carry for the two lovers to reach the Montague orbital."]

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Chapter 2 and epilogue

"Juliet's escape has thrown the entire atomic balance into crisis, forcing some Montagues to change levels in order to maintain overall stability. Then, when the couple comes to the Montagues, they cry out for revenge, and the couple is then forced to flee again.

The Montagues set out in search of Romeo and Juliet but fail because it is not possible to reconstruct the trajectory followed by the two lovers.

The story unfortunately ends in tragedy: the two do manage to free themselves from the influence of their families, but they still understand that they cannot be together. Now condemned to separation, the two lovers decide to draw up a schema of the place (the atom) where they met to remember it forever.

[Instructions to learners: "Discuss with your teammates why this trajectory cannot be reconstructed. End the story with a tragic ending, explaining the reasons for the separation sentence.

EPILOGUE Construct with your teammates a possible model of the scheme realized by Romeo and Juliet."]

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Interpreting the narrative

Reading the account I had a very mixed response. I am very keen on approaches that use the familiar everyday as ways into teaching complex, abstract ideas; but subject to two provisos:

• these everyday analogies are interim supports ('scaffolds'), to be withdraw as soon as they are no longer needed;
• teaching needs to focus on the 'negative analogy' (things that do not map across) as well as the 'positive analogy' (the aspects of the comparison that 'work').

The approach here seemed somewhat different. The learners had already been taught a model of the atom earlier in the year, and this activity was intended to be an opportunity to review this prior learning and apply it – and an opportunity for teachers to identify any alternative conceptions elicited by the activity.

Metaphorical meanings?

Romeo and Juliet are not the lovers in the stage play, but electrons. Therefore, in reading the story I identified scientific information (electron Romeo is in a 4s orbital in an atom) and material that seemed to be metaphorical (the electrons Romeo and Mercutio go on 'raids'). I therefore saw the task of reading the story as being in part a decoding of the metaphors that were used.

So, the idea of Romeo and Mercutio being relatively "upside down" was not to be taken literally (electrons do not have ups or downs) but to be a metaphor for spin +¹/₂ and spin –¹/₂, often referred to metaphorically as 'spin up' and 'spin down'. Going on raids was more tricky: in some chemical reactions electron pairs are considered to shift during bond formation (or bond breaking, but that would not refer to an atomic species), but 'raid' suggests a temporary excursion.

I could not understand in what sense Mercutio (the electron, not the fictional character) could be said to be faithful. Electrons respond to physical forces, not personal attachments. Perhaps, I was over-thinking this, and not all the narrative elements did map onto the atomic system? Perhaps that was meant to be part of the challenge for the learners?

A fundamental concern with this kind of comparison is that all electrons are inherently identical, and are only distinguished by the accidental features they acquire in a particular system.

• A 2s electron is on average closer to the nucleus, and experiences a greater effective core charge (it is not shielded as much from the nucleus as a 4s electron is) – so the 'tie' (bond) to the nucleus can be understood as analogous to the attractive force operating between the electron and nucleus. ²
• The reference to being more calm perhaps refers to how the 2s level is at a 'lower' energy so the 'particularly lively' 4s electrons can be more dynamic?

If Romeo and Mercutio, or even Romeo and Juliet, were swapped it could make absolutely no difference and no one could tell. By giving electrons personal identities they seem to be more like us and less like electrons. Electrons cannot be bold or calm. Romeo and Juliet behave differently because they are in different orbitals at different energy levels, not because they are different electrons. Could learners miss this critical point? If Juliet (or Romeo) moved to a different energy level then she (or he) would change 'personality' – but that would undermine the narrative.

I was not sure how the two families related to anything. Within an atom we could class some electrons alike because they are in the same 'shell' (have the same principal quantum number) – so perhaps the two families were in the n=2 and n=4 levels (the L and N shells being their metaphorical 'houses'). I also could not understand where the ball was meant to be held:

• were the electrons to be moved to a new set of orbitals (requiring promotion)
• were the electrons meant be moved to outside the atom (requiring ionisation), or
• was the ball to take place with the electrons in their current orbitals (but for some reason behaving differently than when no dance was taking place?)

The attraction between Romeo and Juliet (the electrons, not the fictional lovers) was difficult to understand. Certainly, if we adopt a model of electrons moving about in different orbitals ³ then they could sometimes be nearer to each other as atomic orbitals interpenetrate – and if so they would influence each other more (due to their charge and spin) at these times: but this would primarily be a repulsion.

