The Amazing Story of Quantum Mechanics (18 page)

Figure 22:
Page from
Learn How Dagwood Splits the Atom
in which Mandrake the Magician, having shrunk Dagwood Bumstead 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.

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 Strassmann 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 spacing 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 (mass times velocity), the greater the kinetic energy (momentum squared divided by twice the mass). 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. Assume 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 analogy, 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 assume 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.”