1. The Atomic Nature of Matter

It is one of the most amazing facts of nature that essentially everything in the world around us is made from fewer than 100 naturally occurring different kinds of atoms. An atom has a central nucleus composed of protons and neutrons surrounded by electrons. In atoms that are electrically neutral, the number of electrons equals the number of protons. An element is some material that consists of atoms, all of which contain the same number of protons. Thus, atoms with one proton are said to constitute the element hydrogen, atoms with two protons constitute the element helium, and so on. While atoms of a given element all have the same number of protons in their nuclei, they may have different numbers of neutrons. Two atoms with the same number of protons but different number of neutrons are said to be different isotopes of the same element. Different isotopes behave almost identically as far as chemical reactions are concerned, because chemical reactions involve atomic electrons only, not the atomic nuclei.

Protons and neutrons both weigh about 2000 times more than electrons. So most of the "stuff" of an atom resides in its nucleus. Nonetheless, atoms are mostly empty space. The most common isotope of hydrogen consists of one proton and one electron. Suppose we represent the proton in a hydrogen atom by the following dot: •. About how far away from this dot would the electron be on average if this dot were the actual size of the proton? Where the period next to the dot is? Maybe a centimeter? 10 centimeters? A meter? No. Actually, the electron would spend most of its time roughly 100 meters away! The average diameter of the electron orbit in hydrogen is about 100,000 times the diameter of the proton. In atoms with more protons, the electrons spend more time nearer the nuclei, but no matter how many protons and electrons they contain, atoms are mostly empty. Despite that, it is very hard to squeeze the electrons of an atom closer to their nucleus. It is also difficult to make the electrons of two atoms interpenetrate. If that weren’t true, it would be impossible for objects to have more-or-less permanent shapes and sizes.

The number of atoms in a macroscopic object may well exceed 10²⁰. The interactions of these vast swarms of atoms lead to qualitatively different states of matter. In all materials at all temperatures, the constituent atoms are in ceaseless, disorganized motion. In solids, the microscopic agitation of atoms is sufficiently confined that the atoms typically do not exchange places. As a consequence, solids have an essentially permanent shape. In fluids­that is, gases and liquids­however, atoms can pass by each other. This swapping of atomic positions produces the macroscopic phenomenon of flow and the microscopic phenomenon of diffusion or atomic mixing. Fluids flow around inside solid containers and adopt shapes defined by the containers. Fluids don’t have a permanent shape. While solids are characterized by the regular and enduring arrangement of their atoms, fluids are characterized by atomic chaos.

Biological materials typically share features of both the solid and fluid states. (This delicate balancing act is encapsulated in the colorful phrase, "life exists on the edge of chaos") For example, biological membranes that surround cells or sub-cellular components are basically two-dimensional highly ordered structures that also have a large degree of mobility within them. Their constituent phospholipid molecules tend to be aligned parallel to each other, but can move about within the plane of the membrane quite rapidly by diffusion. Such highly ordered, but yet fluid structures are termed liquid crystals. A second significant example is the gel-like nature of cellular cytoplasm. Gels have some of the properties of solids, including a rigidity, but can be greatly deformed as well. Cytoplasm is a complex material consisting of thousands of different macromolecules, including proteins, nucleic acids, phospholipids, polysaccharides, as well as smaller organic molecules and salts. Under the control of several filamentous proteins that supply an internal structural rigidity, the cytoplasm can be changed back-and-forth between conditions that are more fluid-like and more solid-like.

2. Mass, Density, and the Size of Atoms

Mass is a fundamental property of matter. For now, it is sufficient to think of mass as a measure of the substance of a body. Mass can be measured by an ordinary bathroom or grocery market scale, if the body whose mass is being measured is of moderate size, and by more sophisticated scales if the body is either too large or too small. The SI unit of mass is the kilogram (kg). A kg is roughly the mass of a rock the size of a grapefruit. A kg weighs about 2.2 pounds. It is possible to determine the masses of individual atoms with a delicate scale called a "mass spectrometer." Compared with a rock an atom doesn’t have very much mass. A rule for assessing the approximate mass of an atom is to look up the number of "atomic mass units per atom" (designated u/atom) for the atom of interest on a periodic table, then multiply by 1.66x10^-27 kg/u. The number of atomic mass units per atom is essentially the average number of protons plus neutrons in all isotopes of the element in question found on Earth.

