George Gamow used the newly established quantum mechanics to explain the puzzling phenomenon of radioactive alpha decay.
In 1928, George Gamow provided a theoretical explanation of the phenomenon of radioactive alpha decay. The newly established quantum mechanics
Radioactivity is a probabilistic phenomenon. All radioactive nuclei change as a result of one or more of the three types of disintegration, but when disintegration occurs to one particular nucleus, it is unpredictable. It may happen instantly, or it may occur in the remote future. Some nuclei (isotopes) disintegrate rapidly, whereas others disintegrate slowly. The probabilistic character of the phenomenon required physicists to use statistical concepts such as the “half-life” to describe and discuss them. The half-life of an isotope is the time for one-half of any given quantity of the nuclei to disintegrate. Half-lives vary vastly from one species of nuclei to another. Some isotopes are very radioactive; in one-trillionth of a second, a half of this type of atom could change its identity. Some isotopes are radioactively very stable; it may take one trillion years for half of this type of atom to change.
In 1911, two physicists in Rutherford’s group, Hans Geiger and John Mitchell Nuttall, derived from experimental data a remarkable law that relates the half-life of a species of nuclei to the energy of the alpha particles emitted from them: the parent nuclei. The Geiger-Nuttall law
In 1927, Rutherford published his discovery of the phenomenon of alpha decay. Gamow conceived his quantum theory of tunneling from this publication. From the standpoint of classical physics, the phenomena were simply paradoxical. First, the experiment of atomic scattering made it clear that every atom has a positively charged, small, and heavy nucleus. As alpha particles are also positively charged when they approach a nucleus, because of the mutual repulsion between electricity of the same sign, they are rejected and scattered by the nuclei. Thus, for positive charges, including alpha particles, the atomic nucleus is surrounded with a barrier of potential energy.
By shooting alpha particles of different kinetic energy at various species of nuclei, Rutherford assessed the height of the potential barrier around a nucleus, which could be as high as 25 to 35 MeV, several times the kinetic energy of alpha particles. For example, uranium 238 is a radioactive species that emits alpha particles of 4.2 MeV. The scattering experiment showed that the potential barrier around the uranium 238 nucleus might be as high as 25 MeV, more than five times the kinetic energy of the alpha particle that the same nucleus sometimes emits. It was not known how a 4.2 MeV alpha particle could escape a 25 MeV barrier. Rutherford proposed an ingenious classical solution to the puzzle. He suggested that, starting from the nucleus, each alpha particle is accompanied by two electrons that neutralize its positive charge. For this neutralized alpha particle, the potential barrier is no longer a barrier, and it has no difficulty passing the barrier zone. After sending off the alpha particle, the two electrons somehow separate from it and return into the nucleus. Gamow, however, thought this theory was too ingenious; he believed that the phenomenon was another quantum event inexplicable to classical physics.
Louis de Broglie’s first step in 1925 toward the establishment of quantum mechanics was a startling suggestion. He argued, on the basis of analogy with classical physics, that every elementary particle is associated with a “matter wave.” One year later, following de Broglie’s lead, Erwin Schrödinger introduced a general “wave equation.” He stated that his differential equation should solve microcosmic problems in general—such as Sir Isaac Newton’s equation, the second law of motion, in classical mechanics. Werner Heisenberg formulated his version of microcosmic mechanics in 1925. Atomic spectra are sharp lines representing radiations with definite frequencies, intensities, and polarizations. One of Niels Bohr’s basic ideas was that spectral lines were transitions between quantum states. As the easiest way to specify a quantum state is to assign an integer to it, the transition between two quantum states could be specified by a pair of integers. Heisenberg pursued this line of thinking and concluded that every microcosmic “observable” should be specified the same way: by a pair of integers. Consequently, Heisenberg’s mechanics was formulated with matrices—that is, square arrays of numbers. This was the origin of matrix mechanics,
In 1927, Heisenberg and Born succeeded in arriving at important results that would clarify the physical meaning of the new quantum mechanics: Heisenberg formulated the “uncertainty principle”
In the summer of 1928, Gamow applied these empirical and theoretical results to solve a long-standing paradox in the phenomenon of radioactivity. He followed de Broglie in using an analogue from classical physics, the relation between geometrical and wave optics, especially with regard to the issue of total reflection, which is a logical consequence of geometrical optics. According to the wave optics, however, no total reflection is total. Gamow pointed out that, according to wave mechanics, penetration into a potential barrier of a microcosmic particle, although with insufficient kinetic energy, is not impossible. Gamow solved the Schrödinger equation of this problem and showed that the wave function beyond the barrier did not vanish. Thus, according to Born’s statistical interpretation of the wave function, the probability for the particle to tunnel through the barrier is not nil. Probability should depend on how large the barrier is. The new quantum mechanics could calculate the exact dependence of the probability on the height and the width of the barrier: The higher and wider the barrier is, the smaller the probability becomes. The theory also shows that, for an ordinary baseball or tennis ball, for example, the chance of penetration, let alone tunneling through, is practically zero.
