The Amazing Story of Quantum Mechanics (21 page)

Detectors were eventually constructed to observe these particles, and their existence was confirmed in 1956. These particles not only really exist, aside from photons they are the most common particle in the universe. Their interactions with matter are governed by the weak nuclear force, which is one hundred billion times weaker than electromagnetism (the force by which electrons interact with matter). Neutrinos consequently barely notice normal matter (it takes more than two light years of lead—that is, a length of more than ten trillion miles—to stop one). If you hold out your thumb and blink, during that time period more than a billion neutrinos will pass through your thumbnail.

Dr. Solar, after his radiation overdose, must have gained an uncontrolled ability to induce beta decay in any object with which he came into contact. If a gold atom, with seventy-nine protons, seventy-nine electrons, and 118 neutrons, has one of its neutrons spontaneously decay into a proton and an electron, then it will have eighty protons, eighty electrons, and 117 neutrons. The lightest, stable configuration of mercury has eighty protons, eighty electrons, and 118 neutrons, so Dr. Solar will have created an unstable isotope of mercury in Figure 27. The half-life of this isotope of mercury with 117 neutrons is roughly two and a half days, so there will be time for Solar to finish his adventure and try to restore the transmuted mercury back to its original golden state. While transforming one element into its periodic-table neighbor via neutron beta decay is not quite the alchemist’s dream of transmuting lead into gold (normal beta decay would convert platinum, with seventy-eight protons, into gold, with seventy-nine protons, so, depending on world exchange prices, you may wind up losing money on the deal), a process known as “reverse beta decay” would turn mercury into gold. While we cannot initiate such a conversion on Earth at will, fortunately this inverse process occurs constantly in the center of the sun, keeping the sun shining and providing the basis of all life.

The light from the sun—which is transformed by photosynthesis into chemical energy stored within plants, which in turn provides us with the energy we need to maintain our metabolisms—originates from nuclear transformations in the star’s core. Four protons, that is, hydrogen nuclei, subjected to the extreme pressures and temperatures at the center of the sun, are fused together to form helium nuclei. But a helium nucleus consists of two protons and two neutrons, not four protons. Recall that neutrons are necessary as mediators of the strong nuclear force that holds the nucleus together. Thus, to make helium out of hydrogen, you first have to combine two protons and then through
reverse
beta decay convert one of the protons into a neutron.

I argued above that a single proton cannot convert into a neutron, as the mass of the proton is less than that of the neutron, and lighter objects cannot decay into heavier products. If two protons collide, the weak force operates on the protons, turning one into a neutron through reverse beta decay, as illustrated in Figure 28. The proton and neutron, subject to the strong force, become bound (now a deuterium nucleus—an isotope of hydrogen) and lower their en-ergy compared to an isolated proton and neutron. This lower energy is reflected in a smaller mass for the deuterium nucleus, relative to a free proton and neutron. While the mass difference is very small, through E = mc
²
the energy difference of the bound deuterium is significant, and it emits a 2.225-million-electron-Volt gamma-ray photon during formation. In addition to the neutron generated by the weak force, the reaction creating a deuterium nucleus yields an antimatter electron (which has a positive electrical charge like a proton, but the mass of an electron) and a neutrino.

The weak force extends over a length scale roughly one thousand times smaller than that of the strong force, which itself acts only over distances less than the diameter of a nucleus. Two protons, both being positively charged, repel each other, and the closer they are, the greater the repulsive force. So one must force the two protons very close together, overcoming their electrical repulsion, in order for there to be an opportunity for the weak force to transform, through reverse beta decay, one of the protons into a neutron. The temperatures and pressures in the center of the sun are enormous, so that there are many opportunities for high-velocity collisions between two protons. However, even at the center of the sun the proton speeds are not sufficient to overcome the electrical repulsion when they draw too close. How do they manage to get past this electrical barrier? Through quantum mechanical tunneling!
⁴⁵
Just as the alpha particles in radioactive decay use tunneling to escape the strong-force barrier around the nucleus that keeps the protons and neutrons together, the two protons that join together, forming the simplest isotope of hydrogen, must tunnel to overcome the barrier of their mutual repulsion.

The deuterium nucleus created in the center of the sun is stable and continues to collide with other protons. Combining this deuterium with another proton forms a nucleus with two protons (that is, helium) but only one neutron (making it helium 3, a lighter isotope of helium). Here again quantum-mechanical tunneling is required to get the second proton close enough to the deuterium nucleus, overcoming the electrical proton-proton repulsion, for the strong force to hold the second proton in the now larger nucleus. The lower energy of this bound state results in the release of another gamma-ray photon. This reaction is much more likely than for two deuterium nuclei to combine to form normal helium (two protons and two neutrons).

There are then many different ways that the helium 3 or deuterium nuclei can interact to form a stable helium nucleus, all of which involve quantum mechanical tunneling to get the positively charged nuclei close enough for the strong force to operate, resulting in the release of a great deal of energy in the form of kinetic energy of the nuclei, gamma rays, and neutrinos. The neutrinos pass right through the sun and head off in all directions, while the gammas heat up the nuclei and electrons in the center, accelerating them and causing them to emit electromagnetic radiation at all wavelengths. The light created in the center of the sun is scattered many, many times before reaching the surface, where it then takes the brief, eight-and-a-half-minute journey to Earth. Before reaching the surface, the average photon spends forty thousand years colliding with the dense nuclear matter in the sun’s interior. The outward energy pressure counteracts the inward gravitational pull and keeps the diameter of the sun fairly stable.

