Captured Solar Energy: Its Final Destination
As we saw in chapter 11, nearly 2 billion billion (2 x 1018) kJ of solar energy are captured each year by photosynthesizing plants.
What becomes of all the captured energy? Some of it travels from plants to herbivores and on to carnivores, up a number of familiar food chains, and is partly dissipated by respiration at each level. But what happens to the rest—the energy still unused when the animals at any level of a food chain die?
The bulk of the captured energy, in any case, never gets beyond the lowest level of a food chain: enormous quantities of vegetation die without being eaten. Where, then, does all the energy in the dead vegetation go?
The answer to both questions is the same: the energy trapped in dead organisms, whatever their trophic level, is ultimately released by decay or by burning. One or the other— decay (more formally, decomposition) or burning (combus-tion)—terminates the temporary existence of the organic molecules that living matter consists of: the organic molecules are broken down to inorganic ones, preponderantly carbon dioxide and water, and the chemical energy stored in them is liberated. At the same time, oxygen is used up. In other words, the photosynthetic reaction described in chapter 12 happens in reverse, thus:
Here CH2O is shorthand for carbohydrates in general and represents the organic molecule being broken down.1 With inconsequential changes, the formula could be adapted to describe the breakdown of any organic molecule.
The important point is that the quantity of energy liberated when organic matter is destroyed is always exactly equal to the quantity of solar energy used to create it. This is true irrespective of whether combustion or decomposition brings about the disintegration. Combustion, as in a forest fire, usually happens fast, so that a large proportion of the energy released is free energy (see chapter 10). Decomposition is slow; much of the energy released is at a low temperature—it is entropy. We must next consider what causes decomposition: How does it happen?
Decomposition is the consumption of dead plant and animal matter by the many kinds of bacteria and molds that feed on it; these bacteria and molds, known collectively as decomposers, use dead organic material as their energy source. Decomposers, as a group, belong to food chains of their own, distinct from (though linked to) the familiar plants-herbivores-carnivores food chains we considered in chapter 11. The decomposers' food chains are known as detritus food chains. Like "ordinary" food chains, they transfer chemical energy from one group of organisms to another in a series of steps. Although the organisms concerned are for the most part microscopic, the energy they transfer is considerable.
Large amounts of detritus—dead organic material—can be found lying around nearly everywhere you look (the cautious "nearly" is to exclude deserts, and also concrete and other synthetic surfaces). Its presence is too obvious for comment; it attracts attention only when we have to rake fallen leaves or scramble over downed trees.
The bulk of detritus consists of dead plant material. If we exclude vegetation that happens to be consumed by fire, about 90 percent of all plant material becomes detritus;2 either the plants die or else they are eaten and excreted undigested in herbivores' feces. All dead, uneaten animal remains become detritus too. It is the material at the bottom of every detritus food chain, and its energy, stored as the chemical energy in organic molecules, is ultimately derived from the sun. In terms of trophic levels, detritus is to a detritus food chain what living vegetation is to an "ordinary" food chain.
Some of the energy in detritus is dissipated in the life processes of the bacteria and molds that consume it. But a lot of the energy is passed on when the decomposers themselves are eaten by larger organisms, known as detritivores. Typical detritivores are beetle grubs feeding on rotting (that is, decomposing) wood, maggots feeding on rotting meat, immature aquatic insects feeding on "drowned" leaves at the bottom of still water, and clams feeding on detritus particles in salt water. The detritivores appear to be eating dead food; in fact, they are eating the decomposers together with some of the incompletely rotted organic material softened by the decomposers. Many of the detritivores are themselves eaten, perhaps by insect-eating birds, perhaps accidentally by grazing mammals. When this happens the energy is transferred into an ordinary, macroscopic food chain at one of the carnivore levels. The matter containing the energy becomes flesh, and in due course, dead flesh; that is, it becomes detritus again, at the starting point of another detritus food chain. Any given organic molecule may cycle through macroscopic food chains and detritus food chains alternately, over and over again, before ultimately disintegrating to carbon dioxide and water.
