Section 1–2 Matter is made of atoms

(Solid / Liquid / Gas)

Feynman states the atomic hypothesis as all things are made of atoms that are moving perpetually, attracting each other when they are in a relatively short distance apart, and repelling upon being squeezed into one another. Currently, this is a fact because we can “see” individual atoms by using a scanning tunneling microscope and move them from one location to another. Importantly, atoms were initially defined as indivisible and indestructible fundamental entities, but they are reformulated as systems of nucleons that are made of quarks. In a sense, quarks are now the fundamental physical entities and have the traditional meaning of “atoms.” However, we explain properties of water, steam, and ice in terms of atoms instead of quarks.

Note: In volume 2, chapter 6 of The Feynman Lectures, he mentions that the field-ion microscope provided human beings with the means of seeing atoms for the first time.

1. Properties of water (liquid):

“… a picture of water magnified a billion times, but idealized in several ways (Feynman et al., 1963, section 1.2 Matter is made of atoms).”

Feynman describes the use of best optical microscope available, roughly 2000 times, to magnify a water drop. He would revise this section considerably because scanning tunneling microscopes are now available. Donald Eigler of IBM’s Almaden Research Centre is the first person to manipulate an individual atom in a controlled way such that we can “see” atoms. This technical achievement was predicted by Feynman in a lecture titled There’s Plenty of Room at the Bottom given at an American Physical Society meeting at California Institute of Technology on December 29, 1959. In Feynman’s words, “[t]he principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom. It is not an attempt to violate any laws; it is something, in principle, that can be done; but in practice, it has not been done because we are too big (Feynman, 1999, p. 137).”

Interestingly, Feynman mentions three limitations of Figure 1–1 (Water magnified one billion times). First, the particles are idealized in the figure as having sharp edges. As an alternative, the edges could be blurred because the particles are almost everywhere in the sense that they may be found in locations further away with lower probabilities as predicted by quantum mechanics. Second, the particles are sketched in a two-dimensional figure. Therefore, the figure does not show possible three-dimensional arrangements of particles. Third, the figure is a static representation of water molecules. Currently, the movements of water molecules can be illustrated in e-books by using applets that can represent concepts dynamically.

On the other hand, Feynman states that “the jiggling motion is what we represent as heat: when we increase the temperature, we increase the motion (Feynman et al., 1963, section 1–2 Matter is made of atoms).” This statement of heat as jiggling motion can be confusing to students. If heat (Q) is defined as the kinetic energy of molecules in a body, it causes confusion because it has a similar meaning as the term “internal energy” (U) in the equation, ΔU = Q + W. Thus, it is not a surprise that students have confusion with the term heat and internal energy (e.g. Kautz, Heron, Loverude, & McDermott, 2005). Although Feynman also uses the term heat as a verb, this is different from physicists and physics educators who define heat as a process of energy transfer. The definition of heat as a process clearly means that it is not a form of substance or fluid.

2. Properties of steam (gas):

“… to an excellent approximation, if the density is low enough that there are not many atoms, the pressure is proportional to the density (Feynman et al., 1963, section 1.2 Matter is made of atoms).”

Students may not understand why Feynman uses the word approximation to explain that the pressure of a gas is proportional to the density of the gas. This relationship is exact if we apply the ideal gas equation, PV/T = NkT. To be more accurate, we use the van der Waals equation of state, [p + a(N²/V²)](V – Nb) = NkT. Feynman has this equation in mind when he says that “if we consider the true nature of the forces between the atoms, we would expect a slight decrease in pressure because of the attraction between the atoms… (Feynman et al., 1963, section 1.2 Matter is made of atoms).” The term a(N²/V²) is needed to correct the effect due to the attractive intermolecular forces which become stronger as the molecules get closer. Next, the volume for a random molecular motion to take place is lesser by Nb because gas molecules are not point particles and have finite volume. (The constants a and b can be determined experimentally depending on the gas selected.)

Curiously, Feynman explains that Figure 1–2 (Steam) fails in one respect because there would not be as many as three water molecules at ordinary atmospheric pressure. However, this is not definitely incorrect, but it is a matter of probability. In general, most figures having the same size are likely not to have even one molecule. Perhaps it should be emphasized that the figure does not give the idea of random motion of particles. On the other hand, he simply mentions that there is a 105^o 3′ angle between the hydrogen atoms. Alternatively, we can explain that a water molecule has a tetrahedron shape in which two of the “attachments” are electron clouds containing two electrons each, and the other two “attachments” are a hydrogen atom each sharing two electrons with the oxygen atom. Moreover, the hydrogen atoms are 104.5^o from each other because of the greater repulsion between the two electron clouds that force the hydrogen atoms slightly closer together.

3. Properties of ice (solid):

“… minimum amount of motion that atoms can have is not enough to melt a substance, with one exception: helium (Feynman et al., 1963, section 1.2 Matter is made of atoms).”

Feynman mentions that Figure 1–4 (Ice) is wrong because it is drawn in two dimensions. In addition, he states that the material has a definite place for every atom. However, the figure does not show that the atoms are vibrating “in place” or oscillating in fixed locations. That is, the picture is a static representation of water molecules. Interestingly, as we decrease the temperature, the vibration decreases until it reaches near absolute zero; there is a minimum amount of vibration that the atoms can have, but not zero based on quantum physics. Thus, we explain that ice has thermal energy because the atoms have kinetic energy. (As mentioned earlier, physicists and physics educators may not agree with the phrase “ice has heat” that was used by Feynman.)

According to Feynman, helium is an exception among atoms because it does not freeze at absolute zero unless we increase the pressure high enough to make it solidify. Physicists may question Feynman how it is possible to achieve absolute zero according to Nernst’s theorem. The temperature “absolute zero” is a theoretical concept and it is practically impossible to cool an object to absolute zero within a finite number of steps in an experiment. Thus, it is more appropriate to use the phrase “near absolute zero” instead of “at absolute zero.” 

More important, there are reports that helium may behave like a supersolid, another state of matter that has the crystalline structure of a solid, and it flows like a liquid. Nevertheless, definitions of solid, liquid, and gas are usually simplistic. Strictly speaking, it is possible to have intermediate states between solids and liquids: e.g. liquid crystals. It is worth mentioning that glass is sometimes known as an amorphous solid or a supercooled liquid. There is also research on two different states of liquid water.

Questions for discussion:

1. Explain properties of water in terms of atoms and discuss limitations of figure 1–1 in representing a liquid.

2. Explain properties of steam in terms of atoms and discuss limitations of figure 1–2 in representing a gas.

3. Explain properties of ice in terms of atoms and discuss limitations of figure 1–4 in representing a solid.

The moral of the lesson: Do not be confused by misleading figures in textbooks that represent solid, liquid, and gas.

References:

1. Feynman, R. P. (1999). The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. Cambridge, MA: Perseus.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

3. Kautz, C. H., Heron, P. R. L., Loverude, M. E. & McDermott, L. C. (2005). Student understanding of the ideal gas law, Part I: A macroscopic perspective. American Journal of Physics, 73(11), 1055-63.