In addition to providing us with energy, this fusion process is the mechanism by which elements heavier than helium are synthesized. Our sun is actually a second-generation star that formed after a much larger star passed through its life cycle and “went supernova.” Our sun converts a great deal of hydrogen as it generates energy—approximately six hundred million tons per second. But eventually stars exhaust their supply of hydrogen, and the star collapses until the temperature and pressure rise to the point where helium nuclei begin to fuse, forming carbon. The process continues, generating nitrogen, oxygen, silicon, and other heavy elements up the periodic table to iron and nickel. However, the larger the nucleus created, the less energy is released per reactant, and at the iron/nickel point, the outward flow of energy is insufficient to counteract the inward gravitational pull. At this stage the star collapses onto itself; in the process, all elements heavier than iron are created, and there is an explosive outpouring of energy as the star becomes a supernova, releasing as much energy in a period of several weeks as our sun does over its entire lifetime. It is from the elements synthesized in a much larger star that lived and underwent a violent demise that the planets and sun of our solar system formed.

The power of the atomic bomb results from the breaking apart of large nuclei, such as uranium or plutonium, in a fission process, described in Chapter 9. Current nuclear power plants, such as the one that went critical and injured Dr. Solar at the start of this chapter, are fission reactors. They require rare radioactive isotopes as fuel, and their by-products are unstable isotopes, which are themselves radioactive and harmful to people. After the atomic bomb, the hydrogen bomb was developed. This weapon utilizes a fission reaction to initiate a fusion reaction—the energy of an atomic bomb is employed to force heavy isotopes of hydrogen and helium to fuse and release even more energy. For more than fifty years, scientists have been attempting to construct a fusion reactor that could create energy for electricity production, harnessing the power of the hydrogen bomb and the sun for peaceful, controlled terrestrial needs. The required fuel for a fusion reactor involves isotopes of hydrogen (typically deuterium and tritium), which may be harvested from naturally occurring isotopes of seawater, and the reaction products are nonradioactive. The obstacle is to replicate, in a controlled manner, the temperatures and pressures at the center of the sun. While the engineering challenges have indeed been formidable, a consortium of nations including Europe, Russia, Japan, and the United States are constructing a pilot fusion power plant (the International Thermonuclear Experimental Reactor, or ITER) to examine the feasibility of using nuclear fusion for electricity generation.

Back in the late 1980s there was a brief flurry of interest in reports that nuclear fusion had been achieved in a small tabletop experiment involving the electrolysis of heavy water using a palladium electrode. This so-called cold fusion process proposed that the deuterium nuclei, embedded within the metal electrode, were undergoing fusion and creating helium nuclei, with a concurrent release of excess heat. Whatever was going on in their device, it was not nuclear fusion, and it’s a good thing for the chemists involved in this project that they were not in fact generating fusion reactions. A by-product of this particular fusion reaction is high-energy neutrons that would have killed anyone unlucky enough to be in the lab at the time. Moreover, as discussed earlier, fusion reactions within the center of the sun, at temperatures of millions of degrees, require quantum mechanical tunneling for the protons to overcome their electrical repulsion. Fusion at room temperature in a palladium electrode is even more dependent on tunneling to proceed. A well-established feature of quantum mechanics is that the tunneling probability is very sensitive to the mass of the object involved. The smaller the mass, the lower the momentum and the longer the de Broglie wavelength, which can extend farther through the forbidden region, increasing the probability of finding the object on the other side of the barrier. Yet the initial investigators of “cold fusion” found no difference whether they used heavy water or ordinary tap water, whereas the difference in mass should have had a large effect on the fusion process.

For cold fusion to be a real phenomenon, it would require a suspension or violation of the principles of quantum mechanics, which underlies our understanding of solid-state physics, lasers, transistors, and all of the personal electronic devices they enable. Nevertheless, one might be tempted to give these up, if we could make cold fusion a physical reality. After all, a small cylinder capable of generating the power of the sun would make an awesome power supply for a jet pack!

The agreement between theoretical
predictions of atomic properties using quantum mechanics, such as the wavelengths of light emitted when an excited hydrogen atom relaxes back to its ground state, and experimental measurements of these wavelengths is nothing short of amazing. But if that were all that quantum mechanics could do, it most certainly would not have “made the future.” We would still be living in the “vacuum-tube age” and would not have laptop computers, cell phones, DVDs, or magnetic resonance imaging devices.

The quantum descriptions of Schrödinger and Heisenberg accurately account for the properties of a single atom, but very rarely does one encounter an isolated, single hydrogen atom, or any type of atom or molecule by itself. A typical cubic centimeter of a liquid or solid, about the size of a sugar cube, contains roughly a trillion trillion atoms. The power of quantum mechanics is that it also provides an understanding of the properties of these trillion trillion atoms and accounts for why some materials are metals, some are insulators, and others are semiconductors. Fortunately for us, it turns out that if one understands the behavior when
two
entities are brought close enough to each other that their Schrödinger wave functions overlap, then this tells us nearly all we need to know to understand the results of a trillion trillion entities in close quarters.