We wish to demonstrate how knowledge of macroscopic properties sometimes can be converted into knowledge about atoms. Let’s start with the question, how many atoms are contained in a 1 kg mass of known composition? Suppose, for example, we are told that the mass is solid gold. A periodic table tells us that gold has about 197 u/atom. So the mass in kg of a gold atom is 197 u/atom x 1.66x10^-27 kg/u = 3.27x10^-25 kg/atom. The 1 kg is some number of atoms times the mass per atom, so if we divide the latter value into 1 kg we find that 1 kg of gold contains 1 kg/3.27x10^-25 kg/atom = 3x10²⁴ atoms. That’s a typical number for solids: 1 kg of a solid contains from about 10²⁴ to about 10²⁶ atoms.

A macroscopic measurement of density of a solid body allows us to answer the question, how far apart are atoms in the body? Average density, r, is defined as mass/volume. If we divide the density of a solid body by the mass per atom we get atoms per unit volume. If we take the reciprocal of that, we get volume per atom. Now, if we pretend that each atom is a little cube of side d₀, the volume per atom is d₀³. Thus, d₀ is the cube root of the volume per atom; it is also the average distance between adjacent atoms. For iron we have 7900 kg/m³/(55.8 u/atom x 1.66x10^-27 kg/u) = 8.53x10²⁸ atoms/m³. The volume per atom in solid iron is then (8.53x10²⁸ atoms/m³)^-1 = 1.16x10^-29 m³/atom, and the cube root of that, 2.26x10^-10 m, is the average atomic spacing. The distance 10^-10 m recurs frequently when considering atoms. You will sometimes find 1x10^-10 m referred to as 1 ångstom = 1 Å, though in keeping with the SI conventions it is more fashionable these days to use the nanometer: 1x10^-9 m = 1 nm. Thus, 2.26x10^-10 m is either 2.26 Å or 0.226 nm.

The average distance between atoms in any elemental solid is roughly the same as for iron. Now here is a very familiar result: it is exceedingly difficult to increase the density of a solid by squeezing it. In other words, in a solid, the atoms are crammed together about as closely as possible. This fact and the fact that the average spacing of atoms is about 0.2 to 0.3 nm for all elemental solids tells us the very interesting and surprising result that all atoms are about the same size­despite the fact that their atomic masses vary by a factor of over 200!

You might be tempted to conclude that because liquids flow and have no permanent shape that the spacing of atoms in liquids would be a lot larger than in a solid. Let’s see. How about in water? Water is a molecular liquid. The u/molecule for water is about 18 (2 for the two hydrogen atoms and 16 for the oxygen atom). Since there are three atoms per molecule, the average mass per atom is 6 u. The density of water is about 1000 kg/m³. Consequently, the average molecular spacing in water is about 0.22 nm­more-or-less the same value as in solids. The remarkably different physical properties of solids and liquids arise from only very small differences in how their atoms are spaced.

What can we say about atomic spacing in gases? The most familiar gas is air, a mixture of primarily nitrogen and oxygen molecules. Let’s say that the average u/molecule for air is about 29. Because nitrogen and oxygen molecules contain two atoms, the average u/atom for air is about 14.5. The density of air at room temperature and at sea level atmospheric pressure is 1.29 kg/m³­a value that is something like 1000 times less than water. The average atomic spacing in air is about 2.7 nm, that is, about 10 times greater than in a solid or liquid. If we squeeze a quantity of air down to 1/1000th of its normal volume, it becomes a liquid; the densities of liquid oxygen and liquid nitrogen are almost exactly 1000 times that of air.

Because biological materials have properties midway between the solid and liquid states the spacing of atoms in them is about 0.2 to 0.3 nm. We can use this idea to assess how many atoms one might find in a typical biological cell. Cells have somewhat different sizes, but a typical cell is roughly about 20x10^-6 m = 20 micrometers = 20 mm on a side. That is, a cell has a volume roughly about 8x10^-15 m³ (obtained by cubing 20 mm). If a typical atom spacing is 0.25 nm, the volume occupied by an atom is about (0.25 nm)³ = 1.5x10^-29 m³/atom. Consequently, the number of atoms per cell is about (8x10^-15 m³/cell)/(1.5x10^-29 m³/atom) = 5x10¹⁴ atoms/cell.

