Atoms

Copyright © Karl Dahlke, 2022

At a high level, the Greeks believed matter was made of earth, wind, water, and fire - but they knew earth was a broad category. There were all sorts of rocks and metals, and the dirt that grows crops, and sand, and glass, and volcanic ash, and clay, etc. How do all these different materials come about? Are they made of more basic materials in different arrangements?

The Greeks wondered what would happen if you cut a stone in half, and in half again, and again, and again; if you had an infinitely sharp knife could you do this forever? Is it solid stone all the way down, or do you eventually reach blocks of matter that cannot be further subdivided? Based solely on intuition, they believed matter was made up of small indivisible building blocks, as one might build a house out of lego today. You wouldn't dream of breaking a piece of lego in half. There are about 100 different kinds of common lego blocks, that can be combined to build various structures. As it turns out, there are about 100 kinds of atoms, that make everything around you, everything you can see, everything you can touch, and you as well, so your lego experience may prove helpful.

The Greek word tomos means slice, or cut in half, and the Greek prefix a means not. We see that prefix in a few English words, such as apolitical, atypical, amoral, and asexual. Thus the word atom means something that cannot be divided. It was just a name for an idea, based solely on intuition, and that intuition turned out to be correct.

Democritus, circa 370 B.C., believe that atoms were infinite in their shapes and sizes (false), uncreated (true, with some caveats about the big bang and supernovae), eternal (true, unless you take a very long view) - and the properties of an object depend on its constituent atoms (true), and atoms can separate and recombine to make different materials (true). This was a remarkable paradigm shift, so radical that even Aristotle rejected it. Democritus explained, “Iron atoms are solid and strong with hooks that lock them into a solid; water atoms are smooth and slippery; salt atoms, because of their taste, are sharp and pointed; and air atoms are light and whirling.” This isn't entirely true, but it isn't completely wrong either. Perhaps he thought about atoms losing their bonds and slipping past each other as metal was heated to the melting point. Perhaps he thought about salt dissolving in water, then crystalizing back into solid form when the water evaporated. Whatever his reasoning, Democritus was centuries ahead of his time.

How do we know his theory is right? How do we know the world is made of atoms, whence you can't cut a stone in half forever? Proof would not come for another 2,000 years, and I'll get to that below.

Lego Man

Suppose you built a living creature out of lego, and that creature possessed intelligence and curiosity. He might speculate about atoms, as Democritus did, or in his case, lego blocks, but he wouldn't be able to see them, or any evidence of them, because they are too small. Intelligence is a complex property requiring trillions of interconnections, thus a thinking lego brain might be as big as a football stadium, and the lego man might stand a mile high. His eyes are the size of houses, and he cannot see the lego blocks that form the foundation of his world.

This is merely a thought experiment, but it suggests that any intelligent life, on any planet, will not be able to perceive the atoms around him, because he is too large, relative to those atoms. He must develop tools, and strategies, and technology, to demonstrate the existence of atoms, and eventually to see them, as we do today with the scanning tunneling microscope.

Size and Shape

So how big is an atom, or are they, as Democritus thought, all different sizes? There are about 100 different kinds of atoms, and they are all roughly the same size. In fact, chemistry would be impossible if they were different sizes. If some lego blocks were 100 times larger than others, you couldn't fit them together in any meaningful way. It seems like a lucky coincidence, then, that atoms are approximately the same size, else life would not exist, and you wouldn't be here to read this book. We'll see this over and over again - the speed of light has to be what it is, the charge on the electron has to be what it is, various constants have to be what they are, or there is no life in our universe. One could speculate on why this is so, and there's nothing wrong with that, but that is a matter of philosophy, not science, and it is thus beyond the scope of this book. I'll just say that atoms are all the same size, and I'm glad they are.

So how big are they? Your finger is about 1 centimeter across. Divide that distance by a million, and then divide that distance by 100, and that is the width of an atom. We can hardly imagine something so small. No wonder it took centuries to prove their existence.

To first approximation, the shape of an atom is a sphere. This is very different from lego blocks, and yet it is consistent with Democritus' view. He thought atoms were little balls, with hooks, or some type of connectors, that let them fasten together to make larger structures. This is not too far from the truth. Those connectors are electrons, and they join atoms together into discrete molecules or bulk solids. I'm going to start with discrete molecules, and deal with bulk solids later, because I believe molecules are more intuitive. For instance, 6 carbons and 12 hydrogens and 6 oxygens combine to make one sugar molecule, and it tastes sweet. It also stores energy for living things, which is the reason plants make sugars in the first place.

