March 2018

# Part 2: The evolution of models

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Dr. David C. Stone, Department of Chemistry University of Toronto, Toronto, Ontario

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In part one of this series,1 I described how switching between macroscopic, microscopic, and symbolic representations of concepts and theories can be confusing for students, especially for those still operating as dualist (right and wrong only), concrete operational thinkers. I also described the nature of scientific models, and the need to carefully identify their inherent limits.
I closed by pointing out the need to explicitly identify key conceptual features of models and visualisations, and warned that we should never say, “So we throw this model out and get a new one!”

To explain this warning, consider the models encountered in describing atomic theory. These have an obvious linear, historical, sequence that makes it easy to focus on why each one fails; however, students quite reasonably ask, “Why bother teaching obsolete and broken ideas?” A more productive approach is to show how the models evolved over time, each one adding concepts as new experimental data expanded our understanding.

## Building a foundation: Dalton’s atomic theory

We start with John Dalton’s atomic theory (published in stages from 1803 to 1810) and the “billiard ball” model of the atom.2 I won’t reiterate the four postulates here. Rather, I will focus on the key features of Dalton’s theory:

· That atoms have a definite physical reality (characteristic size)

· That all atoms of a specific element have a characteristic mass

Fig. 1. Plates from Dalton’s book2 showing: symbolic representation of elements and compounds

Fig. 1. Plates from Dalton’s book2 , showing calculations based on packing of spheres

Dalton famously drew up symbolic representations of the elements as circles with different markings, allowing both chemical compounds and chemical reactions to be depicted in a rational and consistent manner (Fig. 1). The choice of circles was, in some respects, arbitrary, although a sphere is the simplest three-dimensional shape. And modern chemistry books abound with illustrations representing atoms as solid spheres!Further, it is the geometric packing of spheres having definite masses and radii that are used to explain and calculate the density of different crystalline

materials, both metallic and ionic. And for this purpose, imagining the atoms as close-packed solid spheres is good enough to enable useful descriptions and predictions to be derived from Dalton’s theoretical conceptualisation of the nature of atoms.

##### Suggested Activity #1

Have your students identify as many physical properties of matter as possible that can be explained solely on the basis of Dalton’s theory using a set of billiard balls (table tennis balls may be substituted for reasons of safety and cost!)

Decorating the foundation: Thomson’s atomic theory Joseph John Thomson’s “plum pudding” model, based on his discovery of the electron in 1897,3 is easily dismissed because it rarely gets much coverage in chemistry texts. However, it remains important because it further informs our understanding of atoms.

Specifically, in addition to the features of Dalton’s model we see that:

• All atoms have a defined internal structure, and are not completely indivisible
• All atoms contain negatively-charged sub-atomic particles (electrons)
• All atoms must therefore contain a balancing positive charge
• Some electrons may be removed from the atom under appropriate conditions (ionization)

The “plum pudding” analogy also fails to adequately represent Thomson’s model. In fact, Thomson’s 1904 description of the model4 contains concepts that foreshadow both the Bohr-Rutherford model and Gilbert Lewis’ electron-dot symbolism. For example, one description has the electrons uniformly spaced and travelling “at high speed” in a series of concentric “rings” (i.e., orbits), with progressively more electrons in each ring as distance from the atomic centre increases. Another scenario allowed the electrons to orbit at right-angles to the plane of the rings, resulting in a series of concentric shells of electrons. It was likely the difficulty of depicting this last scenario in a two-dimensional image that led to the “plum pudding” analogy (Fig. 2).

Fig. 2. Thomson’s atomic model: raisins in a plum pudding;

Fig. 2. Thomson’s atomic model: electrons in concentric rings located in a positively charged medium.

##### Suggested Activity #2

To help your students develop a more multiplist mind-set and gain a better understanding of the provisional nature of scientific models, have them consider the following questions:

• Given that they are spatially distributed within atoms, are all electrons as easily removed, or are some more accessible than others?
• Given the electrostatic force between opposite charges, will it be easier, as easy, or harder to remove a second electron after removing the first?
• When studying the packing of atoms or ions in a crystalline solid, do we treat “plum puddings” any differently from “billiard balls”?

Obviously, these anticipate the concepts of valence and core shell electrons, first and subsequent ionization energies, and ionic versus covalent radii. Note, however, that:

1. The new model is good enough for describing and making predictions about these atomic and ionic properties.
2. The old model is implicit in the new, such that the method of predicting the density of crystalline solids is the same: only the values of certain parameters are changed.

##### Suggested Activity #3

Have your students explore the limits of both models by considering the following questions:
• What properties of an electron are defined or explained by the data, theory and model?
• What relevant questions might you ask that are not defined or explained?

For example, Thomson’s experiments implied that an electron has a negative charge, but only allowed the calculation of its mass-to-charge ratio; it wasn’t until Robert Millikan’s 1909 oil-drop experiment that scientists understood just how small an electron actually is. The model and theory also fail to answer the question: what exactly is an electron?