All these seemingly negligible natural events are not negligible at all when taken together as transfers of energy. Bacteria "consume almost everything in their environment ... [and] reproduce more rapidly than other living organisms." This makes them "a major source of energy for other consumers."3 If we disregard fires, then bacteria and molds are the final dissipaters of captured solar energy. The energy has to go somewhere, and only a minute fraction of it goes into long-term storage in fossil fuels—coal and oil—and into short-term storage as peat.
Detritus food chains are as important in the ocean as on land. Huge numbers of plankters—both green phytoplankters and the zooplankters that feed on them—escape being eaten by larger organisms and simply die; the result is a rain of tiny bodies sinking slowly through ocean waters nearly everywhere. They are the detritus of the ocean, and they form the base of marine detritus food chains.
The chemical energy in an organic molecule lasts for as long as the molecule lasts, from its creation to its disintegration. The lifetime of a carbohydrate molecule, for instance, starts with its "birth," energized by sunlight, and ends with its "death" by bacterial decomposition or fire; its lifetime may be a few seconds or millions of years. Consider the extremes. When fire destroys growing grass, some of the energy liberated must have been captured only seconds before. When bacteria decompose the last sliver of wood from what was once an ancient rain-forest tree, the final molecules to disintegrate may have existed for thousands of years, first while the tree was alive and then as it gradually decayed.4 The tiny fraction of detritus fossilized to form coal and oil can persist with its energy intact for millions of years; some of the energy is dissipated when the fuel is burned by humans; as for the rest, all we can say is that it won't outlast the planet.
As we've noted before, nearly all living things obtain their energy, directly or indirectly, from the sun. Here we consider the organisms that the word nearly excludes. They are bacteria that obtain their energy as chemical energy, direct from inorganic molecules—from molecules of mineral origin. They don't need the energy of light, which means they can function in the dark. The process is called chemosynthesis to differentiate it from photosynthesis.5 Both kinds of synthesis require two things—a source of energy and a source of carbon. The difference between them is in the energy source; the carbon source is the same, carbon dioxide in air or carbonate in water. Both kinds of synthesis "fix" carbon.
The discovery that organic molecules—the molecules living organisms are made of—could be synthesized in the absence of chlorophyll, by a process other than photosynthesis, was one of the giant steps in nineteenth-century science. It was made by the Russian biochemist Vinogradsky, who, inexplicably, has not achieved the widespread fame he deserves.6
He wrote, "[Chemosynthesis] is contradictory to that fundamental doctrine of physiology which states that a complete synthesis of organic matter cannot take place in nature except through chlorophyll-containing plants by the action of light."7 He discovered that, on the contrary, some bacteria can gain the energy they need for growth and reproduction by oxidizing inorganic compounds.
One species of bacteria that does this is Thiobacillus oxidans; members of the species are the bacteria responsible for acid mine drainage. They oxidize sulfur compounds such as the mineral pyrite (otherwise known as iron sulfide or fool's gold) to sulfuric acid and in so doing liberate the energy they require to synthesize the organic molecules necessary for life and growth. Another sulfur compound they often oxidize is the "rotten egg" gas, hydrogen sulfide. Thiobacillus oxidans and other so-called iron bacteria also oxidize iron; the reaction they cause is the same as rusting, which, as we saw in chapter 10, is an exothermic (energy yielding) reaction. Various species of iron bacteria live in the water of acid bogs, where they oxidize dissolved forms of iron, leaving the rust-colored coating (indeed, it is rust) often found on the bottom of bog pools when they dry up.8
Another group of chemosynthetic bacteria are the nitrifying bacteria that live in the soil. Some species obtain their energy by oxidizing ammonia to nitrite and others by oxidizing nitrite to nitrate.9
Note that chemosynthesizing bacteria use the chemical energy they capture in the same way that photosynthesizing plants use the light energy they capture. In both cases the energy is used to fix carbon and create organic molecules. Then, while they live, the bacteria (like the plants) break down some of the organic molecules to release energy for life processes. Some bacteria (not all) do this by ordinary respiration.