(Consider a school with very limited space for sports pitches. Perhaps they mark up a soccer pitch and a field hockey pitch overlapping. If both soccer and hockey players train at the same time there will be places that are part of both pitches, and players from the two sports can come close together in those areas. {This is just an analogy. The two sports would need to schedule practice at different times to avoid accidents!})

It seemed to me that the learners were being asked to read the account at two levels – some features of the story were metaphors (such as when the lovers left the atom only to find they had separate indeterminate trajectories) when other features seemed to be simply plot devices to provde an engaging narrative. I thought that the students were being asked to work out which bits of the story they should take seriously as corresponding to part of an atomic model, and which just moved the narrative on. I though this might be challenging for the 14-15 year old learners (as I was struggling!)

Orbitals and transitions

Some features of the story seemed potentially likely to encourage alternative conceptions. Juliet's preference for light of wavelength 486 nm risks the association of a spectral line with an electron or an energy level, rather than with a transition.

The specific references to 486 nm and 457 THz radiation seemed to suggest that a quantative model was needed – where an atom would actually show spectral lines reflecting transitions associated with radiation of these specific characteristics.

The rationale

Unlike the students, I had access to some of the resource designers' thinking as the paper included a rationale for the storyline. This acknowledged that

The specific location of the grand ball remains implicit [?], as it is challenging to conceive of electrons dancing outside the metaphorical context of "moving swiftly". However, all the other character details are essential for initiating the story and allowing mathematical and physical problems and situations to emerge."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

This seemed to confirm that the learners were expected to build a quantitative model. This was reiterated later in the rationale

"Through calculations of energy transitions and the resulting orbital distances, students gain insight into the quadratic proportionality that underlies these phenomena [?], prompting a gradual reshaping of their personal notions regarding orbital distances."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

I was not sure what was mant by 'orbital distances', and return to this point below. I was also not sure how quadratic proportionality underlay energy transitions.

This was only one of the points in the paper where I got the impression that in the teaching model adopted, energy levels and orbitals were not only being associated, but at times almost seen as equivalent and interchangeable.

A diagnostic assessment opportunity

The rationale seemed to confirm that the activity was deliberately testing whether students associated spectral lines with energy levels rather than transitons between levels,

"To elucidate the intriguing connection between emission and electron transitions to different energy levels, we introduce a romantic-comedic twist, employing Juliet's passion for color harmony as a plot device. Juliet's preference for the color purple is strategically chosen to align with her energy level, prompting students to contemplate the intriguing relationship between spectroscopy lines and electron energy transitions."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

On the other hand, my suspicion that I had been reading too much into the narrative, and trying too hard to interpret plot twists was rather undermined by being told,

"Take, for instance, Romeo's desire to gain Juliet's attention and their joint pursuit of a life away from their feuding families. This narrative intricately parallels the fundamental interplay of orbitals within the model, establishing a direct and compelling link between the characters' human drama and the pivotal role of orbitals in the model."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Indeed? I was struggling to map across some of the story, even when (unlike the students) I had access to the rationale:

"At the outset, the consequences of Romeo and Juliet's choices become apparent: the voids within the nucleus [?] are replenished with new electrons [?], ultimately disturbing the equilibrium of the two feuding families. This disruption leads them to share orbits [sic], not fueled by anger but by fate. The Montagues seek revenge, yet they grapple with the inability to reconstruct the electrons' orbitals due to the uncertainty principle."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

A lot of this went over my head.

The uncertainty principle would not interfere with characterising orbitals, only with being able to posit specific electron trajectories. The orbitals do not belong to electrons ("the electrons' orbitals") but are characteristic of an atomic system with its configuration of charges.

A hybrid model?

Perhaps, in part, my confusion was due to my not being clear about what the target knowledge was- exactly which kind of model was it hoped the students would produce?

"After studying the planetary and Bohr atomic models, students cannot easily move beyond them"

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

It seemed clear from the paper that the learners were expected to have moved beyond a model with planetary orbits, to a model with orbitals, and so from the idea of electrons moving on definite trajectories, to being found somewhere within the orbitals. ³

There was historically a range of models of the atom (even 'the Bohr model' was actaully a series of models), and long ago Rosaria Justi and John Gilbert (Justi & Gilbert, 2000) pointed out that often in teaching we end up presenting 'hybrid' models – that is, models which have features drawn from across several of the different scientific models. Did the curriculum these students followed set out such a hybrid model for students to learn? ⁴

An atom with seven energy levels?