A cell has lots of stuff in it. All cells contain DNA, for example. Drawings of pieces of DNA in textbooks show it as a long, double helix structure. But, just how long is it? DNA consists of multiple subunits called base pairs ("C-G" and "A-T"). The number of atoms per pair is 27. Typical animal cells have about 5x10⁹ pairs in their DNA. That corresponds to about 1.4x10¹¹ atoms. Suppose that all of the atoms in the DNA molecule were strung end-to-end in a linear chain. The chain would be about (1.4x10¹¹ atoms)x(2.5x10^-10 m/atom) = 35 m long! Of course, clumping atoms into base pairs of about 30 atoms each saves space. Even so, if the pairs were strung out in a linear chain, the DNA would still be about 1 m long. Obviously, DNA in a cell can’t be a linear chain because it would burst through the cell membrane. It must be stored in a tight coil when "not in use" and only small portions must be pulled apart when transcription or replication occur. Similar conclusions can be made about other important ingredients of a cell, such as large proteins, for example.

3. Weight and Gravity

When we place some tomatoes on a grocery scale, the tomatoes cause a spring to stretch and a needle to deflect. The deflection of the needle is taken to be a measure of the "weight" of the tomatoes. This happens primarily because the Earth somehow pulls the tomatoes down toward it and the scale somehow gets in the way and keeps the tomatoes from falling. The word more commonly used by physicists for a pull (or a push) is force. The force the Earth exerts on the tomatoes is called gravity. There’s a wondrous thing about gravity: gravitational pulls exist even though the bodies involved don’t touch. The Earth reaches out across empty space and pulls on the tomatoes. (Of course, the space between the Earth and the tomatoes isn’t really empty: it’s filled with air. But, we can get rid of the air­in a vacuum chamber, for example­and when we do we find that the pull of gravity is almost exactly the same.) Forces that exist across empty space are said to be field forces. In the field force picture, the Earth is viewed as creating a "gravitational force field" in the space around it. When the tomatoes are placed in the Earth’s field they respond by falling toward the Earth. The scale, on the other hand, is doing something more directly to the tomatoes. It appears to stretch only when it is in direct contact with the tomatoes. The force the scale exerts on the tomatoes is an example of what is called a macroscopic contact force. When the tomatoes hang from the scale without moving, the force down on them by the Earth is said to equal the force up on them by the scale.

The Earth isn’t the only object that creates gravity. Every mass creates a gravitational pull on every other mass. You actually pull the tomatoes you weigh in the grocery toward you a little (and they pull you, too). It’s just that the Earth’s pull is so much greater than yours, you don’t realize you’re doing it. Mass plays two roles in producing a gravitational force. First, one mass creates a gravitational field in the space around it. Then, a second mass placed in the field of the first experiences a force due to the first’s field. The two masses reciprocate in their pulls. The second makes a field of its own and the first, being in the field of the second, feels a force due to it. We say that a gravitational field has a direction­it points toward the mass making it­and a size, or magnitude. Let’s call the magnitude of the gravitational field made by a mass M, g_M. The magnitude of the force this field produces when a mass m is placed in it is defined to be . Like mass and length, force has its own SI unit, the newton (N). Gravitational field is gravitational force divided by mass, so the units of gravitational field are newtons per kilogram, N/kg.

We say that a body’s weight (near the Earth) is the gravitational force the Earth exerts on that body. Thus, a mass m weighs

(1)

Why is the condition "near the Earth’s surface" important? Well, it turns out that the strength of a mass’s gravitational field gets weaker the farther away one is from the mass. Very careful measurements in the laboratory show that if the centers of two uniform (that is, no holes or irregularities), spherical masses, M and m, are separated by a distance r then M pulls m with a gravitational force whose magnitude is given by

(2)

(3)

4. The Electric Force

Suppose we suspend a copper wire that is 1 m long and has a cross-sectional area of 10^-6 m² so it hangs vertically. Let’s estimate the gravitational force the wire exerts on an atom at the very end of the wire. We approximate the wire as a small sphere. The volume of the wire is 10^-6 m³ and its mass is (9000 kg/m³)(1x10^-6 m³) ~ 10^-2 kg. The gravitational field of the wire at its end, ~ 0.1 m from its center, is ~ (10^-10 N-m²/kg²)(10^-2 kg)/(0.1 m)² ~ 10^-10 N/kg. A copper atom at the end of the wire feels a gravitational field due to the wire of about 10^-10 N/kg up and gravitational field due to the Earth of about 10 N/kg down. Because the Earth’s field is about 10¹¹ times greater than the wire’s, the atom would fall to the Earth if gravity were the only force holding it in the wire. So would the next atom, and the next, and the next, and so on. In short order, all of the atoms in the wire would rain down to the Earth. A piece of copper wire cannot be held together by its own gravity­nor can a bacterium, nor you, nor the building you live in.