It soon became evident that the quantum effect of “tunneling” also could be derived directly from Heisenberg’s uncertainty principle, more specifically, from its energy-time format. This was a satisfying step that further demonstrated the inherent consistency of quantum mechanics.
Following the initial theoretical success, Gamow discussed the tunneling of potential barriers with John Douglas Cockcroft
The empirical equations of alpha decay—the Geiger-Nuttall law—together with the conspicuous fact that radioactive half-lives vary in a vast range (from a trillionth of a second to trillions of years) were now given a unified quantum theoretical explanation. The great success of the new theory in a new realm of physical phenomena, and on the difficult issues of the probabilistic nature of the microcosm and the statistical character of its theory, left an immediate and dramatic impact in scientific circles.
The founding of quantum mechanics between 1925 and 1927 represented a denouement of prolonged and collective effort in explaining physical and chemical phenomena pertaining to the structure of the atom. To the practicing physicists of the time, the denouement was also a propitious beginning. The significant development showed that microcosmic phenomena needed a new type of mechanics, intrinsically different from the classical Newtonian mechanics so that it could be used to extend and refine the original crude theories of atomic and molecular structures.
The timely appearance of publications by Gamow, Ronald Wilfred Gurney, and Edward U. Condon signaled the beginning of the theoretical study of the atomic nucleus. More significant, their theory of quantum tunneling dramatically furthered the success of quantum mechanics and strengthened confidence in this new and strange theory. Quantum tunneling is not trajectory, but wavelike; it is not exact, but statistical; or, as physicists and philosophers believe, it is not deterministic, but indeterministic. The theory has to be statistical because microcosmic phenomena themselves are probabilistic.
Scientists such as Albert Einstein did not accept the statistical interpretation of the wave function. To a lesser extent, de Broglie and Schrödinger, cofounders of quantum mechanics, shared Einstein’s viewpoint. The majority, however, disagreed with Einstein, de Broglie, and Schrödinger. Most theoretical and experimental physicists were won over by the indeterminism of the new microcosmic mechanics. In this serious academic debate, the theoretical success achieved by Gamow, Gurney, and Condon played a significant role. Long before any theory was proposed, radioactive phenomena had been recognized as statistical. It is very satisfying for most physicists that such phenomena are explained by a theory that is intrinsically statistical.
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Boorse, Henry A., and Lloyd Motz, eds. The World of the Atom. Vol. 2. New York: Basic Books, 1966. Chapter 67, “The Barrier Around the Nucleus,” includes two parts: an explanatory essay by the editors and an English translation of Gamow’s “Quantum Theory of the Atomic Nucleus,” originally published in German in 1928. The first part is accessible to readers with little scientific background. -
Born, Max. My Life: Recollection of a Nobel Laureate. New York: Charles Scribner’s Sons, 1978. A substantial volume valuable for its historical scholarship. Several chapters discuss the history of quantum mechanics. Careful readers will gain a clear picture of Born’s contribution to the founding of quantum mechanics. -
_______. Physics in My Generation. 2d rev. ed. New York: Springer-Verlag, 1969. An important work for anyone seeking to understand the history of quantum mechanics. Suitable for the general reader. -
Ford, Kenneth W. The Quantum World: Quantum Physics for Everyone. Cambridge, Mass.: Harvard University Press, 2004. Explains the concepts of quantum physics in nontechnical language for lay readers. Illustrated. -
Gamow, George. Thirty Years That Shook Physics: The Story of Quantum Theory. 1966. Reprint. Mineola, N.Y.: Dover, 1985. Very interesting anecdotal history of quantum mechanics. Discusses the evolution of the quantum theory of the nucleus in chapter 2. -
Gamow, George, and Russell Stannard. The New World of Mr. Tompkins. Cambridge, England: Cambridge University Press, 2001. Revised and updated (by Stannard) edition of Mr. Tompkins in Paperback, a 1965 volume that combined Gamow’s two classic popular science books, Mr. Tompkins in Wonderland (1940) and Mr. Tompkins Explores the Atom (1945). Provides an excellent introduction to many scientific concepts for lay readers. -
Heisenberg, Werner. Nuclear Physics. New York: Methuen, 1953. Discusses radioactive phenomena in chapter 3, and clearly explains the tunneling theory in chapter 6. Accessible to interested lay readers. -
Rutherford, Lord Ernest. The Newer Alchemy. 1937. Reprint. Whitefish, Mont.: Kessinger, 2003. A brief discussion of nuclear physics by a great authority. Probably still the best introduction to radioactivity for the general reader, although somewhat dated.
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