At the start of the story, the students were told "Romeo is …found in an atom with seven energy levels". I am not sure any real atom could only have seven energy levels. My understanding is that any atom has in principle an infinite number of energy levels, but the the spacing of the levels gets successively smaller, so they converge on a limit (which makes ionisation feasible). Even the hydrogen atom has an infinite number of energy levels, but only one is populated with an electron.

So, I wondered if possibly this was meant to be read as "Romeo is …found in an atom with seven populated energy levels"?

A sensible starting point for a student is to assume the atom is initially in its ground state (as under normal circumstances they usually are). If the reference to seven energy levels means populated energy levels, and students are to assume the atom starts in the ground state then presumably learners are meant to assume the atom they need to model is one of the first transition series (i.e., elements with electronic configurations from 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹ to 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰: that is an atom from one of the elements scandium to zinc).

However, later there is a reference to electron Romeo wanting to "jump to emit a purple trail". But he needs to jump 'down' (to a lower energy level) both to get closer to Juliet and indeed to "emit a purple trail" (i.e., for Romeo to be promoted, light would need to be absorbed not emitted) – which is only possible if the atom is NOT initially in its ground state, so that there will be an orbital at a lower energy level not fully occupied. That potentially complicates the model to be built.

For one thing, if the atom is not in its ground state, then atoms of elements of lower atomic mass than scandium might be the target atom to be modelled? Indeed, any atom from the element nitrogen (in the highly excited configuration 1s¹ 2s¹ 2p¹ 3s¹ 3p¹ 4s¹ 3d¹ ) on to zinc could theoretically have seven occupied energy levels. It did not help that there seemed to be no information on how many electrons were in this atom – four were specified, and we are told unspecified other 'family' members lived there, and two other characters were name-checked without it being explicit if they were also in the atom or just passing (from the local Abbey perhaps – would that be an atom of a noble gas?)

Interorbital distances?

As noted above, the authors refer to how they "delve into the concept of interatomic orbital distances", but this seems an oxymoron.

"From the analysis of the drawings, it emerges that the students' final drawings can be traced back to three different types of atom representation (R):

• R1: orbits/orbitals represented at varying distances to convey the concept of energy levels more effectively;
• R2: orbits/orbitals represented at correct distances according to the radius;
• R3: attempt to depict the concept of orbitals and the correct distances between them."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

The authors refer to how in a figure assigned to category R3, "The distances between the spheres reflect the correct distances according to n²", but this does not strictly relate to an orbital model.

Orbitals do not have edges, so it is not possible to measure how far they are from anything. Strictly, every orbital reaches to infinity (even if the electron density soon gets so rare that it becomes effectively zero). The point is that this is a gradual falling-off and there is no sudden drop that we might think of as an edge.

Commonly orbitals are represented either with

• probability contour lines, or
• colour or shading showing differnt levels of electron density (i.e., the relative probabilities of an electron in the orbital being 'found' at different regions of the orbital), or
• more simply with probability envelopes.

Those envelopes show where, say, 90% or 95% of the electron density is located – which means 10% or 5% of the electron density (that is inside the orbital) lies outside the envelope drawn. So, these lines are to soem degree arbitrary, conventional and do not correspond to anything physical ('real').

One could measure the distance between the centres of two different orbitals, but this would be a trivial issue when the orbitals are in the same atom. (That is, the atomic orbitals are all centred on the nucleus, so the centres have no distance between each other.)

This is different to a planetary type model where electrons are considered to be a certain distance from the nucleus, so the orbits have quantifiable radii. In moving to an orbital model we have to think of fuzzy overlapping volumes of space, and the notion of there being set distances between orbitals just does not work in this model.

Imagine being asked to report the distance between the soccer pitch and the hockey pitch.

And then imagine having that task when there are no marked out edges to the pitches.

The energy levels associated with the orbitals can be considered to have specific values, and so there are definite differences ('distances'?) between the levels in that sense – but these would be energy gaps: analogical 'distances' on an energy scale, not actual distances.

The authors suggest that,

Despite their discussion about orbitals, [for the students' final drawings] all groups drew orbits, representing them as lines depicting the trajectories of electrons

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

But that is not so clear from the diagrams of the models and the students' own comments.

Student 1: "In a circle, we drew lines. But we know that electrons don't follow that precise path; they exist in orbitals, which are regions where electrons are more likely to be found. So, we don't know the precise radius because it's a region. Therefore, in my opinion, since the radius can always vary, you can't use the radius to depict the atomic model; it's more accurate to use energy levels."

…

Teacher: "Here you have drawn the distances increasingly closer. Why?"