Just how strong is the force that holds ordinary objects together? To get a rough idea we can perform a pulling experiment. For example, let’s attach a weight to the end of the wire we just described. If we add 5 kg to the end of the wire, it will stretch by about 5x10^-4 m (that is, by about 0.5 mm). If we add 10 kg (that is, double the added force), the stretch is about 10^-3 m (double the stretch). A shorter wire of the same cross-sectional area doesn’t stretch as much. A 0.1 m long wire (one tenth as long as the original) that has 10 kg added only stretches by about 10^-4 m (one tenth as much as the original). A thicker 1 m long wire also doesn’t stretch as much as the original. A wire that has a cross-sectional area of 10^-5 m² (ten times the cross-sectional area of the original) and 10 kg added stretches by about 10^-4 m (one tenth as much as the original). These results can be summarized by saying that the amount a copper wire stretches when a force is applied to its ends is: (1) proportional to the applied force, (2) proportional to the original length, and (3) inversely proportional to the cross-sectional area. Interestingly, if we remove the added weight, the wire returns to its original length. Such a stretch with a return to the original form is called an elastic deformation. Of course, all of these observations are invalid if too much weight is added. If too much weight is added, the wire can permanently stretch (plastic deformation) or even break.

The rule for elastic deformation that we have written in words can be written in equation form:

(4)

Young’s modulus for many solids is about 10¹⁰ to 10¹¹ N/m². Polymers and composite materials typically have somewhat smaller values, perhaps 10⁹ to 10¹⁰ N/m². For many solids you get the same value of Y if you squeeze instead of stretch, though some­such as bone­are stiffer one way than the other.

When a macroscopic body undergoes an elastic deformation, the spacing between its atoms changes. We can get an estimate of the magnitudes of the forces holding atoms together in a solid or liquid from Equation (4). Let’s assume we push on the top face of a cube of some material that is resting on a horizontal surface. The force we apply is distributed over the N atoms on the surface of this body. The top plane of atoms pushes on the next plane down, and that in turn pushes on the next, and so forth. Provided the cube of material remains at rest the force applied to the first plane equals the force the first plane exerts on the second, and so on. That is, the force applied to the surface is transmitted from plane of atoms to plane of atoms throughout the whole cube. The area of the surface over which the force is applied equals N times the area per atom; that is,

(5)

If gravity were the force holding a solid together, an atom on the surface of a body would experience a force given by Equation (2). If that atom were pulled away from the body a very small distance, Dd (such as 0.01 nm, for example), the applied force would be proportional to Dd and the equivalent of the interatomic force constant in Equation (5) would be 8prGm/3, where r is the mass density of the material and m is mass of one atom. (This result requires a bit of mathematics to get, but the details are unimportant. It’s the size of the force constant we want to investigate.) If you plug into this formula the density and atomic mass of copper, for example, you find that the "gravitational interatomic force constant" is about 10^-30 N/m. In other words, the actual force holding an atom in a piece of copper is at least 10³⁰ times stronger than the gravitational force of the rest of the body on it.

To explain the origin of the observed Young’s moduli for actual solids requires another property of matter beyond mass and another force beyond gravity. The property of matter responsible for holding ordinary matter together is called electric charge. The electrons and the protons in an atom carry electric charge. The charge of the proton is different from that of the electron. We call the charge of the proton "positive" and that of the electron "negative." Please note that the words "positive" and "negative" don’t have an intrinsic meaning. We could just as well have called the two kinds of charge "black" and "white" or "up" and "down" or "head" and "tail." One should not interpret the word "negative" as meaning "the absence of ‘positive’." The magnitudes of the electron and proton charges are found by experiment to be equal. The SI unit of electrical charge is the coulomb, C. In these units, the proton’s charge is +1.6x10^-19 C, while the electron’s charge is -1.6x10^-19 C. The magnitude 1.6x10^-19 C is usually designated e (for unit of electrical charge). We use "positive" and "negative" in a formal way: if you add as signed numbers all the positive and all the negative charge in a body you get the body’s net charge. When any body­an atom, a cell, or a beaker of water­contains equal numbers of electrons and protons it is said to be electrically neutral (it has zero net charge).

