Neutrinos are also emitted every time we release some nuclear energy. Among all the remarkable practical consequences of nuclear energy, the neutrinos have a unique distinction: they are never useful, and they are never harmful. They have not even been suspected of any mischief.
A radioactive nucleus is one that will eventually disintegrate and release some energy. But when?
One might imagine that a radioactive nucleus would begin to “age” from the moment of its birth, and that after the passage of a predetermined time, the disintegration process would take place. This is how radioactivitymightwork in a deterministic universe. What actually happens to a radioactive nucleus, however, is much more interesting.
At any instant of its life, the radioactive nucleus has some probability of disintegrating in the next second. This probability is unaffected by its age. No matter how long the nucleus has lived, its chance of disintegrating in the next second is always the same. It is as if a game of roulette were being played. The wheel spins, and if its number comes up, the nucleus disintegrates in the first second. If not, the wheel spins again. Each time the wheel spins there is some probability of its number coming up. The precise value of this probability is a characteristic of each particular radioactive species. The higher the probability, the more rapidly the nucleus may be expected to disintegrate. But a given nucleus neednot do at any particular time what is expected of it.
The notion of probability (or chance) has meaning only when applied to a large number of cases. To say that a given nucleus has one chance in a hundred of decaying in the next second means that out of some large number (say 100 million) of such radioactive nuclei, one per cent (one million) will decay in the next second. But it is absolutely impossible to say beforehand which nuclei will be the ones to decay. A particular nucleus may decay immediately or only after some very long time. The collection as a whole, however, will always do the expected thing. (This is the principle on which insurance companies operate.)
The situation is best described in terms of a time span which is called the half-life of the radioactive species. The half-life is defined as the amount of time which is required for one half of a large number of identical radioactive nuclei to disintegrate. It makes no difference what this large number is, provided only that it is large enough.
If the number is not large enough, fluctuations will occur, and instead of 50 per cent of the nuclei decaying during the period of a half-life, it may be 40 per cent or 60 per cent. As a matter of fact the 40 per cent to 60 per cent limits correspond to a sample size of about 100 nuclei. For 10,000 nuclei, the limits will be 49 per cent to 51 per cent. The number of radioactive nuclei with which we customarily deal, is about 10²³ (100,000,000,000,000,000,000,000). This is the number, for example, of radioactive nuclei in about an ounce of radium. For such a large number of nuclei the deviation from 50-per-cent decay during a half-life will be utterly negligible. Thus we live in a universe which, on a macroscopic scale, appears ordered and subject to exact laws; while underlying these laws, on a microscopic scale, nature plays out a game of chance, full of randomness and uncertainty in the individual case.
We may draw a graph showing howN, the number of theremaining radioactive nuclei, varies with the timet. The graph shows that: in the first half-lifeT, half of the original numberN₀ of radioactive nuclei decay. In the second half-life, half of those remaining decay, and so on. After the timeT, one half of the original radioactive nuclei still remain; after 2T, one quarter remain; and so forth.
uncaptioned
Different radioactive species have different half-lives. Many are only a small fraction of a second; some are billions of years. N¹⁶ decays to O¹⁶ (plus an electron and a neutrino) with a half-life of about eight seconds. A free neutron decays into a proton, an electron, and a neutrino with a half-life of 13 minutes. Strontium with weight 90 (Sr⁹⁰) undergoes a beta decay with a half-life of 28 years. (This is an isotope that is not found anywhere in nature, but is made in fairly large quantities in the fission process.) Potassium with weight 40 (K⁴⁰), which is present in the amount of 0.01 per cent in ordinary potassium, has a half-life of one billion years. It has presumably been left over from the time when the primordial elements were formed. Half-lives for gamma decay are extremely short by comparison to those for beta decay. They usually amount to a small fraction of a second.
Radioactivity is characterized by the kind of particle emitted from the nucleus (our examples, so far, have been of beta and gamma particles), by the energy possessed by this particle, and by the half-life in which the radioactive decay takes place.
The biological hazard from radioactivity depends on all three of these characteristics. No matter whether the radioactive nuclei are produced in an atomic explosion or in an atomic reactor, some time will in general elapse before a human population can become exposed. If this time is long compared to the half-life of the radioactive species, most of the nuclei will have disintegrated, and the hazard will thereby be reduced. If, on the other hand, the half-life is long compared to this time, as well as to the life-span of a human being, the rate at which disintegrations occur will be low, and again the hazard will be reduced.