Elements

As mentioned earlier, there are about 100 types of atoms, each with its own properties. The substances made from these atoms are called elements. They are elementary, thus the name. However, atoms are rarely segregated by type in nature; they are usually blended together in a glorious mix, requiring dedicated chemistry to tease them apart. An exception to this rule is gold. This metal seems unwilling to blend with other metals, or even the corrosive oxygen in the air, thus one can find pure nuggets of gold in the ground. If you hold a lump of gold in your hand, every atom in that nugget is the same; every atom is a gold atom. In fact, gold was one of the first metals smelted into objects, both functional and ornamental, because it is already separated from the other metals, it is valuable, it is pretty, and it has a relatively low melting point, about the same as copper, and much lower than iron.

At the other extreme we find sodium, with atoms so energetic, so eager to connect with other atoms, that sodium is never found alone in nature. If you had a block of pure sodium sitting on the table, a soft silvery metal that you could cut with a butter knife, it would combine with the oxygen in the air to make sodium oxide. Humidity speeds this process along, so that the sodium practically bursts into flames in front of your eyes. Energetic elements like these were not isolated until the 1700's.

Symbols and Formulas

A molecule of sugar has 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms, but it would be nice if we could express this more concisely. In fact, we can. Each element is assigned a symbol, and most of these assignments are intuitive. C stands for carbon, H stands for hydrogen, and O stands for oxygen. With this in place, one can write the following formula.

glucose = C₆H₁₂O₆.

And you already know the most famous formula in chemistry, combining 2 hydrogen atoms with one oxygen atom to get water.

water = H₂O

This looks like a great system, but there are 100 elements, and only 26 letters. Therefore, most of the elements have two-letter symbols - the first letter is capital and the second is small. Some of these symbols are intuitive as well. Calcium, which makes your bones strong, has the symbol Ca, while helium, in the floating balloons, is He. This formula tells us limestone has 1 calcium atom to 1 carbon atom to 3 oxygen atoms.

limestone = CaCO₃

Some symbols are not as intuitive, such as Pb for lead. Why isn't it Le or Ld? Many symbols are derived from the Latin name of the substance, since Latin was the language of science in the early renaissance. The Latin word for lead is plumbum, and it has several cognates in English. Throughout the Roman empire, pipes were made of lead, since it is easy to cast and mold; thus a professional who built and maintained these pipes was a plumber, i.e. one who works with plumbum. Another English word is plumb-bob, a lead weight that hangs down from a string and establishes vertical. A carpenter might say, “This horizontal beam is level, and this vertical beam is plumb.”

Another symbol that seems odd is Au for gold, but aurum is Latin for gold, and once again there are several English cognates, including auric, aureate, and auriferous. If you're not familiar with Latin, or Latin words injected into the English language, then you'll just have to memorize some of these symbols. Here is a list of the common elements and their symbols. They are presented in order, by atomic number; that will become clearer in a later chapter. There are a dozen elements beyond this list, but they are usually created in the lab, and only exist for fractions of a second.

Bonds

Each atom has a certain number of "bonds" that connect it to other atoms. These are the hooks that Democritus was envisioning. Hydrogen has just one bond, thus a hydrogen atom connects, via its single bond, to the bond of another hydrogen atom, making a complete molecule of hydrogen, denoted H₂. A room full of hydrogen atoms, if such could ever exist, would quickly collapse into a room full of hydrogen molecules, giving off some heat in the process.

Oxygen has two bonds, and when each of these bonds connects to a hydrogen atom, the result is H₂O, or water. In the air, two oxygen atoms join together by connecting both bonds. This is called a double bond. If you look at an oxygen tank, it often says O₂ on the side.

It is not common, but triple bonds also exist. Nitrogen has 3 bonds, and one atom of nitrogen can join another atom of nitrogen through all three bonds, forming N₂. The air you are breathing now is 80% N₂ and 20% O₂.