Student 2: "Because it represented differences in energy levels."

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Some groups of students seem to have drawn concentric circles representing energy levels rather than orbits or shells or orbitals. Normally, energy level diagrams are not drawn like that, but this seems a perfectly reasonable form of representation providing it is explained.

Spherical orbitals

We also have to bear in mind that only s-orbitals have spherical symmetry. (A 'shell' of orbitals in an atom would be spherically symmetrical only if each orbital was singly or fully occupied. But it was not clear how many electrons were in this atom.)

The first seven energy levels in any atom or ion with more than one electron will be associated with p- and d-orbitals as well as s-orbitals. So, even if orbitals were represented with probability envelopes, and these were treated (incorrectly) as if the edges of the orbitals, then there would be no fixed 'distances' between the edges of any comparisons involving these non-spherical orbitals.

Not all orbitals have spherical geometry (Image by Smiley _p0p from Pixabay)

At this point it is interesting to examine the samples of student models represented in the paper. All of them are drawn with circles. The authors of the paper seemed satisfied with this aspect of the models.

Making sense of 486 nm and the 'THz 457s'

I pointed out above that my reading of the information given about the atom that it seemed the target atom could be from one of a wide range of elements. It seems I got this completely wrong,

We conclude this paper by highlighting a limitation of the story we have designed from a physical point of view. Our story does not fit the real atomic structure. Indeed, we chose to consider a hydrogen atom with multiple electrons because we thought it was easier for the students to manipulate. We are aware of the fact that this may represent a critical point of our story, but in the classes where we experienced the activity it has not created problems, since the students noticed this inconsistency and talked about it with the teacher.

Aquilina, Dello Iacono, Gabelli, Picariello, Scettri & Termini, 2024

Now, by definition, a model is never quite like what is modelled – or it ceases to be a model and becomes a perfect replica. But "a hydrogen atom with multiple electrons" is not an atom at all, but an ion. I am not clear why this is "easier to manipulate" than an atom of a different element, as in models of this kind the nucleus is in effect just a minute point charge – so its composition does not complicate the model in any significant way. If that nuclear charge is +7, say, rather than +1, it makes a difference, certainly (to energy levels), but that does not add any further complexity.

Perhaps the authors chose to retain a hydrogen nucleus because they wanted students to use data from hydrogen spectra? (But if so, this was a little naughty.)

The Balmer series

Again, it did not help that I did not know what the target knowledge set out in the curriculum was.⁴ But, knowing now that hydrogen was the target atom led me to suspect 486 nm and 457 THz radiation linked to lines in the hydrogen spectra – lines in the Balmer series associated with transitions between n=3 and n=2 (656 nm) and n=4 and n=2 (486 nm).

That was all very well, but those transitions referred to the hydogen atom and not to a hydrogen ion. The extra electrons repelling each other in the ion (assuming the ion could be considered stable, which is itself problematic) mean the energy levels (and so the energy gaps; and so the spectral lines) would all be different.

But, if we pretended the ion was stable, and if we pretended that the additional electrons did not change the energy levels (what is what I meant by being somewhat naughty), then the numbers made sense.

A sleight of hand?

Indeed, if we were to adopt the hydrogen atom as the model for our ion, then I sensed I understood why the orbitals were all drawn as circles. In the hydrogen atom, the energy levels are only associated with the principle quantum number. The 2p orbital is at just the same energy level as the 2s orbital. A transition from the N shell to the L shell has the same energy associated with, and so the same frequency of radiation, regardless of whether it involved 2s-4s or 2p-4s or 2s-4p or 2p-4p or 2s-4d or 2p-4d (or indeed 2s-4f or 2p-4f)⁵. That is a considerable simplification, that would make the task much easier for learners.

So, if we are modelling the hydrogen atomic energy levels, we only need to worry about the principle quantum number as there is one level for each value of n. The student diagrams reproduced in the paper suggested all the students understood the reference to an atom with seven energy levels to mean n (that is the principle quantum number related to 'shell') = 1-7.

But an energy level is not an orbital. The n=2 energy level in a hydrogen atom is associated with 4 orbitals, only one of which has spherical symmetry. The n=3 level is associated with 9 orbitals, only one of which has spherical symmetry.