In short the dangerous half-lives are the intermediate ones, not too long, not too short. Sr⁹⁰ is an example.
The positive electric charges within an atomic nucleus repel one another. In the most heavily charged nuclei this repulsion becomes so great that the nucleus can break into two parts, simultaneously releasing a considerable amount of energy. In the case ofspontaneous nuclear fissionthe two parts are more or less equal in size. In the process ofalpha decayone of the parts (the alpha particle) is much smaller than the other.
An alpha particle consists of two neutrons and two protons and is identical with the nucleus of the helium atom. (The symbol for this nucleus is He⁴.) Since two neutrons and two protons can simultaneously occupy the lowest energy state, the alpha particle is an especially stable nuclear unit. As a result, from time to time in heavy nuclei, two neutrons and two protons will coalesce into an alpha particle, which may then attempt to escape.
In attempting to escape from the nucleus, however, an alpha particle encounters considerable resistance because of the short-range nuclear attraction of the other neutrons and protons. This resistance which an alpha particle experiencesin trying to leave the nucleus is usually referred to as an “energy barrier.” If the alpha particle could acquire a little additional energy, it would be able to overcome the barrier and get away from the nuclear attraction. Once outside the nucleus, just beyond the reach of the nuclear attraction, the alpha particle would be accelerated violently outward by the large electrical repulsion between its two protons and the other protons in the residual nucleus.
How an alpha particle escapes from the nucleus. From A to B it goes “uphill,” losing speed. At B its speed is zero and it almost always turns around. With a small probability it may sneak through the energy barrier B to C. Beyond C, it is repelled and emerges with increasing speed.
How an alpha particle escapes from the nucleus. From A to B it goes “uphill,” losing speed. At B its speed is zero and it almost always turns around. With a small probability it may sneak through the energy barrier B to C. Beyond C, it is repelled and emerges with increasing speed.
The alpha particle needs some extra energy to escape. According to the laws of older physics there is no possibility for it to obtain this extra energy and therefore escape is impossible. But the more newly discovered laws governing the motion of neutrons and protons (the laws of quantum mechanics) are not so stringent; they permit the alpha particle to use“borrowed” energy to overcome the energy barrier. Of course the alpha particle must always repay the loan—which it can easily do out of the large fund of electric energy that is released when it gets out of the repulsive range of the residual nucleus. There is no interest on the loan.
Such energy loans are not automatically granted in nature. There are two factors which make the loan improbable: if the amount is big or if the term is long. These restrictions effectively limit the particles which may apply for an energy loan. Objects of great size and weight are unable to qualify, but the small particles of the atomic world often do.
The more energy carried off by the alpha particle after the alpha decay, the less energy must be borrowed in order to overcome the barrier, and the more rapidly the decay may be expected to occur. So sensitive is the decay to the energy of the alpha particle, that an alpha particle carrying twice the energy is emitted a hundred trillion times fester.
Half-lives for alpha decay vary from a fraction of a second to billions of years. But even the shortest half-life for alpha decay is remarkably long compared to the time required for the alpha particle to cross the nucleus. This means that the alpha particle makes a tremendous number of attempts to escape from the nucleus before it actually succeeds. According to the older classical theory the alpha process should never occur, and in fact it occurs with a very small probability.
A single alpha decay is not usually a sufficient process to bring about stability of the daughter nucleus. A whole chain of radioactive decays is usually required before stability is achieved. Most nuclei which emit alpha particles belong to one of these radioactive decay chains.
The heavy nuclei for which alpha decay occurs all contain a large excess of neutrons. Since the alpha particle carries off exactly two neutrons and two protons, the ratio of the number of neutrons to the number of protons is increased in the daughter nucleus. This has an unstabilizing influence. (Actually,in lighter nuclei stability requires that the ratio of neutrons to protons be closer to unity.) The daughter nucleus is thus apt to be beta-active, converting a neutron into a proton (plus an electron and a neutrino) in order to decrease its ratio of neutrons to protons. In this way a chain of radioactive decays may occur, more or less alternating between alpha and beta emissions, with gamma rays being occasionally emitted also.