It is possible, by rubbing two bodies over each other, to exchange some electrons from one to the other. (It’s also possible, in principle, to exchange protons, but because protons are so much more massive than electrons, it’s usually the electrons that move.) Thus, if both bodies started out electrically neutral, after the exchange one would have more electrons than protons (it would have a net negative charge) and the other would have more protons than electrons (a net positive charge). That’s what happens when you scuff your feet on a carpet, or when water droplets bump into each other in a cloud. In each case, "re-neutralization" can lead to a quick exchange of electrons the other way and an often unpleasant and sometimes dangerous phenomenon called a "spark."

Because it is possible to move charge from one body to another, we can perform careful experiments on macroscopic bodies to deduce how the electric force between protons and electrons works. Here’s a quick summary of what is known about the electric force. The electric and gravitational forces share some common features. As already discussed in Section 3, the gravitational force of one mass on another gets weaker as the distance between the masses increases, decreasing as 1/r². Exactly the same is true for the electric force of one charge (proton or electron) on another. Both forces can be attributed to fields. Mass makes a gravitational field, charge makes an electric field. Because gravitational field is gravitational force divided by the mass feeling the force, we say that the gravitational field of a mass varies with distance from it like 1/r². Similarly, electric field is electric force divided by the charge feeling the force. The electric field also varies like 1/r². The precise expression for the magnitude of the electric force of a small charge Q on another small charge q is

(6)

(7)

At the same time, there are also differences. For example, we find that like charges repel each other­protons repel other protons, electrons repel other electrons. Opposite charges attract­electrons and protons attract each other. That’s different from the situation for gravity, in which all masses attract. There is (as far as we know) no gravitational repulsion. And, consistent with our discussion of Young’s modulus, we find that electric forces are much stronger than gravitational forces.

Example How much stronger is the electric force of a proton on an electron than is the gravitational force?

Solution: In Equation (2), let M be the proton mass and m be the electron mass. In Equation (6), let |Q| = |q| = e. If we then divide Equation (6) by Equation (2) we get

. (Plug in the values of k_E, e, G, M, and m to see that this is true.) This ratio is independent of the separation of the proton and the electron, because both the electric and gravitational forces depend on separation exactly the same way and the r²’s cancel in numerator and denominator. The electric force of one proton on one electron is about 10³⁹ times greater than the gravitational force of the proton on the electron at any distance of separation.

The ratio found in the Example is a big number, not radically different from the 10³¹ value we obtain when we divided the actual interatomic force constant in copper by the effective gravitational interatomic force constant. Of course, in the latter situation there are many protons interacting simultaneously with many electrons, but the similarity of the two numbers encourages us to wonder if the attraction of protons for electrons is what holds atoms, molecules, and all ordinary size macroscopic bodies together. (We don’t worry about planets, stars, and galaxies­they are massive enough to be held together by gravity).

5. Why do Atoms All Have About the Same Smallest Size?

Summary of results discussed previously: (1) The measurements of mass density and of atomic mass allow us to deduce that atoms are spaced about 10^-10 m apart in all solids and liquids. (2) Solids and liquids are extremely resistant to being squeezed into a small volume. From this we infer that atoms have a smallest size, about 10^-10 m in diameter. (3) Measurement of the elastic stretching of solids tells us that the force holding atoms together in a solid is many orders of magnitude greater than can be provided by gravity. Furthermore, unlike gravity, this force reaches out across a few atom neighbors only. (4) The latter force is consistent with the electric force exerted by protons and electrons on each other.

Point (2) requires additional consideration. The reason all atoms have a smallest size that is about the same for all atoms is due to quantum mechanics, the rules of behavior of small pieces of matter. In particular, quantum mechanics requires that (a) if you try to confine a body to some finite region of space (as the proton tries to do to the electron in hydrogen) the body automatically has to be moving, and (b) no two electrons occupying the same region of space can be in exactly the same state of motion. The latter requirement is called the Pauli Exclusion Principle.

The first requirement of quantum mechanics says that if a mass, m, is confined to a region of space of linear size, L, it has a smallest average speed given v_QM ~ C/(mL), where C is a constant whose value depends in detail on specifics of the physical situation but which is about 10^-34 kg-m²/s. Equivalently, to confine the mass to this region of space requires an average applied force the magnitude of which is about F_QM ~C²/(mL³). The coefficient C² has the approximate value of 10^-68 and has the equivalent units of N-kg-m³.