Chemosynthetic reactions are crucial to the growth of plants; they ensure that plants get the nitrogen they must have in a form they can use. The energy transfers involved are small, however: chemosynthesis is relatively unimportant from the energy point of view—on our planet at any rate. This is because the bacteria concerned (apart from those that live in soil) tend to occupy uncommon, sulfur-rich habitats in pitch darkness. Some examples: "cold seeps" on the seafloor, where cold water with sulfides and other chemicals dissolved in it seeps up at depths where sunlight can't penetrate;10 oil seeps on the sea floor, also at dark depths;11 and the hot, sulfurous waters of deep-sea hydrothermal vents.12
The characteristic of chemosynthesis that makes it noteworthy in the context of "bioenergy" is that, as Vinogradsky proved, it does not come from sunlight. Chemosynthesis could conceivably be the fuel of life on planets not constantly bathed in strong sunlight as the earth is. To regard a habitat as "unusual" because it is poorly represented on earth is a geocentric prejudice.
As we have just seen, certain bacteria use minerals as fuel. In striking contrast are other tiny organisms that use solar energy to build rocks. Biological "rock
building," the topic we come to now, is the direct opposite of chemosynthesis: whereas chemosynthetic bacteria use rocks to build life, rock-building organisms use the products of photosynthesis to build rocks; the rocks are known as biominerals.
Familiar examples are coral reefs and those limestones that consist of the shells or skeletons of billions of microscopic organisms. Less abundant are flints and cherts, rocks formed from the silica skeletons of microscopic diatoms and radiolarians (fig. 12.1).
First consider coral. The individual organisms in living coral are tiny polyps—miniature versions of sea anemones, to which they are closely related. The polyps secrete the mineral calcite (limestone) and use it to construct cup-shaped external skeletons for themselves. Usually the polyps live in closely packed colonies, with the walls of the cups fused together. When the polyps are dead, the solid masses of calcite skeletons are coral rock—a biomineral.
While they are alive the polyps feed like sea anemones, grasping their prey—mostly plankton animals and minute crustaceans—with their tentacles. Nearly all the coral living in shallow seas where sunlight penetrates have plantlike, photosynthesizing green cells living inside the polyps. The green cells are not part of the polyps; they are separate organisms living in a symbiotic partnership that benefits both. The green cells benefit by being protected from predators, and the polyps benefit because the green cells' photosynthesis absorbs and disposes of surplus carbon dioxide.
Next consider chalk, another form of limestone consisting of the skeletons of other tiny marine organisms. The skeletons collect on the sea floor as calcareous ooze, which, if it is free of sand, eventually hardens to chalk, a soft, pure white rock. Chalk occurs as long ranges of hills in southeastern England and northeastern France, and where the hills have been cut through by the English Channel, the chalk is exposed as the famous white cliffs of Dover. Chunks of flint, formed from the siliceous skeletons of diatoms and radiolar-ians, can be found embedded in the chalk.
The most vigorous calcite producers are certain microsocopic phytoplank-ters known as coccolithophores. They secrete coccoliths, tiny, intricately patterned calcite "scales" that coat the outside of each phytoplankter's cell wall, presumably functioning as protective armor (see fig. 12.1). After the living cells that bore them die, the coccoliths are all that remain, and they are often the most abundant ingredients in calcareous ooze. Other organisms that contribute to the ooze are foraminifera (forams for short), and the rudimentary shells of "sea butterflies" or pteropods, small mollusks often found in great numbers in the surface waters of the oceans. (Note that calcareous ooze can accumulate only at depths less than 4.5 km; below that level, calcite dissolves.)
The link between solar energy and chalk has been most clearly revealed in studies of living coccolithophores of the species Emiliana huxleyi, known to oceanographers everywhere as Ehux.13 As members of the plankton, they float in the uppermost layer of the ocean, where the sunlight they need for photosynthesis can reach them. They sometimes occur in immense "blooms,"
the consequence of population explosions. A bloom colors the sea turquoise in huge, irregular patches; the patches may be larger in area than 100,000 square kilometers (the size of England), and they show up conspicuously in photos taken from space.