There are four radioactive chains. One of them starts with the abundant isotope of uranium, U²³⁸. This isotope undergoes a few alpha decays and a couple of beta decays to become radium, which has a charge of 88 and a weight of 226. All the radium in the world is produced in this manner as a daughter product in the fifth decay of the chain. After a number of further decays, stable lead (weight 206) is produced and the chain terminates.
The other chains are similar to the U²³⁸ chain, though not quite as long. One chain starts with the rare isotope of uranium, U²³⁵; another starts with the isotope of thorium that weighs 232. Both of these terminate in stable isotopes of lead. In all cases the first decay of the chain has a very long half-life. The half-life of U²³⁸ is 4.5 billion years; of U²³⁵, 710 million years; and of thorium, 14 billion years.
The fourth radioactive chain has been made in the laboratory but is not found in nature because its first isotope, neptunium with weight 237, has too short a half-life. It decays in two million years and all the other members of the chain live for even shorter periods. Thus the neptunium chain decayed long ago, whereas the three other chains have survived from the time when the elements were made.
It is interesting to notice that the lesser abundance of U²³⁵, as compared with U²³⁸, is connected with its shorter half-life. Assuming that comparable amounts of both isotopes were present at the beginning of the universe (and there is goodreason to believe that this was the case), one would expect to find significantly less U²³⁵ than U²³⁸ after a period of a few hundred million years. After 710 million years (the half-life for U²³⁵) only one half of the original number of U²³⁵ nuclei would still exist. But 90 per cent of the original U²³⁸ nuclei (half-life 4.5 billion years) would remain. From the presently observed ratio of U²³⁵ to U²³⁸ nuclei (1 to 139), it may be calculated, using the law of radioactive decay, that 6 billion years ago natural uranium consisted of equal parts of U²³⁵ and U²³⁸. The age of the universe is hotly debated. With each passing year the universe seems to be a billion years older. Right now six billion years does not seem widely off the mark.
Natural radioactivity occurs mainly among the heavy elements, but there are a few light elements that are naturally radioactive. Of these, potassium⁴⁰ is an especially interesting one because it can decay either by electron emission or by electron capture. The processes are:
potassium⁴⁰ → calcium⁴⁰ + electron + neutrino,(1.1 billion years)
potassium⁴⁰ → calcium⁴⁰ + electron + neutrino,
(1.1 billion years)
and
potassium⁴⁰ + electron → argon⁴⁰ + neutrino.(11 billion years)
potassium⁴⁰ + electron → argon⁴⁰ + neutrino.
(11 billion years)
Calcium⁴⁰ and argon⁴⁰ are both stable nuclei. The second reaction is followed immediately by a gamma ray emission from the argon⁴⁰. The one per cent of argon found in the earth’s atmosphere comes almost entirely from the second reaction. These radioactivities are also interesting because appreciable amounts of potassium⁴⁰ are always present in human tissue.
All nuclei at the heavy end of the periodic system are radioactive alpha emitters. Uranium, for example, has no stable isotopes; they all undergo alpha decay. But there is anothermode of spontaneous decay of uranium, which is much less frequent than alpha decay but is of much greater practical importance. This is the fission process.
The fission process is just like alpha decay in that the nucleus breaks up into two fragments. The main difference between these processes is in the relative weights of the fragments. In the alpha decay of U²³⁸, for instance, one fragment has a weight of four and the other 234. In the fission process the fragments tend to be more nearly equal in weight. For example, one may weigh 90 and the other 148.[6]Other weight combinations are also possible.
The explanation of spontaneous fission is in essence the same as that of alpha decay. Spontaneous fission, however, is a less probable process because the two fragments are more strongly bound to each other by the nuclear forces than they are in alpha decay. More energy must be borrowed, and it must be borrowed for a longer term in order to penetrate the energy barrier.
The relative likelihoods of spontaneous fission and alpha decay can be appreciated from the following fact. In one hour in a gram of U²³⁸ there occur about 45 million alpha decays but only about 25 spontaneous fissions.
Once the energy barrier has been overcome, the energy released in alpha decay or spontaneous fission is proportional to the charges on the two fragments. For alpha decay, the product of the charges is 2 × 90 = 180; for spontaneous fission, this product will typically be about 40 × 52 = 2,080. Hence one might expect the fission energy release to be 10 to 15 times greater than the alpha energy release. As a matter of fact the fission energy release is even greater than this estimate indicates, being about 30 to 50 times greater than the alpha energy release. That so large an amount of energy is released, is a very important feature of the fission process fromthe point of view of practical utilization of atomic energy.
