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Essential Science for Teachers: Physical Science

The Particle Nature of Matter: Solids, Liquids, and Gases A Closer Look

A Closer Look

Look for the following topics in the video, indicated by the onscreen icon, and click below to learn more.

Scientific Models

Scaling Analogies

Microscopic Reasons for
Macroscopic Properties

Scientific Models

What is a scientific model?

As stated in the video, a scientific model is a “testable idea… created by the human mind that tells a story about what happens in nature.” Another definition is “a description of nature that can predict things about many similar situations.” Models are developed when a scientist’s creativity and insight are combined with data and observations about many similar scenarios. Scientists try to identify and generalize patterns in these observations, and use mathematical language to predict the outcome of related situations. The value of a model is that we can trust its predictions about similar situations even if we don’t encounter each situation.

Let’s look at a simple example. Although most people in 1492 thought that the Earth was flat (because that is what they observed), nearly all educated people knew that the Earth was a sphere. The difference in the spherical model of the Earth and the prevailing model of the time led to differences in predictions: Columbus, for example, knew you could not “fall off” the edge of a spherical Earth. By knowing the radius of that sphere, one could calculate its circumference (C = 2 * Pi * r) and thus plan an expedition to have enough supplies to reach a far-off destination.

In the same way, basic evidence was used to determine that the Earth is round, some of the most powerful insights into nature can be obtained from a model based on a few simple ideas. It is this kind of model that we will be developing in this series for the structure of matter.

What makes a model “good”?

Any model is based on a certain set of observations. A good model must be able to explain as many characteristics of these observations as possible, but also be as simple as possible. This second point is a restatement of the “Occam’s razor” principle alluded to in the video. To extend our spherical-Earth example, sailors in the fifteenth century also noticed that a ship appears to “sink” as it goes over the horizon — the last part of a departing ship you can see is the top of the mast. The “spherical Earth” model explains this well: the curvature of the Earth becomes visible as you deal with greater distances. This model also explains why the “sinking” illusion happens regardless of what direction the ship moves away from you: a “spherical Earth” curves “downward” in all directions from someone standing anywhere on its surface. Both aspects of this observation are explained well by our model.

In addition, a good model must be able to explain phenomena that are seemingly different from the ones we used to develop the model in the first place. For instance, even though the “spherical Earth” model was used to explain sailing phenomena, educated people were able to link this idea to lunar eclipses. A lunar eclipse happens when the Earth passes between the Sun and the Moon. If we subscribe to the “spherical Earth” model, we would expect the shadow of Earth to be round as it passes across the Moon — and indeed, it is. This new, seemingly different situation is explained with the same model.

An example of a model that doesn’t stand up as well to Occam’s razor is the “continuous,” “continuum,” or “plenum” model of matter presented in the video. In an extended interview, science historian Al Martinez described how a proponent of the continuum model might use it to explain how a container of air (like a syringe) weighs the same whether the air in it is compressed or not.

Dr. Martinez pointed out that a particle theorist can easily explain that there are the same number of particles of air in both the open and closed syringe, but that they occupy less space. A continuum theorist, however, would have to cite Aristotle’s theory of four “elements,” which states that everything in the world is made of some combination of Earth and water, the “heavy” elements, and air and fire, the light elements. According to the continuum theory, the air that is contained in the syringe would actually be composed of a combination of air, fire, earth, and water. Hence, when you push in the plunger of the syringe, you would lose some of the light matter and some of the heavy matter through the walls of the syringe, allowing for a net difference of zero in the weights.

Likewise, the continuum theorist would say that when you pull the plunger out, air flows back in through the walls of the syringe. The question then becomes, If there’s now more matter in the syringe, why doesn’t it weigh more than it did when there was less? According to another feature of Aristotle’s theory, some of the air that comes into the syringe actually has negative weight, or levity, because it contains air and fire. Because it has levity, it tends to go upwards, which counteracts the heavy matter that flooded in, this accounting for the fact that, again, the difference in weight is zero.

In this example, it is clear that the continuum explanation is less elegant and economical than the particle one. It’s interesting to note, however, that it took from Aristotle’s time until the eighteenth century, when more was learned about gases, for the continuous model of matter to finally get “cut” by Occam’s razor.

When do scientists change a model?

No scientific model has ever been totally complete. When credible observations of a new situation come into conflict with the predictions of a model, something must be changed because either the data or the model is incorrect. Although Columbus used the “spherical Earth” model to predict the length of his voyage to the Indian subcontinent, his estimate of the Earth’s radius was much smaller than what we now know it to be. Thus, Columbus underestimated the circumference of the Earth and the length of his voyage to India. (Fortunately for Columbus, there were two other rather large continents for him to reach before he ran out of supplies.) Later, the model of Earth as a sphere was refined to include a better estimate of its radius, and thus make better predictions about distances to locations on its surface. The model was correct, but its parameters had to be refined.
We will see in the rest of the series that our particle model will not have to be thrown out when it doesn’t sufficiently explain new data, but adding some detail or refining some parameter of the model will explain these new observations.