Consider the simplest atom, hydrogen, consisting of one proton and one electron. The attraction of the proton for the electron tries to pull the electron into the proton. That is, the proton’s electric attraction tries to confine the electron to a finite region of space. If we set F = ke²/L² ~ C²/(mL³), and solve for L we find L ~ C²/(mke²) ~ 10^-68 N-kg-m³/(10^-30 kg 10¹⁰ N-m²/C² 10^-38 C²) ~ 10^-10 m. This is the only (approximate) distance for which the electric force of a proton on an electron can balance the electron’s quantum mechanical tendency to "fly away." A hydrogen atom can’t be smaller because if it were the electron would have to be traveling faster. But the electrical pull of the proton on the electron isn’t strong enough to overcome the added speed and added tendency to fly away.

So the balance between electrical pull and quantum fly away explains why a hydrogen atom has a smallest size. But why do all atoms have about the same smallest size? To see, start with a nucleus containing Z protons. Add one electron to it. Since the nucleus now has a total charge of Ze the electric force of it on the electron is Zke²/L² and the extent of the region of localization is about L ~ C²/(Zmke²)­about Z times smaller than for hydrogen. In uranium, that first electron added is about 100 times closer to the nucleus than in hydrogen. Now add a second electron. The two electrons repel and try to stay as far away from each other as possible (while still being pulled close to the nucleus). Because of this, each feels attracted to the nucleus, but by fewer than the full Z protons­somewhere between Z and Z-1. When a third electron is added the (b) part of the quantum requirements begins to kick in. The third electron can’t be in the same state of motion as either of the first two, and the net effect is that it spends more time farther away from the nucleus than the first two. The net charge it feels pulling it toward the nucleus is reduced by the repulsion of the other electrons. Roughly, it feels the pull of about Z-2 protons. This story continues until the Zth electron is added. Because of the repulsion of the previous Z-1 electrons it feels only about one proton pulling it. Thus, the situation for the last added electron is pretty similar to that of hydrogen­effectively, one electron pulled by one proton. Consequently, the region of confinement for the last added electron is about the same size as for hydrogen. The big picture is that all atoms are a result of the balance between electric attraction (protons pulling electrons), electric repulsion (electrons pushing electrons), and the aspects of quantum mechanics (quantum fly away and electron exclusion).

6. The Nuclear Forces

Our discussion so far has ignored the atomic nucleus. From the point of view of chemistry, it’s only the atomic electrons that are important. Rearrangements of atomic electrons when atoms get close to each other lead to molecules. But, if the nucleus of an atom weren’t stable, its protons and neutrons would fly apart leaving nothing to hold the electrons in place. Because of their mutual repulsion, the electrons would then also fly apart and, as a result, there would be no stable atoms, no stable bulk matter, no possibility of life. Our world ultimately exists because atomic nuclei are stable.

Both proton and neutron are about 10^-15 m in diameter. Together in a nucleus they cling to each other in a region of space that is about 1,000 to 10,000 times smaller in extent than an atom is. Neutrons have no charge and cannot interact electrically, but protons are positively charged and repel. Because the average separation of protons in a nucleus is so small and because the electric force depends on 1/(distance of separation)², the repulsive force on each proton due to the others in the nucleus is extraordinarily large.

So what holds the atomic nucleus together? Gravity can’t do the trick, because gravity is too weak and a nucleus doesn’t have enough mass. There has to be yet another kind of force­one that is attractive and stronger than the protons’ mutual, electrical repulsion. For want of a better name, this force is called the strong nuclear force. Like gravitational and electric forces, the strong nuclear force is a field force. It is due to another intrinsic property of matter­a kind of "strong nuclear charge"­that is neither mass (which creates gravity) nor electrical charge (which creates electric field). Nucleons (that is, protons and neutrons) apparently carry this "strong nuclear charge," but electrons don’t. Surrounding each nucleon, due to its strong nuclear charge, is a strong nuclear field. When a second nucleon is placed in the strong nuclear field of the first it is attracted to the first. Experiments to test how the strong nuclear field extends in space indicate that it falls to zero much faster than either gravitational or electric fields. The "range" of the strong nuclear field is only about 10^-15 m, about the size of a nucleon.