Being at the end of the periodic system, uranium requires a large ratio of neutrons to protons for its greatest stability. The fission fragments, however, lie in the middle of the system of elements, requiring a much smaller ratio of neutrons to protons for stability. This has two consequences.
One is that the fragments themselves may be expected to be unstable. They will undergo beta decay (electron emission) several times consecutively before a stable combination of neutrons and protons is reached. This radioactivity of the fission products constitutes a potential hazard in any practical application of fission atomic energy. In later chapters of this book we shall consider particularly the possible hazard from the fallout of radioactive fission products created in atomic explosions, and also the hazard associated with the operation and maintenance of atomic reactors.
The second consequence of the neutron excess is that neutrons may boil off from the fragments immediately after the fission process has occurred. This can happen because a lot of disorderly internal motion is generated by the fission process within the fragments, and these fragments do not have a particularly strong hold on their neutrons. The practical value of the released neutrons is something we shall discuss at length in a later chapter. For the present we mention only that these neutrons provide the mechanism whereby a chain reaction is made possible.
Spontaneous fission and alpha decay are responsible for the fact that elements with charge greater than 92 are not found in nature. There is little doubt that these elements were made in the beginning. But they have long since decayed.
An interesting case of spontaneous nuclear fission is californium²⁵⁴ (charge 98), with a half-life of 55 days. This isotope is formed in large quantities in certain stellar explosions called super-novae. Once in a millennium one of a collection of a billion stars flares into incredible brilliance. For a fewweeks this single star shines with the combined energy and luster of a billion ordinary stars—then it fades away gradually. Such a “new” star (nova), with the greatest power of radiation, is called a “super-nova.”
We believe that many nuclear reactions take place in a super-nova. It has been observed that a few weeks after the initial outburst of light, the intensity of light is reduced almost exactly by a factor of two every 55 days for a year or so. This is precisely what would be expected if the energy generated in the star during this time were due to the spontaneous fission of californium²⁵⁴. Here we see a model of what happens to naturally radioactive elements. Of these we have retained on earth only the ones with the longest half-lives, like uranium, thorium, and potassium.
The alchemists tried to transform one element into another artificially. They used heat, they used chemicals; they even used witchcraft. They failed. Their simplest method—to heat the substance in order to transform it—was really correct. The trouble was that their temperatures were too low by a factor of more than 10,000. What is needed, is a temperature of the order of tens of millions of degrees.
At such high temperatures two nuclei may occasionally approach each other in spite of the electrical repulsion between them. Sometimes they may even get close enough to each other to undergo a nuclear reaction. This, of course, happens with least difficulty if the nuclear charge is small. Hydrogen nuclei, which carry charge 1, participate in such reactions most easily.
In the interior of stars temperatures range from about 10 to 100 million degrees, and nuclear reactions do occur. The reaction responsible for the production of energy in the stars is:
4H¹ → He⁴ + energy
4H¹ → He⁴ + energy
Four protons combine to make an alpha particle with a release of energy. Actually this reaction does not take place allat once but several steps are required. That energy should be released, one expects from the fact that the alpha particle is very stable. Any process in which light nuclei combine to form a heavier nucleus with a release of energy is known as “fusion.”
The particular fusion process that goes on in the stars releases its energy in many forms: as positrons, neutrinos, electromagnetic radiation, and motion of the reacting particles. The positrons also carry off the excess charge of the reaction.
The neutrinos fly through the star without interacting, carrying their energy away into outer space, probably never again to make contact with the material universe. The remainder of the fusion energy is deposited within the star’s interior, which is thus kept hot enough so that the fusion reaction can keep going. The name “thermonuclear” is appropriately applied to this type of reaction.
A lot of effort and imagination is being devoted to the problem of making a controlled thermonuclear reaction. The motivation for this project comes from the fact that good thermonuclear fuels, such as deuterium (H²), are abundant and cheap. There is enough deuterium in the oceans of the world to supply man’s energy needs for many millions of years. One difficulty, of course, is to find a container for the reaction.
Even under stellar conditions the rate of fusion reactions is not very great. It takes approximately a billion years for only one per cent of the nuclei to react. Consequently even higher temperatures than those found in stars are required to produce large amounts of energy in a short time. But no known materials can withstand temperatures of more than a few thousand degrees centigrade. One idea is to keep the “burning” fuel away from material walls by means of magnetic fields.