The way photosynthesis—hence solar energy—affects coccolith formation has been discovered by observing the process while it is happening.14 When calcite crystallizes in the absence of Ehux, the crystals are plain rhomboids, independent of one another. But when calcite crystallizes inside an Ehux cell, the process is controlled by giant carbohydrate (polysaccharide) molecules, produced by photosynthesis; the particular polysaccharide involved is structurally "one of the most complicated ever described,"15 and by binding to the growing calcite crystals it controls the pattern they construct. The result is the formation of coccoliths, each a symmetrically patterned, perforated structure only a few micrometers in diameter. The buoyant Ehux cells bearing them are eaten by copepods—minute crustaceans in the plankton—and excreted in the copepods' feces, which sink to the bottom, where they carpet the seafloor over immense areas. In time (millions of years), these carpets of calcite ooze will undoubtedly become chalk cliffs.
To summarize: A variety of rocks are biominerals, consisting of the skeletal remains of microscopic organisms. Four groups of these organisms are especially noteworthy—coccolithophores, forams, diatoms, and radiolarians. Of these, the first two secrete calcite (which forms ordinary limestone and chalk) and the second two secrete silica (which forms chert and flint). Two of the groups (coccolithophores and diatoms) contain chlorophyll, enabling them to photosynthesize; the other two (forams and radiolarians) are animals, somewhat like amoebas with external "skeletons," which obtain their solar energy at second hand. In all four groups, the hard parts are intricately structured and sculpted into astonishingly beautiful forms (see fig. 12.1); they have been called "the miniature jewelry of the abyss."16
Energy, originally from the sun, goes into the construction of these "jewels" and is stored in their elaborate geometrical structures. When the structures are crushed, the structural energy is dissipated. This is a microscopic version of what happens when big rocks are broken by weathering, as we saw in chapter 9. Many of the microscopic skeletons remain undamaged or only slightly damaged within the rocks; it is difficult to foresee how the energy they still hold will ultimately be dissipated.
THE WARMTH OF THE EARTH NUCLEAR REACTIONS SUSTAIN ALL LIFE
Up to this point we have considered energy originating in the sun. Think of the atmosphere: all the winds, from light airs to hurricanes, are energized by the sun's heat. Think of the oceans: ocean currents wouldn't flow were it not for the sun's heat. Think of living things: almost all depend on the energy of sunlight captured by photosynthesis (the exceptions are some species of bacteria mentioned in chapter 12). Heat from the sun causes surface water to evaporate, giving rise to clouds yielding rain and snow, which nourish rivers and lakes. Flowing water, aided by wind and wind-driven waves, causes erosion, which shapes the face of the earth.
Not all the earth's energy comes from sunlight, however. A small fraction—one part in four or five thousand—comes from the earth's internal heat. This is the energy that shifts tectonic plates and that powers earthquakes and volcanoes. It heats rocks to temperatures high enough to change them to metamorphic rocks—limestone to marble, for example, and granite to schist.
It drives the circulation of liquid iron in the earth's core, which makes the whole earth a magnet. It heats hot springs and geysers.
If the sun were suddenly to disappear, the atmosphere and oceans would become silent and still; the oceans would freeze solid, except where submarine hot springs (hydrothermal vents) emerge in the depths; every living thing on the planet's surface would die. At the same time, hot springs would continue to bubble up from the earth's interior; tectonic plates would continue to drift, volcanoes to erupt, and earthquakes to shake our planet. Rocks would still be metamorphosed, and the earth would still be a magnet.
All these energetic events would keep happening even though the energy from inside the earth is, as noted above, four or five thousand times less than the solar energy coming to us from outside. Both kinds of energy eventually leave the earth by radiation skyward: earth's heat does not accumulate. Solar heat is radiated back into space, while the internal heat, what little there is of it, escapes through the surface and is gone forever.
Let's see how these two radiation rates, measured in watts per square meter (W m-2) of radiating surface, compare with a couple of other, easily visualized radiation rates, those of a 100-watt lightbulb and a clothed human body. We now have four radiation rates to consider, measured at the surfaces of the objects concerned. Listing them from greatest to least, they are: for the light and heat from the 100-watt lightbulb, about 2,000 W m-2; for the sunlight reradi-ated from the earth, 340 W m-2; for the internal heat radiated from the earth, 0.08 W m-2; and for the warmth radiated from a clothed person on a very cold, windy winter day,1 0.002 W m-2.