Expanding the foundation: Rutherford’s atomic theory
Next are the 1911 experiments of Hans Geiger and Ernest Marsden, leading to Ernest Rutherford’s nuclear model.5 Visually, this is a radical departure from the previous models. It is also counterintuitive since the smallest physical component of elements (the atom) consists mostly of empty space, yet the distance between nuclear centres in a crystalline solid remains constrained as though it consisted of hard spheres.

This creates problems for dualists and Piaget’s concrete operational thinkers, since they need to rationalise conflicting concepts. How do you visualise something that has no useful concrete, macroscopic analogy? Billiard balls work for Dalton’s atoms because they are hard, spherical, uniformly dense, with definite mass. Table tennis balls are poor analogies for Rutherford atoms because their mass is concentrated at the surface; even if a pea were placed inside, there would be nothing to maintain this ‘nucleus’ at the geometric centre.

When confronted with conceptually challenging or counterintuitive material, concrete thinkers tend to fall back on one of two strategies: find a flawed analogy that makes sense to them, or rely on rote memorization to pass a test before forgetting the information.6,7 Neither is a sound foundation for building further knowledge, so how do we help such students develop more formal operational thinking?

##### Suggested Activity #4

Have students use simple bar magnets to experience incompressible space; similarly use glass rods with different materials to demonstrate electrostatic attraction and repulsion. They can also try dispensing a fine, dry, powder of a polar material into a plastic weighing boat that has been electrostatically charged.

Students can use this macroscopic experience to inform their understanding of events at the atomic level (electrostatic repulsion between the electrons of two atoms limits their closest approach.*

So how does Rutherford’s atomic theory extend and expand those of Dalton and Thomson?

• Most of an atom’s mass is concentrated in a small fraction of its volume
• This nucleus also contains the atom’s positive charge
• The electrons occupy the volume of the atom around the nucleus

Note that definite atomic mass and volume and electrons are all retained. It is also now easier to understand ionization — we simply have to overcome the electrostatic attraction between electron and nucleus, which are physically separated within the atom. The revised model also poses new questions, however, especially if we avoid skipping straight to the Bohr-Rutherford model. For some context, consider that between the Geiger-Marsden experiments and Bohr’s 1913 model:

• Atomic number was a rank-order value which may or may not be related to atomic mass
• While the nucleus was known to have mass and positive charge, neither the proton nor neutron were known to exist

##### Suggested Activity #5

Ask your students to put themselves in Rutherford’s shoes during the period 1911-1915 and consider the questions he might have asked. For example:

• Is the nucleus a single sub-atomic particle, or multiple particles?
• Is the positive charge associated with the mass, or are they separate things?
• How can we explain that atoms are mostly empty space (occupied by extremely low mass electrons) but behave as hard, incompressible spheres?
• Where exactly are the electrons within the atom, and what are they doing?

Obviously, we are still a long way from modern atomic theory. We have already seen, however, that each model is a refinement of the previous model, both incorporating and extending it. And, while our understanding of atoms has changed dramatically, we have not actually “thrown out” any of the preceding concepts and calculations —they are all still there.

In part 3 of this series, we will complete our journey through the development of atomic theory, and consider how we can use this to communicate a better understanding of how scientific theories and models are developed and used.

* This also helps introduce bonding as a continuum of electrostatic interactions from weak (dispersion force and dipole–dipole) to strong (covalent and ionic bonding)

> Part 3: Evolution and revolution, April 2018

#### References

1. D. C. Stone, “Know the limit and teach within it Part 1: Analogies and models”, Chem 13 News, December 2017/January 2018, pages 22-25.
2. John Dalton, A New System of Chemical Philosophy, 1808, https://archive.org/details/newsystemofchemi01daltuoft
3. J. J. Thomson, The Electrician, 1897, 39 and “Cathode Rays”, Philosophical Magazine, 1897, 44(269), pages 293-316. http://dx.doi.org/10.1080/14786449708621070
4. J.J. Thomson, “On the structure of the atom: …”, Philosophical Magazine, 1904, 7(39), pages 237-265. http://dx.doi.org/10.1080/14786440409463107
5. Ernest Rutherford, “The Scattering of α and β Particles by Matter and the Structure of the Atom”, Philosophical Magazine, 1911, 21(125), pages 669-688. http://dx.doi.org/10.1080/14786440508637080
6. D. Perkins, “The Many Faces of Constructivism.” Educational Leadership, November 1999, pages 6-11. www.scribd.com/doc/32920521/Perkins-The-Many-Faces-of-Constructivism
7. D.R. Mulford and W.R. Robinson, “An inventory for alternate conceptions among first-semester general chemistry students.” Journal of Chemical Education, June 2002, pages 739-744.

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