Is there a way to make nuclei react without the extreme temperatures needed in the thermonuclear reactions? Whatone is really trying to do is bring two nuclear particles into intimate enough contact so that the nuclear forces can act between them. There is no reason why one should not use acoldtarget material, which is bombarded from the outside by energetic nuclear projectiles, for example protons or alpha particles. The projectiles, if they are energetic enough, can overcome the electrical repulsion of the target nuclei, and they actually can penetrate. The resulting “compound” nuclei would either be unstable and disintegrate instantaneously, or else be almost stable (i.e., radioactive) and disintegrate after some period of time. In either case nuclei of new elements would probably be formed in the reaction. This procedure sounds simple, but it has its difficulties.
Interior of the sun. The thermonuclear reactions take place mainly in the very hot, very dense central region (shaded). This region is about 20,000 miles in radius and has a density approximately 80 times the density of water.
Interior of the sun. The thermonuclear reactions take place mainly in the very hot, very dense central region (shaded). This region is about 20,000 miles in radius and has a density approximately 80 times the density of water.
The main difficulty is that the nucleus is a very tiny target. Its area is about 100 million times smaller than the area of the atom as a whole. If a piece of matter is bombarded by an energetic particle, chance alone will determine whether the particle is directed toward a nucleus. To be sure, if the particle misses the nucleus of one atom, it still has the opportunity of hitting the nuclei of other atoms which may lie in its path. Itdoes not have many such opportunities, however, because, being charged, it constantly interacts with the atomic electrons, which gradually absorb energy causing the particle to slow down.
As the particle slows down, its chance of hitting a nucleus decreases, even if it is heading directly toward one, because of the repulsion between its charge and that of the nucleus. Unless the particle has sufficient speed, it cannot overcome this repulsion.
Charged particles may be given the required speeds by accelerating them through large electric fields. If a unit charge is accelerated through a potential difference of one volt, it acquires an energy of oneelectron-volt. The energies required for nuclear bombardment are of the order of several million electron-volts, which can be provided by atom-smashing machines such as the cyclotron.
Even at such high energies very few of the nuclear projectiles actually find their way to a target nucleus. Most of them are slowed down by the electrons, wasting their energy in heating up the target material. Perhaps one particle out of a million will be lucky enough to induce a nuclear reaction.
If the purpose of the nuclear accelerating machines were to produce cheap energy, they would not be of much value. A nuclear reaction may typically release five to 20 million electron-volts of energy. But to obtain this reaction, a million particles had to be accelerated to energies of several million electron-volts. The recoverable and useable energy will be only a minute fraction of the total invested.
On the other hand, as a tool for scientific discovery, the atom-smashers have been of great importance. That one event in a million has given us much of our knowledge of nuclear physics.
The achievement of nuclear reactions by particle bombardment did not actually wait on the invention of man-made accelerating machines. Energetic alpha particles are availablefrom the radioactive decay of heavy elements. In 1919 Ernest Rutherford used such radioactive elements as a source of alpha particles. The alpha particles were made to bombard ordinary nitrogen, causing the reaction:
That is, an alpha particle plus a nitrogen¹⁴ nucleus react to produce a nucleus of (stable) oxygen¹⁷ plus a proton. Oxygen¹⁷ is a nucleus with 8 protons and 9 neutrons. The ordinary abundant form of oxygen has 8 protons and 8 neutrons. Natural oxygen contains a small amount of oxygen¹⁷.
Later, in 1934, Irene Curie Joliot (the daughter of the discoverer of radium, Madame Curie) and her husband, Frederic Joliot, used naturally available alpha particles to make artificial radioactive nuclei for the first time. The reaction was:
Phosphorus³⁰ is an unstable nucleus and emits a beta ray (a positron) to become silicon³⁰ (which is stable). The half-life for this decay is about 2.5 minutes. The Joliots’ reaction was the first instance in which man had produced radioactivity and known it. Actually cyclotrons had been producing radioactivity in good abundance for the preceding two years—but physicists had been unaware of this fact.