Note how the radiation rates of the small objects (the lightbulb and the person) bracket the rates at which the earth radiates its two kinds of energy (external and internal). The surface of a 100-watt lightbulb is obviously much hotter, and is radiating much faster, than the surface of the ground. Also (although this is less obvious), the clothes of a person exposed to a bitter winter wind are colder, and are radiating more slowly, than the surface of the ground. In short, if you dress warmly and keep your clothes on, you will lose your warmth more slowly than the earth loses its warmth.
Atomic Nuclei: The Source of All Energy Heats the Earth
We now inquire how the sun's heat and the earth's internal heat come into existence. Nuclear reactions are the most important cause, nuclear fusion in the case of the sun, and radioactivity of a type that can, broadly speaking, be called nuclear fission in the case of the earth. In fact "the energy involved in almost all natural processes can be traced to nuclear reactions and transformations."2 Fusion is the principal source of the sun's heat, and fission is the principal source of the earth's; these are the heat sources we consider in this chapter. Both the earth and the sun also have another supply of heat: the heat remaining from the time of their formation about 4.5 billion years ago, some of which still remains (see chapter 14).
A digression on the basics of atomic structure is necessary here. As is well known, an atom consists of an exceedingly small nucleus surrounded by a "swarm" of even smaller electrons, moving in a comparatively large space centered on the nucleus. Each electron has a negative electrical charge, and the nucleus contains an equal number of positively charged particles (protons), making the whole atom electrically neutral. Every chemical element is distinguished from all the others by the number of electrons it has. An atom of hydrogen, the lightest element, has a single electron; an atom of uranium, the heaviest naturally occurring element, has ninety-two (still heavier elements, with more electrons, have been created artificially).
So far, so good. We are about to consider events in the nuclei of atoms, which, as we shall see, are many orders of magnitude more energetic than chemical reactions of the kind considered in chapter 10. Those reactions—photosynthesis and combustion, for instance—involve only the electron swarms of the participating atoms: the atomic nuclei take no part.
The tremendous energy contrast between ordinary chemical reactions and nuclear reactions cannot be overemphasized. The contrast becomes somewhat easier to appreciate when you compare the relative sizes of atoms and nuclei. Most of the volume of an atom is the space occupied by the electrons, so most of an atom's volume is empty space. The volume of a carbon atom, for instance, is about 2.5 x 10-24 ml (one milliliter is about the volume of a sugar cube). If the carbon atom were represented by a globe the size of the earth, the nucleus would be a ball at the center with diameter less than 100 m.
The contrast in sizes shows that there must obviously be a corresponding contrast in densities. The density of a solid object such as a pebble is its mass divided by its volume, with the measured volume including all the empty space in every atom. Nuclear material lacks empty space, making its density approximately one hundred trillion times greater. In fact, nuclear density is about a quarter of a billion metric tons per milliliter (more precisely, 2.4 x 1017 kg m-3).3
The inconceivably high density of an atom's nucleus makes it intuitively reasonable to suppose that the nucleus is held in one piece—or, to look at it the other way round, prevented from flying apart—by unimaginably strong forces. Intuition is correct: the bonds holding an atom's nucleus together are tens or hundred of millions times stronger than the chemical bonds described in chapter 10, which hold the atoms in a molecule together. This pent-up force is potential energy waiting to be liberated. As we have noted already and will now consider in more detail, the liberation is brought about by nuclear fission in the earth's interior and by nuclear fusion in the sun. The energy is known as the binding energy of the nucleus.
Before going further, we must consider what it is that is bound: What kind of elementary particles are held together in an atom's nucleus? The answer is protons and neutrons. Each has a mass close to two thousand times the mass of an electron.4 Every proton carries a single positive charge of electricity, exactly balancing the negative charge of an electron; neutrons are electrically neutral. Protons and neutrons together, known jointly as nucleons, are the particles that make up nuclei.
The number of protons in the nucleus of any given element is the same as the number of electrons swarming around the nucleus, as we noted above. The number of neutrons varies, from zero in a common hydrogen atom (whose nucleus consists of a single proton) to 146 in the commonest form of uranium. In the nuclei of light elements, such as calcium and carbon, the protons and neutrons in the nucleus are equal in number, but in heavier elements neutrons outnumber protons; in the uranium atom, the number of neutrons is more than 50 percent greater than the number of protons.