Limitations of models

All models have limitations — no model can possibly explain every detail of a scientific phenomena. For instance, if we wanted to predict the distance we would need to travel from one side of the country of Nepal to the other, we could predict it using our “spherical Earth” model, but we’ll find our estimate is far from accurate. Why? Although the Earth is a sphere, there are many topographical features on its surface, including the Himalayan Mountains, which span Nepal. Although we could add all the mountain ranges in the world to our “spherical-Earth” model, this would make the model quite complex and defeat the utility of having a simple model to make useful predictions.

Similarly, we will find that, while our particle model explains many things about matter, it is not comprehensive — for example, it cannot predict why certain materials have different electrical properties. We could add further refinements that are outside the scope of this course to enable it to do so, but it would make our model so complicated that it would no longer be useful to us.

Scaling Analogies With Powers of Ten

It’s not easy to imagine dividing something into ten pieces nine different times.

In order to make the difference in size scales more comprehensible, we can expand the size of the original object to something with which we are familiar. Let’s look at physicist Richard Feynman’s example of expanding a hydrogen atom to the size of an apple.

To make this calculation easier, we round off to the nearest power of ten. Feynman knew that an atom is a few angstroms (10-10 meters) wide. Let’s round off to 10 angstroms = 10-9 meters. An apple is about 10 centimeters (or 10-1 meters) wide. In order to make the hydrogen atom as large as the apple, we have to make it ten times bigger a total of eight times. In other words, we must expand it by a factor of 108:

The size of hydrogen atom (10-9 m) multiplied by the expansion factor (108) equals the size of an apple (10-1 m)

or:
10-9 m x 108 = 10-1 m

An easy trick when multiplying powers of ten is to simply add their exponents (the power to which ten is raised). In the above example, this shortcut gives us

10-9 m x 108 = 10(-9 + 8) m = 10-1 m

To rescale the size of the apple, so that we may compare it to our expanded hydrogen atom, we multiply the size of the apple by the same expansion factor:

The size of an apple (10-1) multiplied by the expansion factor (108) equals the size of earth (107 m or 10,000 km)
or:
10-1 m x 108 = 10(-1 + 8) = 107 m (or 10,000 km)
The diameter of the earth is approximately 12,000 km, so this is a good estimate.

Thus, if you expand a hydrogen atom to the size of an apple, the apple would expand to the size of the Earth. Having a student visualize the difference in scale between an apple and the Earth is more expressive than simply stating that an apple is 108 times bigger than an atom. This is the power of these kinds of analogies.

Microscopic Reasons for Macroscopic Properties of Solids, Liquids, and Gases

Recall the four principles or characteristics of the particle model:

  1. All matter is made of individual particles.
  2. There is empty space in between the particles.
  3. All particles are in constant motion.
  4. There are forces between the particles.

How do these microscopic ideas explain the macroscopic properties of solids, liquids, and gases we gave in the previous video session? Although all characteristics of the particle model help to explain these properties, we also pick out the most important characteristic related to each property.

Phase Property Most important characteristic Microscopic reason
Solid

Holds shape There are forces between the particles. The forces that attract individual particles to one another are strong enough to overcome the tendency of their motion to pull them apart. This results in a rigid structure.
Not compressible There is empty space between the particles. Each particle can be thought of as a rigid sphere. In a solid, the particles are touching each other and therefore cannot be pushed together more.
Liquid

Takes shape of container All particles are in constant motion, and there are forces between the particles. The energy of the motion of particles is strong enough to allow the particles to move past each other, despite the forces between particles.
Not compressible There is empty space between the particles. For a similar reason to solids, the particles can be thought of as touching each other, so no force can compress them further.
Gas

Fills container All particles are in constant motion. The energy of the motion of particles is so great as to overcome the attraction between particles when they collide. Individual particles then continue on until they hit the walls of the container.
Compressible There is empty space between the particles. The resulting space between the particles is much larger than the particles themselves (i.e. they are not touching) so it is possible to squeeze a container to make those spaces smaller, at the expense of increasing the pressure of the gas inside the container.

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Essential Science for Teachers: Physical Science

Credits

Produced by Harvard-Smithsonian Center for Astrophysics. 2004.
  • Closed Captioning
  • ISBN: 1-57680-749-5

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