It is amusing that nature has also provided us with an atom-smashing machine and indeed one that produces far greater energies than any apparatus yet devised by man. This machine operates on the principle of fluctuating, turbulent magnetic fields in interstellar space. Cosmic particles—mainly protons, but also some alpha particles and even heavier nuclei—are accelerated by these changing magnetic fieldsand hurled occasionally into the earth’s atmosphere. The energies of these cosmic particles are enormous, ranging from billions of electron-volts to values a million times higher.
When a cosmic particle gets inside the earth’s atmosphere, it does not go far before colliding with a nucleus of nitrogen or oxygen. Out of this nuclear event emerge all the fundamental particles mentioned so far, and some others known as mesons. Mesons are particles which may be charged or neutral, and which have a weight a few hundred times that of the electron. Some of these particles are believed to be connected with the forces that hold the nucleus together.
The nuclear debris from the collision will itself be very energetic and will further disrupt other nitrogen and oxygen nuclei. There soon develops a cascade of electrons, positrons, mesons, neutrons, protons, and electromagnetic radiation moving toward the surface of the earth.
About once a second every square inch of the earth’s atmosphere receives such an energetic particle from outer space. The cascade that results carries penetrating radiations to the surface of the earth. All living organisms are constantly subjected to this radiation background. It is an important fact that the intensity of this radiation is reduced in its passage through the air, and inhabitants of Denver or Lima receive more cosmic radiation than the inhabitants of Los Angeles or New York.
Some neutrons made by collisions of the primary cosmic particles in the atmosphere may collide with nuclei of nitrogen. When this happens, the following reaction occurs:
Carbon¹⁴ is a radioactive electron emitter with a half-life of 5,600 years. This half-life is long enough so that much of the carbon¹⁴ in the world today was probably made ten to twentythousand years ago. Willard Libby studied this process in a careful and quantitative way, traced the history of the radioactive carbon from the atmosphere into living beings, and, by measuring the carbon¹⁴ content in historical remains, opened up a whole new branch of archeology.
Living organisms breathe in carbon (in the form of carbon dioxide) from the air. Most of this carbon is ordinary stable carbon¹²; a tiny fraction is radioactive carbon¹⁴. The organism is unable to distinguish between the two isotopes, and takes in carbon¹⁴ in the same ratio to carbon¹² as exists in the atmosphere. This ratio persists throughout the organism’s lifetime, but when the organism dies and no more carbon is assimilated, the ratio begins to decrease as the carbon¹⁴ nuclei gradually disintegrate. By observing the ratio of carbon¹⁴ to carbon¹² in fossil remains and other archeological objects, the date at which death occurred can be calculated. In this way the age of ancient Egyptian mummies has been found, and it has been shown that some sequoia wood is more than 1,500 years old. By measuring the carbon¹⁴ in trees that were killed by the last advance of glaciation, and looking into other remains of life from the last ice age, it has been possible to show that this last ice age occurred only 10,000 years ago—instead of 20,000 years, as had been previously believed. Carbon¹⁴-dating has therefore thoroughly revised our ideas about the rapidity with which the empires known to history have emerged from the most primitive conditions. A crucial part of the argument is that isotopes of the same element are chemically indistinguishable.
An alternative reaction which may occur when neutrons strike nitrogen, is
H³, triton, is also radioactive, undergoing a beta decay tobecome He³ (2 protons and 1 neutron) with a half-life of 12.25 years. Tritons too can be used for dating old objects—for example, old wine. The water in the wine cannot be replenished with cosmic-ray tritons after the wine has been bottled. Thus fifty per cent of the tritons disappear every 12.25 years.
We have here two examples of nuclear reactions induced by neutron bombardment. Recalling the disadvantages of charged particles as nuclear projectiles for alchemists, it must surely seem that neutrons would be ideal for this purpose. Being chargeless, they are neither electrically repelled by the nuclei nor constantly slowed down by energy-losing collisions with the electrons. The fate of almost every neutron moving in a large piece of matter is eventual collision with a nucleus.[7]Neutrons are ideal nuclear projectiles, except for one thing: they are hard to get.
Protons and alpha particles are found abundantly in nature as the nuclei of hydrogen and helium atoms. Neutrons, however, are not found in nature, and in the past have been made in nuclear reactions that were themselves initiated by charged particles. For example,
But now we encounter again the difficulty associated with charged particles. Only one alpha particle in a million undergoes a nuclear reaction to produce a neutron. The neutron, of course, makes a nuclear reaction every time. Over-all, then, we obtain two nuclear reactions per million nuclear projectiles, instead of one per million. With such methods we are not so much better off than the old alchemists. A cheap and plentiful source of neutrons would, however, putthe alchemist in business. In this way one could make rare elements and radioactive isotopes, and what is more important, he would be able to utilize concentrated nuclear energy.