Moreover, this assumption that all the orbtials in a shall are at the same energy level ('degenerate') only applies to a hydrogenic species (H, He⁺, Li²⁺, etc.) – that is, atom-like species with a single electron. The 'atom' (ion) with Romeo and Juliet and Mercutio and the nurse and the rest of the Capulets and Montagues (and possibly some clergy) would not have 2s and 2p orbitals that were degenerate. The presence of interacting electrons (repelling each other, that is, not lusting after each other and "quivering with love") would raze the degeneracy- so the 2s and 2p orbitals would actually be at different energy levels. And so also with 3s and 3p and 3d.

It is not the presence of a hydrogen nucleus which leads to degeneracy between the orbitals within each value of n (each shell), but a system of one nucleus and one electron. So if this 'atom' (ion) had seven energy levels, these would not equate to seven shells of electrons.

The model

So, it looks like the target model was an ion with a hydrogen nucleus, and 7 energy levels occupied by an unspecified number (>4) of electrons, which has the same energy structure and levels as a hydrogen atom, but where each energy level only contained an s orbital.

Models simplify, and in modelling we deliberately leave aside some complexity and nuance. However, we have to balance the gain in simplicity with the loss of authenticity.

• A highly charged hydrogen ion could not exist (unless maintained by some very powerful external field)
• Atoms have an infinite number of energy levels (but there is no harm in asking learners to ignore most of them for the time being when working on a task)
• A hydrogen atom has orbitals of different types (s, p, d…) not all of which are of spherically symmetrical.
• The electronic transitions in an ion would not be those found in the related atom, as energy levels of the system depend on the configuration of charges that are interacting. The ion would have many more potential transitions than a single-electron system (such as a hydrogen atom), and these would not have the same energies/frequencies/wavelengths as in the hydrogen atom.
• Orbitals do not have edges, and they interpenetrate, so the concept of interatomic orbital distances does not correspond to anything 'realistic' in the orbital model of the atom.

So, the model seems to put aside a lot of the subtlety of the science. But then are these nuanced ideas suitable for treatment with most 15-16 year olds? I would have suspected not (which is why I started from a position of thinking this whole activity was somewhat ambitious), and that may well be why compromises were made in the teaching model adopted in this study.

But perhaps it would be better not to introduce an orbital model until we feel learners are ready to appreciate the quantum jump from concentric orbits to fuzzy, overlapping, infinitely-extended patterns of electronic probability, and the associated complex patterns of energy levels they generate. (But, again, the teaching model used may simply have been reflecting the target knowledge set out in the school curriculum in this particular national context? ⁴)

After all, as the authors had noted,

Encouraging a new alternative conception?

To take one point. The 486 nm and 457 THz radiation is associated with transitions between n=3 and n=2 (656 nm) and n=4 and n=2 (486 nm) in the hydrogen atom, but NOT in the 'atom' populated with Montagues and Capulets.

Does this matter? After all, the point of the exercise is not to remember these specific values, but to be able to link radiation emitted or absorbed to electronic transitions – so, the particular values of 486 nm and 457 THz are irrelevant. True, but what students are potentially learning here is that the values of energy levels are not affected by the number of electrons repelling each other (here we have an ion with many electrons, but we can simply use the values for a hydrogen atom) – which is an alternative conception.

I also know that this is an alternative conception that learners are likely to readily develop. When students study ionisation energies, and make comparisons between different atoms, they often fail to allow for how the same designation of orbital does not imply an equivalence between differently populated electronic structures.

So, for example, a 2p orbital in an oxygen atom is not only not equivalent to a 2s orbital in the same atom: nor is it equivalent to a 2p orbital in a nitrogen atom. Nor, for that matter, is it entirely equivalent to a 2p orbital in the o^2- anion.

This is not the most serious alternative conception that students can acquire, but given the complexity and challenge of this whole topic area, it might be wise to avoid risk misleading students when possible.

Or am I just being over-critical because I myself found the task too challenging? ☹️

To see through an orbital clearly?

This was an interesting project, and I hope the authors explore the idea further, and perhaps use their experiences with this implementation to further refine the activity. But I am not sure it is helpful in the long term to encourage learners to work with a model that is so constrained that it is likely to encourage new alternative conceptions.

But would that be the case? If the activity is part of a dialogic teaching sequence and the catalyst for engaging students in a discussion of these abstract ideas – a discussion that the teacher carefully steers towards the canonical account – then perhaps the outcome can be more productive. I guess we can only conjecture about this, until someone investigates the long-term effects of learning from the activity.

As usual, it is fair to say "more research is needed".

