Dr. Manhattan is able to change his size at will (as shown in Figure 19) due to the fact that the Schrodinger equation is linear. In mathematics an equation is called "linear" if it depends only on the key variable (in the Schrodinger equation that would the wave function ) and not on that variable squared or cubed, or the square root, and so on.30 A very simple linear equation is = , which is certainly a true statement. In fact, this equation is so simple that it is always true for any value of . So if = 1, then this equation tells us that 1 = 1 (which we already knew). In this case, if is ten times larger, then this simple equation tells us that 10 = 10, which is also a true statement. Given that the Schrodinger equation is linear, there is no change in the physics of the situation if we multiply by a constant, either a larger or smaller one. By multiplying the wave function by a constant (the "normalization" described in Chapter 6), we ensure that 2 acts as a probability density and varies from 0 percent to 100 percent. In addition, the fact that the Schrodinger equation is linear means that if there are two possible solutions to the equation, such as A and B, then their sum A + B will also be a solution (this will be very important in Section 4). Presumably Dr. Manhattan is able to shrink himself down as well, multiplying his wave function by a value less than 1, though we never see him utilize this capability in the comics or the motion picture adaptation.
Jon Osterman, as shown in Figures 11 and 19, gained a bright blue pallor when he rea.s.sembled himself following the unfortunate "incident" in the intrinsic field chamber. As wave functions have no color, there are at least three possible explanations for his being blue: (1) always knowing what will happen in the future has taken all the joy out of life; (2) he's depressed because he realizes that "nothing ever ends"; or (3) he's emitting Cerenkov radiation.
Dave Gibbons, the artist of Watchmen, once stated in a radio interview that he elected to make Dr. Manhattan blue as a visual signifier in order to constantly remind the readers of Jon's transformation. If Dr. Manhattan were red he would look like he was on fire, green was too close to the Hulk, and other colors would look too similar to actual skin tones on the printed comic page. Be that as it may, just because the color choice was one of casual necessity does not mean that we can't obsessively discuss the underlying physics in great detail! For it turns out that given Dr. Manhattan's origin, if he were to glow in any color of the optical spectrum, it would indeed be blue.
Figure 20: Image of a pencil (belonging to a certain fictional physicist) that appears broken at the air/water interface due to the different speeds of light in the two media.
When certain elements undergo radioactive decay, they may emit high-speed electrons as a by-product of their nuclear reaction (we'll discuss the mechanism by which this occurs in the next section). When those electrons (also referred to as "beta rays") travel faster than the speed of light in a material medium, they emit electromagnetic radiation in the blue-ultraviolet portion of the spectrum, which is known as Cerenkov radiation.
This last sentence is no doubt puzzling, for a central principle of Einstein's Special Theory of Relativity is that nothing can travel faster than the speed of light. But this is in fact not strictly correct. The more accurate way to state this principle is that nothing can travel faster than the speed of light-in the vacuum of empty s.p.a.ce! Light speed in a vacuum is three hundred million meters per second and is indeed the fastest velocity in the universe. However, light travels much slower than this when moving through denser media, such as water or gla.s.s.
Anyone who has noted that a straw or pencil in a gla.s.s of water appears to be "broken" at the water-air interface, as shown in Figure 20, has observed an optical effect that results from light moving slower in water than in air. In order to be seen, light must be reflected from the straw and detected by our eyes. The change in the speed of light at the water-air surface causes straight-line light rays to bend, in a phenomenon termed "refraction." The light that bounces off the portion of the straw protruding from the water of course does not bend and travels in a straight line. When we observe the light from the straw in the air and the light that bent upon leaving the water, we interpret the image as a straw with a sharp discontinuity at the water's surface.
Why does light travel slower in water and other media? It is because the electromagnetic waves interact with the electrons surrounding each atom in the material. When running through a swimming pool, you will move slower if you hold your arms out away from your body and increase the drag from the water. Light experiences an "electromagnetic drag" from the electrons that can slow its motion down markedly. The speed of light in water or gla.s.s is only 75 percent of what it is in a vacuum, which is still pretty fast. But high-speed electrons can move through these media with fewer interactions, and thus it is possible for an electron to travel in water faster than light can. When this happens, the electron (which does interact with the electrons surrounding the atoms in the material, only not as strongly as light does) generates an "electromagnetic sonic boom," emitting light in the blue-ultraviolet region of the electromagnetic spectrum. This blue-light shock front is termed Cerenkov radiation, after Pavel Cerenkov, who discovered and explained this phenomenon in 1934 (for which he was awarded the n.o.bel Prize in Physics in 1958).
Air is much less dense than water or gla.s.s, and light slows down only slightly when moving through the atmosphere compared to its largest speed in a vacuum. Nevertheless, for the purposes of explaining the science underlying a fictional character in a comic book, let's stipulate that it is possible to generate Cerenkov radiation from high-speed electrons jetting through the air. Let's also suppose that when Dr. Manhattan rea.s.sembled himself following the removal of his intrinsic field, he did so in such a way that he is continually leaking high-speed electrons, giving him a healthy blue glow. There are always many electrons from the Earth that he can draw upon in order to maintain his charge neutrality. If he wanted to darken his hue (as he does at one point for the benefit of television cameras), he could simply change the speed at which the electrons escape.
Nuclear reactor piles at the bottom of deep pools of water31 give off a blue glow, and this Cerenkov light indicates that the pile is active and emitting beta rays. In Watchmen (spoiler alert!) a character frames Dr. Manhattan, so that he is accused of giving his close friends and an ex-girlfriend cancer. One way to inflict Osterman's a.s.sociates that would plausibly suggest him as the source of the disease is to surrept.i.tiously expose these people to nuclear isotopes, such as strontium-90, that are known to be carcinogenic and are deadly precisely because of their beta radiation emissions.
Another striking characteristic of Watchmen's Dr. Manhattan is his ability to experience the past, present, and future simultaneously. It is specified in the graphic novel that the post-intrinsic-field-removal Jon Osterman is able to see only his own future and thus would not know of events to come unless he either directly experiences or partic.i.p.ates in them or is told about them. Again, if Dr. Manhattan did indeed have control over his macroscopic quantum mechanical wave function, then as the wave function contains all the information about the object's probability density in s.p.a.ce and time, this characteristic is plausible.