Exercise

Get a group of friends or students together, the more the merrier, and stand in an open area with one hand extended and the other hand at your side. Each person is a hydrogen atom, and the extended hand is the bond. Wander around the room aimlessly, while spinning around. By randomness, one student will "collide" with another, hand to hand, and the connection is made. The two students become one molecule. They continue to wander about the floor, spinning around, but they won't connect with any other hydrogen atoms, nor will they separate. After a while all the hydrogen has become H₂.

Perform the same exercise with two hands extended. Each student is an oxygen atom. when two students bump into each other face to face, they can join hands, right to left and right to left, and become an oxygen molecule. The bonds are satisfied, and they do not interact with any more atoms. What happens when two students connect right hand to right hand, as though they are shaking hands? At this point our experiment isn't very realistic. Atoms are balls floating in free space, and one of the balls would quickly pivot around its bond so that the remaining open bonds could connect. In our game, one of the students would have to flip upside down and stand on his head, so left hand could connect to left hand, completing the O₂ molecule.

Let three students form a triangle, each facing the other two. Again, each student is an oxygen atom. Extend both hands, representing the two bonds. Connect these bonds, right to left, right to left, right to left, forming a triangle. This is an ozone molecule, with formula O₃. these molecules are created high in the earth's atmosphere by the sun's ultraviolet light. You may have heard of the ozone layer; it's very thin, but very important.

Let one student be oxygen, with two hands out, and let two more students be hydrogen, with one hand out. Connect the two hydrogen atoms to the oxygen atom to make one water molecule.

Finally ask two students to stand side by side and hold hands, as though they were walking together. Their other hands are also extended; they represent oxygen atoms. Two more students play the role of hydrogen atoms, one joining oxygen at the left and one joining oxygen at the right. This is hydrogen peroxide, sometimes written HOOH, but usually written H₂O₂. This is an unstable molecule; an oxygen atom breaks away easily, leaving water.

Inert Gases

There are 6 elements with no bonds at all. These are helium, neon, argon, krypton, xenon, and radon. They don't connect with each other, or with any other atoms; they stand alone. Continuing the above, let a group of students mill about the room with their hands at their sides. They bump into each other, and the walls, but never connect. It is not surprising that all 6 of these elements are gases, since they fly freely about.

These are called nobel gases, since they do not form compounds with other elements, just as the nobility did not marry commoners. The term is rather misleading however, since nobility did marry other nobility, and yet, helium does not join neon to make a molecule. Well think of a king all alone on his throne, and that might remind you of an isolated atom with no bonds.

These 6 elements are also called inert gases, since they are chemically inert, and do not join with other atoms, or even themselves. This is perhaps a more accurate term for these atoms.

It is possible to force a noble gas to join other atoms to make a molecule, but it isn't easy. An example is Xenon difluoride. fluorine is one of the most reactive atoms - it really doesn't like an unsatisfied bond. Let one student stand still with his hands at his side, he is the xenon atom. Two students approach from either side, each with one hand extended; they are the fluorine atoms. Each student forcibly grabs the hand of the xenon atom and pulls it away from the body, thus creating a bond that was not there before. The result is Xenon difluoride, XeF₂. As strong as fluorine is, this reaction does not take place on its own. A room full of xenon and fluorine would just sit there. However, the molecules can be created using heat or electricity. I mention this example as the exception that proves the rule. We can generally assume that the bonds are what they are, and in any molecule, all the bonds are satisfied, and no new bonds are forcibly created.

Evidence for Atoms

How do we know atoms join together to make compounds? How do we know atoms exist at all?

In the 1700's, chemists learned how to prepare various gases in pure form, so that each could be studied in turn. Whenever two gases combine in a chemical reaction, they are consumed in small, whole number ratios. An example is hydrogen (a gas), and oxygen (a gas), which combine to make water. Exactly 2 gallons of hydrogen combine with 1 gallon of oxygen. (You can use liters, or barrels, or any unit of volume you like.) If you start with 2.01 gallons of hydrogen, that little bit of hydrogen is left over after the reaction is complete. If you start with 1.01 gallons of oxygen, oxygen is left over. so why is the ratio exactly 2 to 1? The atomic theory of matter explains it perfectly. A gallon jug contains a certain number of gas molecules flying about inside it, no matter what the gas is. (This is not true for liquids or solids.) Say it is a trillion molecules, just for a round number. A trillion gas molecules fly about, and bump into each other, and bump into the walls of the container. Now run the chemical reaction. 2 trillion molecules of hydrogen combine with 1 trillion molecules of oxygen, and there is nothing left over. In other words, 2 parts hydrogen and 1 part oxygen make water. If you could see at a microscopic level, 2 hydrogen atoms connect to an oxygen atom, and this happens a trillion times over, leaving nothing behind.