It often happens that not all the atoms of a given element have the same number of neutrons in the nucleus, even though they all have the same numbers of protons. For example, the number of protons in the nucleus of every atom of chlorine is 17, but the number of neutrons is not the same in every nucleus: about 75 percent of them have 18 neutrons, for a total of 35 nucleons; the rest have 20 neutrons, for a total of 37 nucleons. These are the two isotopes of chlorine, known respectively as chlorine-35 and chlorine-37 (or by the symbols 35Cl and 37Cl). The isotopes of uranium are known by name to everybody who has read about atomic bombs and atomic energy; the familiar ones are uranium-235 (with 235 nucleons comprising 92 protons and 143 neutrons) and the far more abundant uranium-238 (with 92 protons and 146 neutrons). Carbon has three isotopes: about 99 percent of all carbon is carbon-12,
1 percent is carbon-13, and a very tiny fraction, far too small to be recorded as a percentage, is carbon-14. Their nuclei all have 6 protons and 6, 7, or 8 neutrons respectively.
This digression on isotopes is a necessary preliminary to the statement that the binding energy of a nucleus depends on the number of nucleons it contains. The strongest of all nuclei—those with the greatest binding energy per nucleon—are those of iron-56, which have 26 protons and 30 neutrons. They are the most stable nuclei, more stable than either lighter ones or heavier ones. The reason a nucleus of intermediate size is held together more strongly than smaller or larger nuclei will become clear in a moment, when we consider the nature of the force holding nucleons together. The force does not act in the same way as the force governing the behavior of larger objects when they are electrically charged.
As everybody who has been infuriated by static cling knows, two electrical charges of the same sign—two positive charges or two negative charges—repel each other, whereas two unlike charges—one positive and one negative—attract each other. This leads one to expect that an atom's nucleus would automatically fly apart, because all its charged particles are positively charged protons. It doesn't because it is held together by a vastly more powerful force, the strong interaction between elementary particles. This strong force holding particles together overwhelms the much weaker electrical force that drives similarly charged particles apart; but it acts only over short distances—exceedingly short distances, a trillionth of a millimeter (10-15 m) or less. If a nucleus is smaller than this in diameter, then every one of its particles is attracted to every other by the strong interaction; therefore the more numerous the particles and, consequently, the more numerous the pairwise strong interactions, the more strongly the nucleus as a whole is held together. In brief, the bigger the stronger, but only up to a limit. If a nucleus consists of so many nucleons that its diameter exceeds the range of the strong interaction, some of its protons will be spaced far enough apart to repel each other by electrical force. The largest nucleus in which every nucleon is attracted to every other by the strong interaction is (as you will have guessed) iron-56. Nuclei larger than this are increasingly unstable. The heaviest nucleus to occur naturally is uranium-238.
Nuclear Fusion: E = mc2
We have reached the stage (at last) where we can describe nuclear fusion and (in the following section) nuclear fission and comprehend the source of the en-
Figure 13.1 (a) Nuclear fusion. (b) Nuclear fission. Masses are shown black, and energy is shown stippled. In each figure the total mass to the left of the arrow, showing the reactant(s), exceeds the total amount to the right, showing the product. The excess mass is liberated as energy. In both cases the loss of mass is exaggerated for clarity.
Figure 13.1 (a) Nuclear fusion. (b) Nuclear fission. Masses are shown black, and energy is shown stippled. In each figure the total mass to the left of the arrow, showing the reactant(s), exceeds the total amount to the right, showing the product. The excess mass is liberated as energy. In both cases the loss of mass is exaggerated for clarity.
ergy these two nuclear events liberate. What happens is shown diagrammati-cally in figure 13.1: the upper panel shows fusion, the lower panel fission.