The fact that there is no other source of information about the future evolution of an object than what is contained in its wave function is significant. If all we have is the wave function, and the wave function can tell us only the probability per unit volume of finding the object in s.p.a.ce and time, then, even in a perfect, idealized situation, we must resign ourselves to knowing only the odds as to the object's location. When we deal with probabilities and statistics in other nonquantum situations in physics, it is simply to make our lives easier. We know that Newton's laws of motion provide a nearly complete description of the interactions of the air molecules in the room in which you are reading this right now. However, to apply these equations to the air would involve solving Newton's laws for all trillion trillion molecules simultaneously. In this and similar situations, it is much more reasonable to describe the average pressure, for example, or introduce the concept of "temperature" (which represents the average kinetic energy per molecule) rather than deal with each molecule separately in turn. In contrast, in the quantum world, the emphasis on probability density is a matter of necessity, not convenience. Even with infinitely fast and infinitely precise observations, we can never know exactly where the object is, but only its average location.
This inability to do better than knowing the odds is a consequence of the wavelike nature of matter. Recall the discussion of the Heisenberg uncertainty principle from the preceding chapter. The wavelength of the matter-wave a.s.sociated with the electron, for example, is directly connected to its momentum. A pure, single wave has only one wavelength, and thus we know exactly what its momentum is, but at the expense of having any information about where the electron is. The more we localize the electron, say, by ensuring that it will be found within the one-third of a nanometer that is the typical spatial extent of an atom, the less defined its momentum becomes. If we had perfect knowledge of its position (which is what physicists desired in order to put the "probability density" aspect to rest), then this would come at the cost of perfect ignorance about its momentum. It could in principle have any momentum between zero and infinity, and we would thus have to contend with a probability interpretation of its motion. As we need both positions and momenta to employ a traditional Newton's law description of a system, probabilities are the best we can ever do.
Of course, knowing the probability that Dr. Manhattan may be in a particular state in the future, such as on Mars having a conversation with his girlfriend, is not a guarantee that he will indeed work out his relations.h.i.+p problems on the red planet. The only time something is absolutely certain to occur is when the probability is 100 percent, just as the only time something will never happen is if the probability is zero.
In most circ.u.mstances the most probable outcome is indeed the one that is observed. But what about the other probabilities that are not realized? What do these wave function solutions to the Schrodinger equation correspond to? One interpretation was provided by Hugh Everett III. Everett suggested that all these probabilities describe actual outcomes on other Earths in an infinite number of parallel universes! If the probability of a certain event occurring is 10 percent, then Everett suggested that on 10 percent of the possible parallel Earths this outcome did indeed occur. The world we live in and experience is one that continually unfolds from this multiverse of possible Earths. For everything we experience, there are alternate Earths where different outcomes are realized.
Everett's ideas were considered too unconventional even by the standards of quantum theory, and his proposal, described in his physics dissertation at Princeton in 1957, earned him his Ph.D. but was otherwise completely ignored by the scientific community. Disappointed, Everett eventually turned away from pure scientific research and worked for the military, calculating fallout yields of various nuclear weapons for the Department of Defense. He pa.s.sed away in 1978, but not before his ideas received some measure of recognition by a small group of theoretical physicists, notably Bryce DeWitt, who actually coined the term "many-worlds interpretation of quantum mechanics" to describe Everett's thesis. Nowadays the number of physicists who subscribe to the many-worlds picture, while still small, is growing, as those who are struggling to reconcile quantum mechanics and Einstein's General Theory of Relativity find application for the many-worlds model.
Parallel universes and alternate Earths are, of course, a common feature in science fiction stories, both prior to Everett's dissertation and since. Sometimes these alternate worlds are profoundly different from ours, as in Flatland, Edwin Abbott's tale of a two-dimensional world published in 1884, or the 1931 short story "The Fifth Dimensional Catapult," by Murray Leinster. In 1896 H. G. Wells told "Plattner's Story," wherein Gottfried Plattner, in an accident involving a mysterious green powder in a chemistry lab at a boys' boarding school, is hurled to a parallel world that orbits a green sun and is inhabited by strange alien creatures with human heads and tadpole-like bodies. It is difficult to imagine the branching of possible wave functions that could have led to such an outcome. In Wells's short story "The Remarkable Case of Davidson's Eyes," Sidney Davidson, through another laboratory accident, gains the ability to see another world, where a s.h.i.+p docks on a South Sea island and stocks up on penguin eggs, despite the fact that all the information from his other senses is consistent with his being in a laboratory in London. Gradually Sidney's normal vision returns, and in time he discovers that the s.h.i.+p that he had seen in this alternate Earth was a real sea vessel that was in fact gathering penguin eggs on Antipodes Island at the time of Davidson's strange visions. While a definitive explanation is not presented, it is speculated that when Davidson stooped between the poles of a powerful electromagnet in the lab, his retina gained the ability to see through "a kink in s.p.a.ce"-though whether of this world or a parallel one remains open to interpretation.
A few years after Everett published his novel solution to the "measurement problem" in quantum mechanics, the DC super-speedster the Flash of the 1960s vibrated to a parallel Earth and had an adventure with the Flash of the 1940s (same power, different costume and alter ego). In the television program Star Trek broadcast in 1967, a transporter malfunction during an ion storm leads Captain Kirk, Dr. McCoy, Engineer Scott, and Lieutenant Uhura to an alternate universe stars.h.i.+p Enterprise, populated by evil twins of the rest of the crew (distinguished by goatees, naturally). In this mirror universe, the crew of the Enterprise are violent and ruthless, but one feature that remains constant in either universe is Captain Kirk's roving eye for the ladies.
In comic books, characters often travel to alternate Earths in parallel universes, and the implication in the stories is that the world of the comic book reader, the one lacking in actual superheroes, is the "real universe." However, a photo that I came across in the archives of the American Inst.i.tute of Physics suggests that the situation may be more complicated than we might think. The photo, shown in Figure 21, doc.u.ments a visit in 1954 to the Princeton University physics department by Niels Bohr (one of the founders of quantum mechanics we encountered in Section 1) as he meets with several physics graduate students. The student on the immediate right of Bohr is Hugh Everett III. The student on the far left appears to be none other than Jon Osterman! Recall that Osterman received his Ph.D. in physics from Princeton in 1957 and so would have indeed been included in the select group of students honored with an audience with one of the grand old men of phys-ics. As mind-bending as the concepts introduced by quantum mechanics into modern thought have been, the suggestion that comic book characters live among us may be a step too far!32 Figure 21: Niels Bohr (center) visiting with some physics graduate students at Princeton University in 1954. Second from the right, to Bohr's immediate left, is Hugh Everett III, who would posit the existence of an infinite number of Earths in parallel universes in order to resolve the "measurement problem" in quantum mechanics. At the far left is Charles Misner, a graduate student with a resemblance to Jon Osterman (inset), who would become Dr. Manhattan in Watchmen.