Neutrons are ideal projectiles for nuclear bombardment because they carry no charge, can approach nuclei easily, and interact with them strongly. These neutral particles, discovered by James Chadwick in 1932, were used soon afterward by Enrico Fermi and his collaborators to bombard most of the elements of the periodic table. Very often in these experiments a nucleus would capture a neutron and become unstable with too much weight for its charge. Stability would then be restored by a beta decay, leaving the nucleus with one more unit of charge than it had to begin with. In 1934 Fermi tried this experiment with uranium, charge 92, the most highly charged element known at that time. He hoped to make a transuranic element with charge 93.
Throughout the experiments the uranium was observed with radioactive counters and found to become far more radioactive than uranium ordinarily is in its natural state. There was no way to account for all this radioactivity except to assume that new elements had been formed in the process of neutron bombardment. A chemical analysis revealed noelements with charges between 86 and 91. From this evidence Fermi concluded that no elements of charge less than 92 had been made and therefore the radioactivity must be due to charges greater than 92. He concluded that transuranic elements had been made in the laboratory.
Neither Fermi nor anyone else, however, was happy with this conclusion. There was far too great a variety of radioactivity for comfort. It had to be assumed that not only was the element with charge 93 being made, but also elements with charges 94, 95, and many more. This was very hard to understand. Ida Noddack,[8]a chemist, published a paper proposing an alternative explanation of the experiment: that a nucleus of uranium, when it captures a neutron, might break up into two fragments that could have any of various weights and charges. In other words, she suggested that Fermi had produced nuclear fission.
Fermi, however, believed that the fission process was an impossibility. He had a convincing proof, based on the measured values of the weights of nuclei and the formula of Einstein, E = mc². From this formula Fermi calculated the energy liberated when uranium breaks into two pieces; then he took into account the energy of electric repulsion between the pieces and found that the energy barrier was so large that the fission process could not take place. This proof was absolutely correct. The only trouble was that the measured values of the weights of nuclei happened to be inaccurate at that time!
But for this accident, fission would have been discovered in 1934 instead of 1938. If it had been, Nazi Germany might easily have been the first country to make the atomic bomb. At that time some German scientists were active in the field of military applications. The American physicists had not yet turned much attention to the subject.
An important feature of Fermi’s experiment is the large amount and variety of radioactivity that he found. The reason for this variety, as we now know, is that the fission process does not take place in a unique manner. The two primary fission fragments are very rarely of equal weight and charge. On the average the lighter fragment weighs about 90, and the heavier one about 140. Sometimes the lighter fragment will weigh as little as 75, and the heavier one as much as 160. As the weight varies, of course, so also does the charge. The charge of the lighter fragment averages 38, which is strontium, and the heavier one 54, which is xenon. All in all there are more than a hundred different species of nuclei represented among the primary fission fragments.
Practically all of these nuclei are radioactive and undergo three or four disintegrations before reaching stability. Overall therefore, several hundred distinct radioactive species are created by the fission process in uranium. Elements with charges 43 and 61 (which are not found in nature) have been identified as fission products in fairly appreciable quantities. Most of the fission products are short-lived electron and gamma emitters that can contribute only to the local and immediate radioactive hazard. Two of the long-lived products are abundant and important. These are cesium¹³⁷ and strontium⁹⁰.
Cesium¹³⁷ has a half-life of 30 years and emits a gamma ray with an energy of 0.6 million electron-volts. Strontium⁹⁰ has a half-life of 28 years and emits an electron with an average energy of 0.22 million electron-volts. The daughter nucleus in this process is yttrium⁹⁰, which emits another electron with an average energy of one million electron-volts. The half-life of yttrium⁹⁰ is 64 hours. In effect, therefore, strontium⁹⁰ emits two electrons, each with an average energy of 0.6 million electron-volts. For the long-term radioactive hazard, particularly the world-wide fallout associated with atomic explosions, the two isotopes cesium¹³⁷ and strontium⁹⁰are the most significant. Strontium⁹⁰ is the more dangerous to living organisms because it is deposited in the bones and retained in the body for long periods.