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Work cited:

Aquilina, G.; Dello Iacono, U.; Gabelli, L.; Picariello, L.; Scettri, G.; Termini, G. "Romeo and Juliet: A Love out of the Shell": Using Storytelling to Address Students' Misconceptions and Promote Modeling Competencies in Science. Education Sciences, 2024, 14, 239. https://doi.org/10.3390/educsci14030239

Justi, R., & Gilbert, J. K. (2000). History and philosophy of science through models: some challenges in the case of 'the atom'. International Journal of Science Education, 22(9), 993-1009.

Taber, K. S. (1998) An alternative conceptual framework from chemistry education, International Journal of Science Education, 20 (5), pp.597-608.
[Download paper]

Taber, K. S. (2002) Conceptualizing quanta – illuminating the ground state of student understanding of atomic orbitals, Chemistry Education: Research and Practice in Europe, 3 (2), pp.145-158 [Download paper]

Taber, K. S. (2019). The Nature of the Chemical Concept: Constructing chemical knowledge in teaching and learning. Royal Society of Chemistry.

Taber, K. S. and Watts, M. (1996) The secret life of the chemical bond: students' anthropomorphic and animistic references to bonding, International Journal of Science Education, 18 (5), pp.557-568. [Downlod paper]

Notes

¹ Of course there are many atoms, and indeed many kinds of atoms – so the use of the definite article ('the') is strictly inappropriate. But, this is common usage,

What seems potentially more problematic is the use of the definitive article when the referent is not a specific individual specimen. Chemistry teachers will say things like "the ammonia molecule is pyramidal" when no ammonia molecule is either specified directly or can be inferred to be the case in point from the context. This probably does not seem problematic for the simple reason that it does not matter which ammonia molecule is being referred to: they are all pyramidal. So, statements such as the ammonia molecular is pyramidal; the chlorine atom readily accepts an electron; the K shell is nearest the nucleus; and the iodide ion is a good leaving group; etcetera, will be true regardless.

These statements 'work' in a way that some apparently parallel statements from outside of chemistry would not: the house has a blue door, the man walks with a limp, the baby sneezed all night, the bicycle has squeaky brakes, etcetera. Some houses have blue doors – many do not…So, we should not say 'the house has a blue door' unless we have made it clear which house we are referring to. Yet, we do not need to say which particular water molecule is polar, as they all are (i.e., it may be considered an essential quality of a water molecule). So, the question here is why a teacher would say 'the ammonia molecule is pyramidal' when they are not actually referring to a particular specimen, and the point they are making is actually that (all) ammonia molecules are pyramidal.

Taber, 2019, p.128

And, even if we can refer to 'the carbon atom' when we mean any and all carbon atoms, to simply refer to 'the atom' seems a slight to the periodic table – surely we need to say which (kind of) atom we are modelling? That point certainly proved to be critical in the context of the modelling task discussed in this article!

² The force is symmetrical – the same magnitude force acts on the nucleus and the electron, with each being pulled towards the other. Students commonly have alternative conceptions about this such as thinking the force only acts in one direction (from nucleus to electron) or that the force on the electron is greater.

Read about Newton's third law and common alternative conceptions

³ In the planetary model of the atoms, electrons moved in orbits. In the orbital model we can think of electrons moving about the orbital, and the 'electron density' as a kind of average over time of where they have been. However, it may be more in keeping with the quantum model of the atom to suggest the electrons do not actually move around but rather have probabilities of being located at different points under conditions of observation. (According to a very common interpretation of quantum theory, the notion of an electron being somewhere specific only makes sense at the point of observation.) This is pretty difficult to appreciate (especially for most school-age learners), and I suspect most chemists are happy enough most of the time to think of the electrons moving around in their orbitals.

⁴ Five of the six authors, including the corresponding author, were based in Italy (the other author gave an affiliation based in Canada), so I assume the schools from which the work is reported is in Italy. The paper reports the task set and the student responses in English, so it is not clear if English was used as the language of instruction in the school (this seems unlikely unless this was an International School, but the paper does not report that material has been translated into English).

⁵ 4f orbitals are not usually relevant to atomic structure till we consider cerium, element 58. But the familiar order of filling orbitals as we imagine we are building up atoms (1s < 2s < 2p< 3s < 3p < 4s < 3d < 4p… *) refers to species with more than one electron. For a hydrogen atom, a 4f orbtial is at the same energy level as the 4s orbital, as when occupied the atom's electron, neither would be sheilded at all from the nucleus by other electrons.

(* Ironically, the familiar descriptions of the discrete orbitals designated in this way are based on calculations for a hydrogen atom and do not strictly apply to multi-electron atoms. However the moodel generally works well, and is widely used.)