TALES OF THE ATOMIC KNIGHTS.
Our Friend, the Atom.
In the 1949 Warner Bros. musical motion picture My Dream Is Yours, a young Doris Day auditions for a spot as a featured singer on a popular radio show. Her manager, played by Jack Carson, advises her to curry favor with the sponsor by crooning a tender love ballad. She instead decides to belt out a bouncy, up-tempo ode to a "new invention . . . [no] larger than an adding machine . . . [that] few have ever seen." As the song continues, joined by the refrain of "tic, tic, tic," it becomes clear that Doris Day is singing the praises of-and comparing her quickly beating heart to-a Geiger counter!
Five years later, a ticking Geiger counter in another film would lead uranium prospector Mickey Rooney onto an atomic bomb testing site. Not realizing that a nuclear weapon detonation was imminent, he innocently took refuge in a test house populated with mannequins and helped himself to a peanut b.u.t.ter sandwich as the countdown progressed. Rooney survived the nuclear explosion without having to take refuge inside the model refrigerator. The resulting exposure to radioactivity would transform Mickey Rooney into The Atomic Kid, and he would go on to employ his newfound ability to glow in the dark and issue explosive sneezes to help the FBI break up a communist spy ring.
A few years after Mickey Rooney's misadventures on a nuclear weapon testing site, a darker though equally inaccurate depiction of the effects of radiation exposure would be presented in The Beast of Yucca Flats (1961). In this cautionary tale, former Swedish wrestler Tor Johnson (of Plan 9 from Outer s.p.a.ce fame), also accidentally wanders into an atomic bomb test run. Johnson plays defecting Russian scientist Joseph Javorsky, who, while fleeing KGB a.s.sa.s.sins, winds up on the famous desert Yucca Flat testing range right before an atomic bomb detonation. The resulting radiation transforms Johnson in a hulking, mindless homicidal monster (though he looks pretty much the same as before the explosion).
Certainly the true effects of radiation exposure were publicly known at least by August 1946, with the publication in the New Yorker of John Hersey's "Hiros.h.i.+ma." But in the years immediately following the conclusion of World War II, popular forms of entertainment maintained, for the most part, an optimistic view of the benefits to come in an atomic-powered world of tomorrow. The 1957 television program Disneyland featured Dr. Heinz Haber, a German rocketry expert, in Our Friend, the Atom, which likened atomic power to a genie in a bottle that could grant us three wishes for a brighter future. The first wish would be for power, from the generation of electricity to atomic-powered airplanes. The second wish was for food and health and involved using radiation to sterilize foodstuffs and in the treatment of diseases. The third wish was for wisdom, to use nuclear energy wisely and peacefully.
In 1952 Collier's Magazine commissioned a series of articles by science writers from Wernher von Braun and Heinz Haber to w.i.l.l.y Ley to envision the future of s.p.a.ce travel. With ill.u.s.trations by Chesley Bonestell, who did the background artwork for Destination: Moon, and Rolf Klep, these articles were published as three issues of the magazine and later compiled into book form under the t.i.tle Across the s.p.a.ce Frontier. Here again, the "genie" of atomic energy would provide the power to run s.p.a.ce stations and enable manned missions to Mars. Before the grim realities of mutated Swedish former wrestlers set in, there was a real sense of optimism-that the taming of the atom and our understanding of nuclear physics would make the promised utopias of science fiction a reality.
What went wrong? While we fortunately avoided glow-in-the-dark Mickey Rooneys, we never got the atomic planes either. Well, the atomic planes were a bad idea from the start. Haber's Dell paperback companion to the Disneyland television program argued, "In aviation, the weight of the fuel has always been a discouraging limitation." (Now it's the cost of the jet fuel. But back in 1956, no one envisioned the end of cheap oil.) While a smaller nuclear reactor can replace a large quant.i.ty of fuel, the s.h.i.+elding necessary to prevent killing or sterilizing the pa.s.sengers and crew would more than compensate for the missing fuel weight. Haber suggested using water as s.h.i.+elding, but the now heavier plane would require a runway miles long-all of which hardly seems worth the trouble simply to be able to avoid refueling on long flights.
Similarly stillborn were plans for atomic automobiles. In 1957 Ford proposed a car called the Nucleon,33 in which the internal combustion engine would be replaced by a small nuclear reactor located in the back trunk. The heat from a nuclear fission reaction would boil water, and the steam would turn turbines, providing torque for the wheels and electrical power, as in a nuclear electrical power plant. The hazard to the driver from exposure to nuclear radiation, and to other motorists from a traffic accident, was to be offset by the improved mileage-it was antic.i.p.ated that the Nucleon could travel five thousand miles before the atomic core needed replacement. Though never built, the three-eighths-scale model unveiled by Ford is notable for a mini-cooling tower behind the pa.s.senger section for the nuclear reactor and tail fins nearly as tall as the car itself.
Certainly the benefits of atomic-powered travel outweigh the costs when considering underwater transportation. The first U.S. Navy nuclear-powered submarine, the Nautilus, was launched in 1954, and since then a considerable fraction of the global fleet of submarines is powered by small nuclear reactors. The Nautilus in Jules Verne's Twenty Thousand Leagues Under the Sea was powered by electricity drawn from the ocean, via a mechanism not clearly described ("Professor," said Captain Nemo, "my electricity is not everybody's and that is all I wish to say about it. . . . "), and consequently was also able to travel great distances without refueling (twenty thousand leagues refers to the distance the Nautilus travels, not its depth beneath the water's surface, and is equivalent to sixty thousand miles). As the sole market for submarines is the military,34 profitability constraints do not apply.
It is true that nuclear power is extremely efficient compared to other methods of generating heat, at least when compared to the equivalent ma.s.s of fossil fuel needed to produce the same energy. The devil is in the details-particularly in the waste products. While there is danger in the waste exhaust of fossil fuels, there the hazard is long-term, while radioactivity is of immediate concern to all it strikes. To see why we must be concerned when a nucleus decays, we first need to understand why any nucleus sticks together in the first place.