Besides radioactivity there is another feature of the fission process which is so conspicuous that it may seem hard to understand how Fermi failed to notice it—namely the large amount of energy released. The fission of a single nucleus of uranium releases an energy of 200 million electron-volts as contrasted with ordinary radioactive decay energies of 5 to 10 million electron-volts. (The energy released from the burning of one atom of coal is only 4 electron-volts.)
Of the 200 million electron-volts released in fission, about 10 million go into gamma rays and neutrons created in the fission process itself. This energy contributes to the immediate and local radiation danger. Another 24 million electron-volts go into radioactivity of the fission products, and of this, about half go into neutrinos, which are neither dangerous nor useful; the other half is carried by electrons and gives rise to the delayed radioactive hazard. But the bulk of the energy, over 160 million electron-volts, goes into kinetic energy of the two primary fission fragments. Of this amount, 100 million, on the average, go to the lighter fragment.
One hundred million electron-volt fission fragments should certainly have been noticed by Fermi’s radioactive counters—if they had been able to reach the counters. The fragments were not able to reach the counters, however. The reason is that Fermi was a careful worker. He knew that his sample of uranium would emit some radioactive particles even before neutron bombardment. This natural radioactivity he did not want to get mixed up with the radioactivity that would be produced in the experiment. So he put an absorbing foil between the uranium sample and the radioactive counters. The fission fragments could not get through the foil.
It is amusing that shortly afterward another noted physicistrepeated Fermi’s experiment, but this time without the foil. He reported that he was unable to get any significant results because his counter, for reasons unknown, started to spark.
Thus fission remained a secret. But in England Leo Szilard obtained patent papers on the nuclear chain reaction. He pointed out that in some nuclear reactions free neutrons might be released. These neutrons might then succeed in producing further reactions which would produce more neutrons. Provided that at least one neutron made in each reaction were able to induce a reaction in another nucleus, a chain reaction would take place.
The main problem, of course, was to avoid excessive neutron losses. There are two ways in which the losses mainly occur. One is by wasteful, nonreproductive capture in the nuclei; the other, by neutron leakage from the material surface. This second loss, Szilard showed, could be minimized by using a sufficiently large amount of chain-reacting material.
The point is that a neutron born in a nuclear reaction must travel on the average a certain distance before it can produce another reaction. If the size of the chain-reacting material is much less than this distance, practically all of the neutrons produced will be able to escape through the material surface, and no chain reaction will be possible. If the size of the material is large compared to this distance, the leakage loss becomes negligible, and the possibility of a chain reaction depends entirely on the magnitude of the first kind of loss, the wasteful captures in nuclei. If this loss is not too great, and a chain reaction is possible, there will be acriticalsize of the material at which on the average exactly one neutron per reaction will be able to induce another reaction. A just critical chain reaction of this kind is what is needed for an atomic reactor.
If the size of the material is greater than the critical size,on the average more than one neutron per reaction will cause another reaction and the chain reaction will run away. If, for example, two neutrons can cause another reaction, there will be two neutrons after the first generation, four after the second, eight after the third, and so forth. This is the principle of the atomic bomb.
After about 80 generations, an appreciable fraction of all the nuclei in the material will have undergone a nuclear transformation and so much energy will have been released that the material will not stay together even for the short time needed to produce the next generation. The whole material begins to fly apart, the system becomes sub-critical, and the chain reaction stops. The entire process lasts only a fraction of a microsecond.
Thus even before fission was discovered, Szilard laid the basis for constructing the atomic bomb and the nuclear chain reactor. As materials in which a chain reaction might conceivably be made to occur he named thorium, uranium and beryllium. On beryllium he was wrong because the mass of this atom was incorrectly known. On thorium, his guess was good. On uranium, he hit the bull’s eye.
Finally in December 1938 the secret broke. Hahn and Strassmann in Germany made a chemical analysis of a uranium target that had been exposed to neutrons. They were far more thorough than previous investigators had been, and they found barium, charge 56, which had not been present in the target material before the experiment. The only possible explanation was the fission process. Within a few weeks the violent kicks caused by the fission products in counters were found, and in the following days this experiment was repeated around the world.
There was no doubt that neutrons could induce fission in uranium nuclei. A few more weeks, and it was ascertained that the fission process released neutrons which might lead to more fissions.