Fusion occurs when two lightweight nuclei happen to come so close to each other that the strong interaction pulls them together, overcoming their tendency to repel each other because both are positively charged electrically. They combine to form a larger nucleus. The larger nucleus (the product nucleus) has a slightly smaller mass than that of the two nuclei (the reactant nuclei) that combined to form it. The seemingly vanished mass hasn't really vanished, however; it has been converted into energy, in accordance with Einstein's famous formula, E = mc2. E is the energy, measured in joules; m is the mass, in kilograms, that has "gone missing"; and c is the velocity of light, 300 million meters per second or, in scientific format, 3 x 108 m s-1.
The fusion of a pair of nuclei of "heavy hydrogen" will serve as an exam ple.5 Heavy hydrogen (also called deuterium) is an isotope of ordinary hydrogen: whereas an atom of ordinary hydrogen has a single proton for its nucleus (its symbol is 1H), heavy hydrogen has a nucleus of two nucleons, a proton and a neutron (its symbol is 2H). When two of these heavy hydrogen nuclei collide, they combine to form a single nucleus of helium, which has four nucleons (two protons and two neutrons); its symbol is 4He. The combined mass of the two reactant nuclei is 6.68901 x 10-27 kg, and the mass of the product nucleus (helium) is 6.64649 x 10-27 kg.6 The mass of the product is therefore 0.04252 x 10-27 kg less than the mass of the reactants. This is the number to be substituted for m in the "famous formula"; c2 is 9 x 1016 m2 s-2. It takes only a pocket calculator to confirm that E = mc2 = 3.827 x 10-12 J. Finally, we convert joules to electronvolts (1 J = 6.24 x 1018 eV; see chapter 10), as the more convenient units for measuring such minuscule amounts of energy. The answer is E = 24 million electron volts, written 24 MeV, per nucleus of helium.
This is the energy liberated when two heavy hydrogen nuclei combine to form a helium nucleus, and it is also the bonding energy of the helium nucleus. To split a helium nucleus into two heavy hydrogen nuclei, you would have to supply 24 MeV to get the job done. The 24 MeV you provide would become converted into mass—the mass by which two heavy hydrogen nuclei exceed the mass of a single helium nucleus. Whichever way the reaction goes, fusion or fission, the mass-plus-energy (or mass-energy for short) is the same at the end of the reaction as it was at the beginning: it is conserved. This is an informal statement of the law of the conservation of mass-energy, which replaced two famous nineteenth-century laws: the law of the conservation of mass and the law of the conservation of energy.
Note that the bonding energy of a helium nucleus, namely 24 MeV, is more than 5 million times the energy needed to separate the two hydrogen atoms forming a hydrogen molecule, which, as we saw in chapter 10, is 4.5 eV. This is a good example of the tremendous difference between the energy holding a nucleus together and the energy holding the atoms in a molecule together.
On a more "human" scale, we can say that the fusion energy obtainable from 150 milligrams of heavy hydrogen (picture a 500 milligram vitamin C tablet for comparison) is about the same as the combustion energy produced by burning 2,700 liters of gasoline.
Nuclear fusions do not happen naturally on earth (their unnatural occurrence is considered in chapter 19). This is because natural conditions on earth never allow a pair of nuclei to come close enough to each other for the strong interaction force to take hold and drive them together. Collisions between nu clei happen only in environments where the temperature and pressure are, literally, out of this world; they happen in the interiors of stars, including the sun. The fusion of pairs of heavy hydrogen nuclei to form helium nuclei is, indeed, the sun's chief source of energy. The whole reaction has a few more steps than the simple fusion described in detail above, because the sun's "ordinary" hydrogen must first be converted to heavy hydrogen. The principle is the same, however, and the energy liberated per helium nucleus formed is a little more: it is 24.7 MeV.7
Bear in mind that though nuclear fusion never happens naturally on earth, it provides practically all the energy we have. It happens in the sun. "Homegrown," locally produced energy amounts to only one part in four or five thousand of the total energy that keeps the earth going, as we noted at the beginning of this chapter. Most of it is produced by nuclear fission.
Nuclear Fission: E = mc2 Again
Nuclear fission takes place when a heavy nucleus splits into two or more product nuclei. The combined mass of the product nuclei falls short of the mass of the reactant nucleus (the one that split), and the vanished mass instantly becomes energy.