When Ernest Rutherford's lab conducted experiments involving high-speed alpha particles (consisting of two protons and two neutrons, essentially a helium nucleus) scattering from thin metal foils, they observed that occasionally, say one time in ten thousand, the alpha particles were reflected backward from the metal foil. These data led them to conclude that the atom was mostly empty s.p.a.ce (which we now understand to be occupied by the "probability clouds" for the electrons) and a small inner core in which the positive charges reside. The positive charges have to be in the center, for only a concentrated volume of positive charge could generate a repulsive force sufficient to deflect the high-velocity alpha particles (which themselves contain two positive charges) backward from their initial trajectory. This nucleus had to be small, in fact, roughly one ten-thousandth the diameter of the atom itself, in order to account for the fact that only one in ten thousand alpha particles experiences a significant deflection (as a direct hit is necessary to send the alpha reeling backward).35 Knowing that the positive charges in the atom were in the nucleus answered the question of the structure of the atom but raised several more. It was known from chemistry that the number of positive charges in an atom (balanced by an equal number of negatively charged electrons) determined its chemical nature. Hydro gen has one proton in its nucleus, helium has two, carbon has six protons, while gold has seventy-nine. The electron's ma.s.s is nearly two thousand times smaller than a proton's, so nearly all of the ma.s.s of the atom derives from its nucleus. But the weight of an atom does not correspond to the number of net positive charges it has. Hydrogen has a ma.s.s equivalent to a single proton, but helium's ma.s.s is equal to that of four protons, carbon's is twelve, and gold's ma.s.s would suggest that it has 197 protons in its nucleus.
How can helium have a nucleus with only two positive charges, but a ma.s.s four times larger than that of hydrogen? For a while, physicists thought that the nucleus contained both protons and electrons. That is, a helium nucleus would consist of four protons and two electrons. That way, it would have a ma.s.s four times larger than hydrogen's single proton, as observed, but a net charge of +4-2 = +2, which also agreed with the experiments. As the electron has a much smaller ma.s.s than the proton, measurements at the time were not precise enough to rule this possibility out.
Experiments on the nuclear magnetic field (remember that protons have small magnetic fields, as discussed in Chapter 4) and how it influenced the manner by which the electrons in the atom absorbed light (more on this when we discuss magnetic resonance imaging) led scientists to conclude that a helium nucleus, for example, could not have four protons and two electrons. Instead there must be two protons in a helium nucleus, and two other particles that weigh as much as a proton but have no electrical charge. In 1932, James Chadwick bombarded beryllium with alpha particles and detected a new part of the atom: the neutron. Thus one mystery about the nucleus was solved-the atom consisted of electrons...o...b..ting a nucleus that contained protons and neutrons.
But this left another, more challenging mystery. As it is well known that like positive charges repel one another (this was, after all, the basis by which Rutherford had discovered the nucleus-by observing it repel positively charged alpha particles), then why do the positively charged protons in the nucleus not fly away from one another? The answer is-they do! Protons "feel" electrical forces inside the nucleus just the same as outside the nucleus. The fact that they stay inside the small nuclear volume implies that they feel a second, stronger force that prevents them from leaving the nucleus. A clue about this force is found by considering the heavier siblings of each element, termed "isotopes." Two atoms are isotopes if their nuclei have the same number of protons (thus making them identical chemically) but differing numbers of neutrons (thus giving them different ma.s.ses). There are versions of hydrogen that have one proton and zero, one, or two neutrons,36 but there are no isotopes of helium or any other element that have two or more protons and no neutrons. This indicates that the neutrons in the nucleus play a crucial role in providing the "strong force" that holds the nucleus together (the same strong force we encountered in Chapter 5).
How much stronger is this force than electromagnetism? If this additional force were ten times greater than the electrical repulsion, then it would be hard to make heavy elements such as silicon, with fourteen protons, or t.i.tanium, with twenty-two protons. If the force were a thousand times stronger, then we might expect to see elements with several hundred protons in the nucleus, and we do not. The fact that the heaviest natural element found on Earth is uranium, with ninety-two protons, indicates that this strong attractive force holding the nucleus together is roughly one hundred times greater than the electrical repulsion between the protons.
But even uranium is not stable, and if you wait long enough, all of your uranium will undergo trans.m.u.tations to smaller elements by a process known as radioactive decay. Lead, with fifty-six protons and 126 neutrons, is the largest element that does not decay and is therefore stable. You can construct heavier nuclei, but when the "tower of blocks" of protons and neutrons becomes too tall (for each additional proton means more neutrons have to be present to keep it together), eventually the slightest perturbation will cause the tower to collapse. When it does, it loses energy by emitting radiation in the form of high-energy photons (gamma rays) or high-speed subatomic particles, such as electrons, neutrons, or alpha particles.
In fact, some of the larger nuclei are so unstable that all you have to do is give them a tap, and they fly apart. Uranium, so valuable in the middle of the 1950s that it would tempt Mickey Rooney out into an atomic testing site, is one such element. A dictionary from the end of the nineteenth century described uranium as "a heavy, practically worthless metal." But this was before Otto Hahn and Fritz Stra.s.smann split a uranium nucleus apart in 1938.
Nuclear fission is the breaking apart of a large nucleus into two roughly equal nuclei. It turns out that to get a uranium nucleus to split into smaller pieces, one must hit it gently with a slow-moving neutron. Electrons are too light to do much damage, and protons or positively charged alpha particles are deflected by the large positive charge of the uranium nucleus and therefore can't get close enough to do any harm. Thus, until the discovery of the neutron by Chadwick in 1932, there was not a suitable tool with which to strike the uranium atom.
However, the neutrons released from radioactive decays in Chadwick's experiment were too energetic. A fast neutron has a large momentum, and through the de Broglie relations.h.i.+p (Chapter 3), the larger the momentum, the smaller the de Broglie wavelength. Finding the nucleus within an atom is always a difficult trickif the electron's probability cloud, which denotes the "size" of the atom, were the size of your thumbnail (about one square centimeter) then the nucleus on the atom would be a single cell in the thumbnail. In 1937 Italian physicist Enrico Fermi discovered that pa.s.sing a beam of neutrons through a length of wax caused the neutrons to slow down as they collided with the large paraffin molecules, but not come to rest, as they did when striking a similar length of lead. The slower the neutron is moving, the lower its momentum, and the larger its de Broglie wavelength. A larger wavelength gives the neutron more of a chance to intersect with the nucleus's matter-wave, just as you have a greater chance of coming across a bush in a garden at night if you walk with your arms outstretched rather than flat against your sides.
If the neutron strikes the uranium nucleus, then there is a chance that the strong force within the nucleus will capture this neutron (recall that the strong force has a very short range, and the neutron has to be right at the nucleus to feel it), making the uranium nucleus slightly heavier. But the tower of protons and neutrons in the uranium nucleus is already barely stable, and the addition of one more neutron turns out to be too much for the nucleus to support. So it usually tumbles into two smaller nuclei (typically krypton, with thirty-six protons and eighty-nine neutrons, and barium, with fifty-six protons and 144 neutrons, but alternative fracture products are observed), along with releasing either two or three more slowly moving neutrons,37 and energy, in the form of kinetic energy of the smaller nuclei and gamma rays.
