* The spirit of this calculation is very old. The opening sentences of Archimedes’ The Sand Reckoner are: ‘There are some, King Gelon, who think that the number of the sand is infinite in multitude: and I mean by the sand not only that which exists about Syracuse and the rest of Sicily, but also that which is found in every region, whether inhabited or uninhabited. And again, there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude.’ Archimedes then went on not only to name the number but to calculate it. Later he asked how many grains of sand would fit, side by side, into the universe that he knew. His estimate; 1063, which corresponds, by a curious coincidence, to 1083 or so atoms.
In a burnt apple pie, the char is mostly carbon. Ninety cuts and you come to a carbon atom, with six protons and six neutrons in its nucleus and six electrons in the exterior cloud. If we were to pull a chunk out of the nucleus – say, one with two protons and two neutrons – it would be not the nucleus of a carbon atom, but the nucleus of a helium atom. Such a cutting or fission of atomic nuclei occurs in nuclear weapons and conventional nuclear power plants, although it is not carbon that is split. If you make the ninety-first cut of the apple pie, if you slice a carbon nucleus, you make not a smaller piece of carbon, but something else – an atom with completely different chemical properties. If you cut an atom, you transmute the elements.
But suppose we go farther. Atoms are made of protons, neutrons and electrons. Can we cut a proton? If we bombard protons at high energies with other elementary particles – other protons, say – we begin to glimpse more fundamental units hiding inside the proton. Physicists now propose that so-called elementary particles such as protons and neutrons are in fact made of still more elementary particles called quarks, which come in a variety of ‘colors’ and ‘flavors’, as their properties have been termed in a poignant attempt to make the subnuclear world a little more like home. Are quarks the ultimate constituents of matter, or are they too composed of still smaller and more elementary particles? Will we ever come to an end in our understanding of the nature of matter, or is there an infinite regression into more and more fundamental particles? This is one of the great unsolved problems in science.
The transmutation of the elements was pursued in medieval laboratories in a quest called alchemy. Many alchemists believed that all matter was a mixture of four elementary substances: water, air, earth and fire, an ancient Ionian speculation. By altering the relative proportions of earth and fire, say, you would be able, they thought, to change copper into gold. The field swarmed with charming frauds and con men, such as Cagliostro and the Count of Saint-Germain, who pretended not only to transmute the elements but also to hold the secret of immortality. Sometimes gold was hidden in a wand with a false bottom, to appear miraculously in a crucible at the end of some arduous experimental demonstration. With wealth and immortality the bait, the European nobility found itself transferring large sums to the practitioners of this dubious art. But there were more serious alchemists such as Paracelsus and even Isaac Newton. The money was not altogether wasted – new chemical elements, such as phosphorous, antimony and mercury, were discovered. In fact, the origin of modern chemistry can be traced directly to these experiments.
There are ninety-two chemically distinct kinds of naturally occurring atoms. They are called the chemical elements and until recently constituted everything on our planet, although they are mainly found combined into molecules. Water is a molecule made of hydrogen and oxygen atoms. Air is made mostly of the atoms nitrogen (N), oxygen (O), carbon (C), hydrogen (H) and argon (Ar), in the molecular forms N2, O2, CO2, H2O and Ar. The Earth itself is a very rich mixture of atoms, mostly silicon,* oxygen, aluminum, magnesium and iron. Fire is not made of chemical elements at all. It is a radiating plasma in which the high temperature has stripped some of the electrons from their nuclei. Not one of the four ancient Ionian and alchemical ‘elements’ is in the modern sense an element at all: one is a molecule, two are mixtures of molecules, and the last is a plasma.
* Silicon is an atom. Silicone is a molecule, one of billions of different varieties containing silicon. Silicon and silicone have different properties and applications.
Since the time of the alchemists, more and more elements have been discovered, the latest to be found tending to be the rarest. Many are familiar – those that primarily make up the Earth; or those fundamental to life. Some are solids, some gases, and two (bromine and mercury) are liquids at room temperature. Scientists conventionally arrange them in order of complexity. The simplest, hydrogen, is element 1; the most complex, uranium is element 92. Other elements are less familiar – hafnium, erbium, dysprosium and praseodymium, say, which we do not much bump into in everyday life. By and large, the more familiar an element is, the more abundant it is. The Earth contains a great deal of iron and rather little yttrium. There are, of course, exceptions to this rule, such as gold or uranium, elements prized because of arbitrary economic conventions or aesthetic judgments, or because they have remarkable practical applications.
The fact that atoms are composed of three kinds of elementary particles – protons, neutrons and electrons is a comparatively recent finding. The neutron was not discovered until 1932. Modern physics and chemistry have reduced the complexity of the sensible world to an astonishing simplicity: three units put together in various patterns make, essentially, everything.
The neutrons, as we have said and as their name suggests, carry no electrical charge. The protons have a positive charge and the electrons an equal negative charge. The attraction between the unlike charges of electrons and protons is what holds the atom together. Since each atom is electrically neutral, the number of protons in the nucleus must exactly equal the number of electrons in the electron cloud. The chemistry of an atom depends only on the number of electrons, which equals the number of protons, and which is called the atomic number. Chemistry is simply numbers, an idea Pythagoras would have liked. If you are an atom with one proton, you are hydrogen; two, helium; three, lithium; four, beryllium; five, boron; six, carbon; seven, nitrogen; eight, oxygen; and so on, up to 92 protons, in which case your name is uranium.
Like charges, charges of the same sign, strongly repel one another. We can think of it as a dedicated mutual aversion to their own kind, a little as if the world were densely populated by anchorites and misanthropes. Electrons repel electrons. Protons repel protons. So how can a nucleus stick together? Why does it not instantly fly apart? Because there is another force of nature: not gravity, not electricity, but the short-range nuclear force, which, like a set of hooks that engage only when protons and neutrons come very close together, thereby overcomes the electrical repulsion among the protons. The neutrons, which contribute nuclear forces of attraction and no electrical forces of repulsion, provide a kind of glue that helps to hold the nucleus together. Longing for solitude, the hermits have been chained to their grumpy fellows and set among others given to indiscriminate and voluble amiability.
Two protons and two neutrons are the nucleus of a helium atom, which turns out to be very stable. Three helium nuclei make a carbon nucleus; four, oxygen; five, neon; six, magnesium; seven, silicon; eight, sulfur; and so on. Every time we add one or more protons and enough neutrons to keep the nucleus together, we make a new chemical element. If we subtract one proton and three neutrons from mercury, we make gold, the dream of the ancient alchemists. Beyond uranium there are other elements that do not naturally occur on Earth. They are synthesized by human beings and in most cases promptly fall to pieces. One of them, Element 94, is called plutonium and is one of the most toxic substances known. Unfortunately, it falls to pieces rather slowly.
Where do the naturally occurring elements come from? We might contemplate a separate creation of each atomic species. But the universe, all of it, almost everywhere, is 99 percent hydrogen and helium,* the two simplest elements. Helium, in fact, was detected on the Sun before it was found on the Earth – hence its name (from Helios, one of the Greek sun gods). Might the other chemical elements have somehow evolved from hydrogen and helium? To balance the electrical repulsion, pieces of nuclear matter would have to be brought very close together so that the short-range nuclear forces are engaged. This can happen only at very high temperatures where the particles are moving so fast that the repulsive force does not have time to act – temperatures of tens of millions of degrees. In nature, such high temperatures and attendant high pressures are common only in the insides of the stars.