As an example, let's compute the energy liberated when a nucleus of ura-nium-235 splits into one nucleus of strontium-90 and one nucleus of cerium-144 plus a neutron (there are also four leftover electrons).8 The mass that "disappears" amounts to 0.3561 x 10-27 kg. Applying the formula E = mc2 shows that this mass becomes 32.05 x 10-12 J, or about 200 MeV. This is the energy liberated by the fission of one uranium-235 nucleus.
The arithmetic is straightforward, but where and why does nuclear fission happen? The question has two answers: First, it happens naturally and spontaneously, in radioactive elements contained in the rocks the earth is made of. This naturally occurring nuclear fission is what maintains the warmth of the earth's interior, keeping the tectonic plates in motion, causing mountains to rise up, and driving a variety of other natural processes.
Second, it can be made to happen, unnaturally fast, by technological means. "Atomic" bombs, of the kind first used in war in 1945, get their energy from nuclear fission that is caused to happen in a confined space and at a tremendously rapid rate. (In contrast, "nuclear" or "hydrogen" bombs are powered by nuclear fusion.) Controlled nuclear fission, proceeding at a more leisurely pace, is the energy source in current atomic power stations.
Unnatural nuclear fission is discussed in chapter 19. Here we consider how natural nuclear fission warms the earth. The nuclei of several elements are involved.9 The fissions responsible differ from the example already described in that the nuclei resulting from the split are very unequal in size. In the fission we've already considered, a nucleus with 235 nucleons split into nuclei with 90 and 144 nucleons plus one "spare" neutron. By contrast, in the fissions whose energy warms the earth, a heavy nucleus splits unequally: one of the product nuclei is a helium nucleus with 4 nucleons (2 protons and 2 neutrons), and the other is a nucleus only 4 units lighter than the original.
Fission of this kind—the splitting off of a lightweight helium nucleus from a heavy nucleus—is known as radioactive a-decay (a is the Greek letter alpha); it is one kind of radioactivity. There are other kinds as well, namely 0-decay and y-decay, but they add negligibly to the earth's interior heat, the topic that concerns us here. Radioactive a-decay isn't a typical example of nuclear fission because the products of the fission are so unequal in size. It is called a-decay because radioactivity was discovered, and its different forms named, years before it became clear that the a-particles emitted in radioactive a-decay are identical with the nuclei of helium atoms. Indeed, the terms "a-particle" and "helium nucleus" mean the same thing.
The nuclei whose splitting contributes most to the earth's heat are two isotopes of uranium (uranium-238 and uranium-235) and one of thorium (tho-rium-232). A single nucleus of any of these splits repeatedly, hiving off a helium nucleus and releasing energy at each split, before winding up as a stable nucleus immune to further splitting. Electrons in the space controlled by the nucleus are also lost, so that the final, stable nucleus differs chemically from its "ancestor" nucleus as well as having fewer nucleons.
Thus a nucleus of uranium-238 splits off 8 helium nuclei in succession, for a loss of 32 nucleons in all; it also changes chemically, becoming an isotope of lead, namely lead-206. In similar fashion, a nucleus of uranium-235 loses a total of 7 helium nuclei before reaching stability as a different isotope of lead, this time lead-207. Thorium-232 loses 6 helium nuclei and becomes lead-208.
The time intervals between successive fissions are a matter of chance; they are intrinsically unpredictable. Some of the nuclei persist for millennia, others for less than a second.
These three "decay" processes provide most of the earth's internal heating at present. The three "fuels" (uranium-238, uranium-235, and thorium-232) are, of course, in the process of being consumed—used up—as surely as, though more slowly than, fossil fuels like coal and oil are being used up by hu mankind. What's more, the natural process is unstoppable. It also follows that the quantities and the relative proportions of the different radioactive elements in the earth are continuously changing through geologic time; some that were present in the distant past have already been used up. More on the subject in chapter 14.
In the meantime, it's worth reemphasizing that practically all the energy available on earth comes from nuclear reactions of one kind or another. Nuclear fusions in the distant sun are the most lavish source. Nuclear fissions, deep underground where the sun's warmth cannot penetrate, continuously heat the earth's interior and energize the many processes always going on there.
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