Where does the kinetic energy of the nuclear fission by-products come from? Electrostatics. While gravity and electromagnetism can exert a force even when objects are miles and miles apart (though the force gets weaker the greater the distance), the strong force holding the nucleus together disappears for lengths larger than the diameter of a neutron. Consequently, once the two large nuclear fragments break apart in the fissioning uranium, there is no strong force to hold them. But the thirty-six protons in the krypton nucleus and the fifty-six protons in the barium nucleus repel each other, and as they are initially very close, the repulsive force between them is strong. The kinetic energy of the nuclear fission products, which accounts for the horrible destructive capacity of an atomic blast, derives from basic electrostatics. Elements such as uranium or plutonium are easier to break apart than lighter elements, but all matter would violently explode if the strong force could be, even momentarily, turned off, as in Watchmen's unfortunate Dr. Osterman from Chapter 5.
Many chemical reactions, such as when dynamite undergoes combustion, give off heat as a by-product. By "heat" I mean that the reaction products have a larger kinetic energy than the initial reactants. Nearly all chemical reactions have an energy scale of roughly one electron Volt per molecule, within a factor of ten or so (that is, sometimes the reaction takes a fraction of an electron Volt, while in some other cases, depending on the chemistry, the reaction could involve ten electron Volts or more). In contrast, a single uranium nucleus undergoing fission and splitting into two smaller nuclei releases about two hundred million electron Volts of energy. Consequently, the energy released in fission is much higher, per atom of initial material, than in a chemical reaction. But two hundred million electron Volts, from a single uranium atom, would be less noticeable than a mosquito bite. By gathering together several thousand trillion trillion uranium atoms, the resulting energy released can be devastating, even though these thousand trillion trillion uranium atoms would weigh only a few pounds. It would take more than twenty thousand tons of dynamite to release an equivalent amount of energy.
A given ma.s.s of uranium is dangerous, but half this ma.s.s is not. Why not? When the uranium nucleus captures a slow-moving neutron and fissions into two lighter nuclei, it also releases two or three slowly moving neutrons. Thus, the decay of one uranium atom provides the means to cause two more uranium nuclei to undergo fission, and each one of those can make two more nuclei decay. Starting with the fission of a single atom, a large number of additional atoms can be induced to decay in a chain reaction-but only if the neutrons emitted from the first uranium atom strike other nuclei. Remember that most of the atom is empty s.p.a.ce and that the diameter of the nucleus is only one ten thousandth that of the atom itself. If the decaying uranium atom does not have a sufficient number of other atoms surrounding it, then there will be low-level decays that provide energy (useful for an electrical power plant) but not enough reactions to yield an explosive chain reaction.
The trick to making an atomic bomb is to have two separate pieces of uranium, each less than the "critical ma.s.s" (so defined as at this ma.s.s a chain reaction is ensured), and bring them together into one volume quickly enough that the reactions do not die out but continue to grow. It's not the ma.s.s itself that is critical for a chain reaction, but the number of uranium atoms, so that the released neutrons have a high probability of striking another nucleus and initiating another fission event. In this case a hundred pounds of uranium is transformed into an atomic bomb that can annihilate several square miles and cause extensive damage at larger distances.
Children in the early 1950s could learn all about radioactivity if their parents sh.e.l.led out fifty bucks for the Gilbert's U-238 Atomic Energy Lab. This kit was the nuclear physics version of a chemistry set and came complete with radioactive sources that emitted alpha, beta, and gamma radiation, a Geiger counter, and a mini-cloud chamber for seeing the tracks created by high-speed radioactive particles. The kit included both an instruction manual and an informational comic t.i.tled Learn How Dagwood Splits the Atom. This comic featured text that was scientifically thorough and accurate, with an introduction by Joe Considine, an International News Service correspondent who covered the Bikini Atoll nuclear tests and wrote the script for the 1947 docudrama about atomic energy The Beginning or the End (not to be confused the 1957 science fiction film The Beginning of the End, which featured the attack of radioactive giant locusts), and a foreword by Lieutenant General Leslie R. Groves, the head of military operations at the Manhattan Project. In the accompanying comic, Mandrake the Magician shrinks Dagwood b.u.mstead, his wife, Blondie, and their kids and dogs to subatomic size, so that they, together with Popeye, Olive Oyl, and Wimpy, can observe firsthand the inner workings of nuclear decay and fission. Figure 22 shows a page from this booklet, as Dagwood, unable even with Popeye's a.s.sistance to overcome the strong nuclear force holding a uranium 235 nucleus together, is nevertheless able to initiate a chain reaction of fission decays when he uses a "neutron bazooka" to strike the nucleus just right.
While the world read in their newspapers on August 7, 1945, of the previous day's successful detonation of an atomic bomb by the U.S. military over Hiros.h.i.+ma, j.a.pan-this was not the first time atomic weapons entered the public consciousness. Figure 23 shows a Buck Rogers newspaper strip published in 1929. When the submarine Buck and his colleagues are on is held fast by a giant octopus, their only hope is to blast themselves free, using the awful destructive potential of an atomic torpedo. A full sixteen years before the Manhattan Project, Phil Nowlan and d.i.c.k Calkins, creators of the "Buck Rogers, 2429 A.D." comic strip were confident that their readers would know that an atomic torpedo was a more powerful version of the regular underwater missile.
Moreover, according to adventure pulp magazines, j.a.pan knew as well of the ability of atomic weapons to destroy a major city, six years before the U.S. bombing of Hiros.h.i.+ma and Nagasaki. In Secret Service Operator No. 5, issue # 47, published in September 1939, it is the United States that is attacked by the invading troops of the "Yellow Vulture," a thinly disguised, racist version of the j.a.panese Empire. In a tale t.i.tled "Corpse Cavalry of the Yellow Vulture," the troops of the Yellow Vulture obliterate Was.h.i.+ngton, D.C., killing the president, Agent Q-6 (father to Operator no. 5), and most of the Was.h.i.+ngton establishment by using an atomic bomb.
Figure 22: Page from Learn How Dagwood Splits the Atom in which Mandrake the Magician, having shrunk Dagwood b.u.mstead and his family to subatomic size, narrates the mechanism of a uranium fission chain reaction, while Dagwood grabs his daughter and tries to quickly exit the nuclear pile.
One of the earliest recorded uses in fiction of "atomic" as a modifier to signify the enhanced lethality of a weapon is in a 1914 science fiction novel by H. G. Wells. In The World Set Free, Wells describes atomic bombs raining down with horrible destructive power and dropped from noiseless, atomic-powered airplanes.