Let's run this reaction with 6 people. Two people join both hands together in a double bond, forming an oxygen molecule. Another pair joins together by one hand forming a hydrogen molecule. The last pair forms another hydrogen molecule. All three pairs of people bump into each other and the bonds separate. Keep your hands extended, 2 for oxygen and 1 for hydrogen. The bonds are now unsatisfied, and that's not good. Reconnect in triples, with 2 hydrogens attached to each oxygen, making 2 water molecules. Do this exercise a few times, until you can picture the reaction at an intuitive level. The reaction is written like this.

O₂ + 2H₂ → 2H₂O

Every time gases combine to make a new compound, whole number ratios are observed. The ratio might be 1 to 1, hydrogen + chlorine, or 2 to 1, hydrogen + oxygen, or 3 to 1, hydrogen + nitrogen, but the ratio is always a small whole number. If matter was just stuff all the way down, rather than discrete units, then any ratio would be possible, such as 1.37 to 1, or 2.54 to 1. these whole number ratios, seen over and over again, provide the first hard evidence that atoms do exist, and they combine in different ways to make different substances. Democritus was right!

In some cases the reaction can be reversed. Water can be separated into hydrogen and oxygen by electricity, and if you collect the resulting gases, you get exactly twice as much hydrogen as oxygen. The ratio isn't 2.03 to 1, it is exactly 2 to 1. It is possible to do this at home using water, baking soda, and an AA battery. Warning - don't use table salt, as that produces chlorine gas, which is dangerous. Cut 2 insulated wires about a foot in length and strip the ends. Attach the end of one wire to the positive node of the battery, and the end of the other wire to the negative node of the battery. Place the other ends of the wires in a bowl of water, a couple inches apart. If you use a metal pan, don't let the wires touch the pan, or you have a short circuit. Place a piece of plastic, or any insulator, between the wires and the pan. Add baking soda to the water until it tastes salty. Place inverted glasses, or jars, over the ends of the wires to capture the bubbling hydrogen and oxygen. At the outset, the jars must be full of water, with no air. Glasses should be clear so you can see the gases displace the water, and measure the gas volumes. You can tape the ends of the wires to pennies for more surface area and faster electrolysis. See this article for more details. As gas accumulates in the jars, the ratio is exactly 2 to 1, twice as much hydrogen as oxygen. Or you can purchase an electrolysis unit from a chemical supply house, which measures the volume of hydrogen and oxygen more precisely. Either way, you have confirmed the atomic theory at home. You don't have to take my word for it - as Lil Jon says, “You can do it all by yourself.”

You can breathe in the oxygen if you like, it's just oxygen. You can even breathe in the hydrogen, but there's something more interesting you can do with that - light it on fire to reproduce water. Place a lid on the jar, or your hand, before you take the jar out of the water, so that the jar contains only water and hydrogen, with no air. Air and hydrogen would form an explosive mixture, and we don't want that. Place the jar upright on the table with its mouth covered. Ask your friend to light a tall candle and stand at the ready. In one swift motion, pull your hand, or the lid, off the jar, and stand back while your friend puts the candle flame over the mouth of the jar. The hydrogen will burn at the H₂ air interface with a soft, almost invisible flame. It is best viewed in a dark room. The flame could melt the rim of the jar if it is plastic, or crack it if it is glass, so make sure it isn't a family heirloom. Empty 2 liter pop bottles are great containers for this experiment. They can collect a lot of hydrogen and oxygen, and the narrow mouth ensures the flame will burn for a long time. If the rim melts, you can recycle it, which is what you were gonna do anyways.

Note the transformation of energy. The AA Battery contains chemical energy, which turns into electrical energy when the circuit is running. This splits water into hydrogen and oxygen, which store chemical energy. Finally the hydrogen burns in the air, turning the chemical energy into heat and light. At the end of the day, all the energy of the AA battery has been turned into heat, raising the temperature of your room 0.01 °. We'll talk about forms of energy in a later chapter.