How strong is this nuclear force? Apparently, it isn’t strong enough to overcome the electrical repulsion one proton feels when it is 10^-15 m from a second, because no nucleus consisting of just two protons has ever been seen. On the other hand, if a neutron is "sandwiched" between two protons then the strong nuclear interaction is sufficient to hold the three together. About one helium nucleus (a nucleus with two protons) in a million found in nature has one neutron (the rest have two). Obviously, neutrons­because they buffer the mutual repulsion of the protons­are essential for stabilizing nuclei. In fact, a perusal of the periodic table indicates that the vast majority of stable nuclei have a slight excess of neutrons over protons.

Parenthetically, we note that a curious thing happens when a nucleus has too many neutrons: a neutron can convert into a proton (thus reducing the number of neutrons and increasing the number of protons). In this process, an electron is ejected from the nucleus (along with a bizarre particle called a neutrino). The fact that neutrons can convert into protons suggests that neutrons (and, by extension, protons) are composite structures of even smaller bits of matter, now commonly referred to as quarks. In addition, the neutron conversion process is not explainable by the strong nuclear force. So, yet another force is required. This force is called the weak nuclear force and, yes, there’s a weak nuclear field and a weak nuclear charge responsible for making the field. Like the strong nuclear force, it has a very short range.

At this moment in the history of the human intellect we think that there are only four fundamental forces (the forces between the smallest pieces of matter): gravity, electric, and the strong and weak nuclear. In the current picture of the zoology of matter, the strong nuclear force binds quarks together to form protons and neutrons, and protons and neutrons together to form nuclei; the electric force binds nuclei and electrons together to form atoms, and atoms together to form molecules and extended bodies; and, finally, gravity binds large globs of matter together to form planets, stars, and galaxies.

A macroscopic body consists of a very large number of small pieces of matter in different states of confinement. The confinement of the nucleons inside the very small regions of space of the nuclei demands that they be traveling with average speeds of about 10⁺⁸ m/s (almost the speed of light). The confinement of electrons in atoms demands that they be traveling with average speeds of about 10⁺⁶ m/s (about 1% the speed of light). The confinement of atoms for each other to about 0.1 Å of free motion demands that they be traveling with average speeds of about 10⁺² m/s. Inside any macroscopic body there’s a whole lot of shakin’ goin’ on. But, very little of this motion is coherent. That is, when one little piece of matter goes one way another goes the other and the net result is the internal motions of all of the pieces of a macroscopic body tend to cancel out. There are huge amounts of motion in atomic nuclei and in atomic electrons. But the business of living matter is not conducted with either. Rather, almost all of the motion and processes of life stem from the relatively tame quivering of atoms.

Before closing this section a few remarks are in order concerning the difference between the fundamental forces and forces observed on a macroscopic scale. The fundamental forces between and among quarks and electrons are always field forces. On the other hand, macroscopic forces are sometimes field forces and sometimes contact forces. The interaction of two macroscopic bodies results from vast numbers of quarks and electrons in each interacting through the fundamental forces. A macroscopic force is the sum of a vast number of microscopic, fundamental interactions. The nuclear forces are so short-ranged that their sum is always zero across macroscopic distances. Gravity and the electric force extend over long distances. Gravity is always a pull and can result in two macroscopic bodies exerting a noticeable force on each other. All of the quarks and electrons in the Earth, for example, pull gravitationally on all of the quarks and electrons in the moon, thus holding the moon in its orbit about the Earth. Of course, because the fundamental gravitational force is so weak there has to be a lot of quarks and electrons for gravity to be significant even on the macroscopic level. The electric force also reaches out across empty space, but because there are electric pushes as well as pulls often the sum of electric interactions between all the quarks and electrons in two, electrically neutral macroscopic bodies is zero, especially if the bodies are separated by a macroscopic distance. When atoms in one body are close to (within nanometers of) atoms in the second, however, atomic interactions can produce a noticeable macroscopic interaction. These interactions only involve atoms at the very surface of each body. The surface atoms interact through their electric fields and through the Pauli Exclusion Principle. The atoms do not actually touch, but because we are not able to see the atomic separation we say that the bodies are "in contact" and that the sum of these surface atom interactions is a "contact force." The force a table exerts on a book to keep it from falling is a contact force, as is the force of friction that you feel when you rub your hands over each other. But, remember, "contact" is a human perceptual artifact, produced by our inability to see atoms; atoms are never in contact