How did the general population know about "atomic weapons" years before the Manhattan Project? It was thanks in part to the writings of Frederick Soddy, Ernest Rutherford's colleague in earlier studies of nuclear radioactivity. Soddy penned a series of popular science books, the best known of which, The Interpretation of Radium: Being the Substance of Six Free Popular Experimental Lectures Delivered at the University of Glasgow, was a best seller when published in 1909. It made quite an impression on Herbert George Wells, who incorporated the concept of atomic-based weapons weighing only a few pounds and releasing tremendous energy and lingering radiation damage into his novel The World Set Free. In Wells's novel, an atomic war between the nations of Europe and the United States leads to the formation of a proto-United Nations, where the surviving world leaders decide to form a new world order and establish a one-world government based upon the principles of socialism, rejecting capitalism, which was to blame for leading the nations into a nuclear confrontation.
Figure 23: Buck Rogers, in his daily syndicated newspaper strip in 1929, employs an "atomic torpedo" to devastating effect.
This novel made a strong impression on one particular reader in 1932. Both Wells's vision of a one-world government run by socialistic principles and, equally important, his descriptions of horrific atomic weapons galvanized Hungarian physicist Leo Szilard. This fan of Wells was no ordinary reader-Szilard would, in 1933, be the first to conceive of a possible nuclear chain reaction (patenting the idea in 1934-four years before Hahn and Stra.s.smann first split a uranium nucleus!). In 1939, Szilard wrote a letter to President Franklin Roosevelt, signed by Albert Einstein, urging the development of a nuclear weapons program, which became the Manhattan Project. Thus a popular science book by Soddy, written for a general audience, inspired an H. G. Wells science fiction novel suggesting the possibility of atomic weapons, and this novel in turn was directly responsible for the creation of actual atomic bombs. When publisher Hugo Gernsback launched his science fiction pulp magazine Amazing Stories in 1926, with a reprint of a story by Wells, it is doubtful that he realized how prophetic would be his magazine's motto: "Extravagant Fiction Today . . . Cold Fact Tomorrow."
The fates of Mickey Rooney and Tor Johnson in The Atomic Kid and The Beast of Yucca Flats, respectively, are of course ridiculous, unrealistic portrayals of the effects of exposure to radiation. By the mid-1950s, Doris Day's lighthearted song about the wonders of a Geiger counter would give way to darker implications regarding the effects of nuclear weapon testing.
Ten years after the use of atomic bombs at the end of World War II, science fiction films would clearly and unambiguously establish that the real risk of exposure to radioactive fallout is unchecked gigantism. James Whitmore and James Arness battled ants mutated to the size of helicopters by lingering radioactivity in the New Mexico desert in the 1954 Warner Bros. film Them! Exposure to an atomic testing site would similarly transform Lieutenant Colonel Glenn Manning into The Amazing Colossal Man (1955), who would return to wage the War of the Colossal Beast (1958); feasting on fruits containing radioactive isotopes would create giant locusts, signaling The Beginning of the End (1957); a diet of radioactively contaminated fish similarly causes an octopus to grow to fantastic size in It Came from Beneath the Sea (1955); and radiation in a swamp would provoke The Attack of the Giant Leeches (1959). Occasionally, radioactive exposure would instead lead to miniaturization, as reflected in the strange case of The Incredible Shrinking Man (1957) and the experiments of Dr. Cyclops (1940), whose shrinking beam was powered by atomic rays five years before the Manhattan Project.
"Radioactivity" is an umbrella term for particle or light emissions from nuclei. As discussed in the previous section, when electrons in an atom move from one quantized energy level to another, they do so via the emission or absorption of light,38 which can span a wide range of wavelengths, from the microwave and infrared, to visible light, to ultraviolet and X-rays. Application of the rules of quantum mechanics to the protons and neutrons inside the atomic nucleus find that similarly, only certain quantized energy levels are possible. The energy s.p.a.cing between these quantized levels is much larger than in the atom, thanks to the Heisenberg uncertainty principle. As the spatial extent of the nucleus is much smaller than that of the atom itself, the uncertainty in the location of the protons and neutrons is reduced. Consequently the uncertainty in the value of their momentum is increased, and the larger the momentum (ma.s.s times velocity), the greater the kinetic energy (momentum squared divided by twice the ma.s.s). While typical electronic transitions in an atom involve energies of about a few electron Volts, and occasionally one can observe X-ray emission, which has an energy of a thousand electron Volts, nuclear energy transitions involving electromagnetic radiation consist of gamma rays with energies of several million electron Volts.
As the protons and neutrons inside the nucleus settle from a higher energy level to a lower level (referred to as the "ground state"), there are other ways for them to shed energy aside from emitting gamma-ray photons. There are some nuclei that can lower their energy by emitting an alpha particle (consisting of two protons and two neutrons). The two protons and two neutrons that comprise a helium nucleus are very tightly bound to each other, so if the large, excited nucleus is going to emit any of its protons or neutrons, it is energetically favorable to do so in packets of alpha particles, rather than expending energy breaking the alpha apart. In this way the number of protons inside the larger nucleus decreases by two, so the electronic repulsion between the protons is reduced as well. The alphas come out with a considerable amount of kinetic energy (several million electron Volts, typically). This made them convenient probes for Rutherford when studying the structure of the atom-investigations that led to the discovery of the nucleus.
Even though the nucleus can lower its energy by ejecting an alpha particle, the particles within the alpha are still subject to the strong force, which acts like a barrier holding the subatomic particles together within the nucleus. This barrier is high enough that ordinarily one would not expect any alpha particles to be able to leave the confines of the nucleus. Since alpha particles have been observed exiting the nucleus, there must be a mechanism by which they are able to leak out through this barrier. Here the bizarre phenomenon of quantum mechanical tunneling comes into play. The strong force is so effective at holding the nucleus together that the alpha particle has only one chance in one hundred trillion trillion trillion of escaping. However, its small spatial uncertainty within the nucleus leads to a large momentum uncertainty, and it "rattles around" inside the nucleus, striking the strong-force barrier a billion trillion times a second. Consequently, if one waits several billion years, one will see an alpha quantum mechanically tunnel outside of a nucleus. Once beyond the range of the strong force, the alpha particle is propelled at a high velocity by the same electrostatic repulsion that imparted energy to the fragments of a fissioning uranium nucleus.
Several billion years is a long time-so how are we able to see alphas emitted by radioactive isotopes without waiting so long? The answer to this question leads to an understanding of the concept of a radioactive half-life and in turn elucidates how we know the age of the Earth.
First a basic point about probability: In a lottery involving the random drawing of three digits from 000 to 999, there are one thousand possible outcomes. The lottery office draws the three digits at random, so one day the winning number may be 275 and the next it may be 130 or 477, and so on. If I purchase a ticket with one particular combination, say 927, there is thus one chance in a thousand that I will win the jackpot. a.s.sume that I always play this same number, 927. I could win on the very first day. It's possible, though there is only one chance in a thousand that I will. It is conceivable that I may have to wait extremely long, much longer than a thousand draws, before my one ticket matches the three numbers. Certain combinations may appear as winning numbers many times before my particular ticket pays off.39 I therefore may need to play the game for a long time before my ticket matches that day's winning numbers.
One important similarity between the lottery scenario and the decay of unstable nuclei is that for both, the chance of an "event" occurring (either matching your ticket's numbers with that day's drawings, or having the nucleus undergo a transition to a more stable configuration, with the release of radiation) is the same on any given day. In a real, standard lottery run by most states, there is no restriction on whether a given set of numbers (from the predetermined pool of possible numbers) can be repeated before all other possible combinations are drawn. On any given day, one particular combination of numbers is as likely as any other. Similarly, as the quantum mechanical transition to a lower energy configuration is a probabilistic occurrence, the nucleus is as likely to decay on the first day, the one hundredth, or the millionth. There is no upper limit on how long the nucleus can exist in the excited state before radiating back to a lower energy state. If the nucleus is able to remain in the excited state for a long time, it is not "due" or "expected" to undergo radioactive decay but is as likely to relax to the ground state on the millionth day as on the first. If one plays the lottery long enough, eventually every number that can occur will be drawn. Similarly, if one waits long enough, every unstable nucleus will decay to a lower energy state.
Depending on the nucleus and the nature of the unstable excited state it is in, the probability of decay may be very high or very low. In the lottery a.n.a.logy, you may need to guess only one number from 0 to 9 in order to win the jackpot, or you may need to match seven random two-digit numbers in precise order. In the first case one would not need to play the game very long before winning, while in the second case it could take much longer than several lifetimes (if the lottery selected fresh numbers every day) before a winning match is obtained. Similarly, some elements' unstable nuclei undergo radioactive decay within, on average, a few days or months, while others may take several billion years. However, in the first case there is no reason any given nucleus could not remain undecayed for a long time, while in the second situation there is no physical reason why any given nucleus could not decay almost immediately. It is possible to hit even a seven-digit lottery jackpot with your very first ticket, though I should be so lucky.
If I start with a large number of radioactive atoms, then a plot of the number that avoid decaying into some other isotope as a function of time follows what's termed an "exponential time dependence." To understand this concept, imagine a car driving at sixty miles per hour that suddenly slams on the brakes. How long does it take the car to come to a complete stop? If we a.s.sume that the brakes provide a constant deceleration of ten miles per hour per second, then in six seconds the car will come to a rest. What if the brakes provided a deceleration that depends on how fast the car is moving at any instant? That is, when the car is moving very fast the brakes provide a large force, slowing you down. But if you were driving much more slowly, in a parking lot, say, then the brakes would provide a lower force. If the deceleration is proportional to the velocity, then it turns out that the car never comes to a full stop! (Well, for long times it may be moving so slowly that we could for all intents and purposes say that it had stopped, but if we were to measure the speed, we might find that it is very, very small, less than one millionth of a mile per hour, for example, but never truly zero.) In the first case, that of a constant deceleration, the auto's speed decreases linearly with time. In the second situation, where the deceleration varies with the speed, initially the car slows down dramatically, as it is moving fast and that means the deceleration is large. But as it goes slower and slower, the braking force decreases, so that for long times it is moving very slowly, but the brakes are exerting only a very weak force. A plot of the car's speed against time would be a concave curve called an "exponential decay function."
While the slowing automobile with velocity-sensitive brakes is artificial, the reverse phenomenon-exponential growth that leads to faster and faster increases-is more familiar, at least for those who have watched their savings grow through compound interest. A small amount deposited in the bank that earns a steady fixed interest rate, compounded continuously, will show a small increase initially. But as time progresses, both the original investment and the total interest earned will be subject to the same interest rate, and the returns will soon become much larger as your bank balance benefits from an exponential growth.
Just such an exponential dependence is found for the decay of tritium, an unstable isotope of hydrogen. Normally hydrogen has one proton in its nucleus. The neutrons, partic.i.p.ating in the strong force, are needed in larger nuclei to overcome the electrical repulsion between protons. As hydrogen has only one proton in its nucleus, it is the only element that does not need neutrons, though it is possible for neutrons to be present in the hydrogen nucleus. In hydrogen, one electron is electrostatically bound in a quantum mechanical "orbit" to the single proton in the nucleus. As the chemical properties of an atom are determined by the number of electrons it possesses, which in turn are set by the number of protons in its nucleus, one could form an alternative form of hydrogen containing one proton and one electron, with an extra neutron in the nucleus, and it would behave, for the most part, like ordinary hydrogen. We would call this isotope deuterium. If there were two neutrons and one proton in the nucleus, about which one electron "orbits," this isotope is termed "tritium."40 As ill.u.s.trated in Figure 24, tritium is unstable and, through a mechanism I describe in the next chapter, decays to form an isotope of helium, along with a high-speed electron (a beta ray) like those in Chapter 8 responsible for Dr. Manhattan's blue glow. Figure 24 shows another page from Learn How Dagwood Splits the Atom, whereby the addition of two neutrons to a hydrogen nucleus (that is, a single proton) yields an unstable result. One of the neutrons converts to a proton and another electron, through a mechanism governed by the weak nuclear force, discussed in detail in the next chapter. The decay rate of tritium is very fast, such that for a given nucleus, after only about twelve and a half years, there is a fifty-fifty chance of the isotope decaying.
If the decay rate is so fast, why is there any tritium still around? Because it is constantly being created, when high-speed neutrons formed from cosmic rays collide with nitrogen atoms in the atmosphere. The now unstable nitrogen nuclei decay to form normal carbon and tritium. The tritium generated in the upper atmosphere can be captured by oxygen atoms and forms a version of "heavy water" (remember that aside from the heavier nucleus, tritium behaves chemically the same as normal hydrogen). This tritium-rich water reaches the ground in the form of raindrops. Because we know the decay curve of tritium, comparisons of water from the surface of the ocean to that obtained from greater depths enable determinations of the cycling time for oceanic circulation currents.
Figure 24: Page from Learn How Dagwood Splits the Atom in which Dagwood, his son Junior, and his dog Daisy witness the radioactive transformation of a tritium nucleus into an isotope of helium.
Ideally, in order to measure the time dependence of the tritium decay, one would like to have samples of rainwater from more than a hundred years ago, as well as more recent years all the way to the present. By measuring the fraction of tritium as a function of the age of the water, one could verify the exponential time dependence of its decay. The problem is that one does not have bottles of rainwater dating back more than a century. In a 1954 paper in the Physical Review, Sheldon Kauffman and Willard F. Libby did the next best thing and examined the tritium content of vintage wines. As shown in Figure 25, a plot of the tritium concentration per wine bottle as a function of time, determined from the vintage label, shows that, when measured in 1954, the tritium concentration was very high in a 1951 Hermitage Rhone, but the concentration was dramatically lower in a 1928 Chateaux Laujac Bordeaux. The full curve is very well described by an exponential time dependence. Based on this curve, if in 1954 we wanted a wine with a tritium concentration half as large as that in the 1951 Hermitage, we would decant a 1939 vintage, from which we conclude that the "half-life" of tritium is 12.5 years.
Different radioactive nuclei have different decay rates. All unstable nuclei have exponential decay functions, but the time scale over which the decay occurs may be very different-from minutes to billions of years. Measurements of nuclei with short decay times, such as the tritium in wine bottles example, confirm that the number of nuclei that decay does indeed follow an exponential time dependence. The physics of the nucleus does not change depending on which element we are considering. For those nuclei that have very low decay rates, so that the time to decay is very long, we can nevertheless measure the initial portion of the exponential decay. Mathematical fitting of this curve indicates when the decay function is expected to reach the 50 percent point, and thus we can determine that the half-life of uranium, for example, is several billion years, even though we have not sat in the lab for this length of time to measure the full decay curve.
Figure 25: Plot of the time dependence of tritium concentration in "heavy water" contained in wine bottles. The age of the water sample is determined by the vintage printed on the bottle's label. The longer one waits, the less tritium is present, due to radioactive decay. The solid line is a fit to the data of an exponential time dependence, with a half-life of 12.5 years. Reprinted figure with permission from S. Kaufman and W.F. Libby, Physical Review 93, 1337 (1954).
For a radioactive nucleus with a half-life of one year, if I start with a million atoms, after one year I will have approximately half a million remaining (there will typically be fluctuations about this average number of half a million, as the decays are probabilistic). As the decay rate is independent of the age of the atom, then in the next year, 50 percent of the remaining atoms will decay. That is from an initial number of one million, I will have approximately half a million after one year, a quarter of a million after two years, 125,000 after three years, and so on.
Because the time necessary for one half of the initial population of nuclei to decay is precisely known, we can use carbon dating to determine the age of archeological artifacts. Let's say we start with a million unstable isotopes of carbon. Normally carbon has six protons (and a corresponding six electrons in quantum mechanical "orbits") and six neutrons in its nucleus and is as stable as anything we know of. As there are twelve particles in its nucleus, this form of carbon is called carbon 12. Occasionally collisions with cosmic rays lead to the creation (through a process that we don't have to worry about now) of a form of carbon with six protons but eight neutrons in its nucleus. As it has the same number of protons and electrons as carbon 12, this heavier isotope is chemically identical to normal carbon. However, this form of carbon with eight neutrons (called carbon 14) is unstable and beta decays into nitrogen 14.
The rare heavier carbon 14 is constantly being created by random collisions with cosmic rays and is constantly decaying away into another element. A very small but constant percentage of the carbon in the world is heavy, unstable carbon 14. This holds for the food we eat, the clothes we wear, and pretty much everything that contains carbon atoms. Consequently, a small fraction of the carbon in our bodies is this unstable heavier form. The half-life for heavy carbon to decay is about 5,700 years. So normally we ingest heavy carbon by its random presence in the food we eat, and we lose heavy carbon through normal biological processes when we eliminate old cell material. This process comes to a rather abrupt stop when we die (the flux of cosmic rays on the Earth's surface is low enough that we don't have to worry about carbon 14 creation in our corpse). At death the amount of heavy carbon in our bodies, our skin, our tissues, and our bones is fixed. A future archaeologist, finding our skeletons, measures the quant.i.ty of carbon 14 and finds that it is only half of the normal amount of carbon 14. She can then confidently state that we died approximately 5,700 years ago. If the amount of heavy carbon is one quarter of the current level of carbon 14, then two half-lives must have pa.s.sed, and our death is placed at roughly 11,400 years in the past. In this way any material containing organic matter, whether it be ancient bones or the shroud of Turin, can be dated from its last point of carbon intake. Willard Libby, who used old wine to obtain new measurements of tritium decays (Figure 25) shared the 1960 n.o.bel Prize in chemistry for developing carbon 14 dating.
Longer-lived isotopes, such as uranium 235 and uranium 238, have half-lives of roughly billions of years. These two forms of uranium were generated in a supernova explosion that created all the atoms that went on to form the planets and moons in the solar system (more on this later). a.s.suming that initially they are created in equal concentrations, ascertaining their half-lives through independent measurements, and seeing the fraction of uranium 235 and uranium 238 present on the Earth today, we can calculate how long the Earth has been around to give the uranium isotopes a chance to decay to their present proportions.41 The answer turns out to be about 4.5 billion years.
We thus know the age of the Earth through our understanding of quantum mechanics, the same quantum physics that underlies the field of solid-state physics. Without quantum mechanics, there would be no semiconductor revolution, and the nearly countless electronic devices we employ would not be possible. It is of course your right to believe that the Earth is actually much younger than its age determined by radioactive isotope dating, but to be consistent, you should stop believing in your cell phone, too!
Elements that emit gamma rays, alpha particles, or beta particles are radioactive-while materials that are exposed to these nuclear ejections are described as irradiated. As mentioned at the start of this chapter, science fiction films in the 1950s ascribed to irradiation the mutation of animals and people into giants, though occasionally a miniaturization effect was possible. What exactly are the real, non-Hollywood movie, effects of exposure to radiation? Not all radioactivity is created equal, and some is more harmful than others.
The emission of radioactivity results when a nucleus makes a quantum transition from a high energy state to a lower energy configuration. Recall that the energy s.p.a.cing between quantum states in the nucleus is on the order of a million electron Volts, while electronic states in an atom are on the order of a few electron Volts. Electronic transitions involve energies in the ballpark of visible light, while the energy scale of nuclear quantum jumps is much larger. When the electrons in a neon atom make quantum transitions, they emit red light, which we a.s.sociate with neon signs. When the neon atom's nucleus ma