The Manhattan Project
Page 2
By mid-1940, understanding of the differing responses of U-235 and U-238 nuclei to neutron bombardment led to the emergence of a new idea for obtaining a controlled (not explosive) chain reaction using natural uranium without enrichment. The key lies in how nuclei react to bombarding neutrons. When a nucleus is struck by a neutron, various reactions are possible. The nucleus might capture the neutron and then fission; it might capture the neutron and not fission but later decay to a more stable isotope of another element; or it might deflect the neutron into a new flight path. Each process has some probability of occurring, and these probabilities depend very sensitively on the speed of the incoming neutrons. Neutrons released in fissions are extremely energetic, emerging with average speeds of about 20 million meters per second; these are ‘fast’ neutrons. As remarked above, U-238 nuclei preferentially capture fast neutrons emitted in fissions of U-235 nuclei. However, when a nucleus of U-238 is struck by a slow neutron—one traveling on the order of a mere couple of thousand meters per second—it behaves very differently, with deflection of the neutron being about three times as likely as capture. But—and this is the crucial point—U-235 nuclei turn out to have an enormous probability for undergoing fission when struck by slow neutrons, over 200 times the capture probability for U-238. This factor is large enough to compensate for the small natural abundance of U-235 to the extent that a slowed neutron is about as likely to fission a nucleus of U-235 as it is to be captured by one of U-238 (figure 1.1); this is why it is possible to achieve a controlled ‘slow-neutron’ chain reaction. This is worth emphasizing: if neutrons emitted in fissions can be slowed, then they have a good chance of going on to fission other U-235 nuclei before being lost to capture by U-238 nuclei. In a nuclear reactor, the slowing is achieved by distributing lumps of uranium within a substance known as a ‘moderator’ which slows neutrons before they strike other uranium nuclei. Within an operating reactor, both fission of U-235 nuclei and neutron capture by U-238 nuclei proceed simultaneously.
Figure 1.1. Schematic illustration of a chain reaction utilizing moderated neutrons. Each fission of a U-235 nucleus liberates two secondary neutrons, one of which goes on to fission another U-235 nucleus, while the other is captured by a nucleus of U-238. Reproduced from [1], figure 1.2.
If U-235 has such an enormous fission probability for slow neutrons, why not build a bomb that incorporates a moderator to slow neutrons and thereby achieve lots of fissions, thus avoiding the difficulties of enriching uranium or breeding plutonium? This question gets to a vitally important point, one worth recalling even if you are already very familiar with this material. Analysis of the efficiency of nuclear explosions reveals that the energy liberated is proportional to the square of a neutron’s speed as it travels from where it is born in a fission to where it is likely to cause a subsequent fission: . (See chapter 3, specifically the discussion surrounding bomb efficiency, equation (3.24). In this equation, is the neutron travel time between fissions, which is inversely proportional to vneut.) Fast neutrons travel at about 20 million meters per second, while slow neutrons travel at about 2000 meters per second, a speed ratio of 10 000. This means that the energy releases will compare as Efast/Eslow = (10 000)2 = 108. In other words, the energy that would be released by a slow-neutron bomb would be only 10−8 of that which would be liberated by a fast-neutron bomb containing the same amount of fissile material. In comparison to a Nagasaki-type 20-kiloton TNT-equivalent fast-neutron bomb, a comparable slow-neutron weapon would release less energy than one pound of TNT! There is no point in making a slow-neutron bomb; in effect, you might as well attempt to drop a reactor on your target. Nuclear bombs utilize fast-neutron reactions in compact cores of highly-enriched fissile material to release large amounts of energy in brief, uncontrolled bursts, whereas reactors utilize controlled, slow-neutron reactions in a physically dispersed mass of non-enriched or low-enriched material to produce power and breed plutonium. So, do not be alarmed by stories where reactors threaten to behave like bombs: they operate far too slowly, and even if their neutron-absorbing ‘control rods’ are rendered inoperative, their fissile-material enrichment is too low to sustain an explosive chain reaction. As seen at Fukushima, an uncontrolled reactor will melt itself into a nasty mess of highly-radioactive fission products, but it will not cause a nuclear explosion.
In an interesting twist of nature, neutron capture by U-238 nuclei turned out to be advantageous for bomb-makers. On capturing a neutron, a nucleus of U-238 becomes one of U-239. Based on some experimentally-known patterns regarding the stability of nuclei, it was predicted in early 1940 that U-239 nuclei might decay within a short time to nuclei of atomic number 94, the element now named plutonium (Pu). It was further predicted that element 94 might be very similar in its fissionability properties to U-235. If this proved to be so, then a reactor could be used to ‘breed’ plutonium from neutron capture by U-238 nuclei while maintaining a self-sustaining, controlled, slow-neutron chain-reaction via fissions of U-235 nuclei. The advantage of this would be that the plutonium so created could be separated from the uranium ‘fuel’ by chemical processes and used to construct a bomb, thus circumventing the need to develop enrichment technologies. These predictions were soon confirmed on a laboratory scale by creating a tiny sample of plutonium via neutron bombardment of uranium.
1.2 The Manhattan Project
The idea that nuclear fission could lead to bombs of immense power occurred very quickly to several researchers in the physics community. In America, three émigré Hungarian physicists, Leo Szilard, Eugene Wigner, and Edward Teller, prevailed upon their friend and colleague Albert Einstein (also then living in America) to sign a letter to President Franklin Roosevelt which described the possibility of fission bombs; their rationale in recruiting Einstein was that he was likely the only physicist famous enough to be known to the President. The letter reached Roosevelt in October, 1939, and prompted the formation of an ‘Advisory Committee on Uranium’ to fund and coordinate research on the physics of uranium fission, on how reactors might be constructed, and on developing technologies for separating U-235 from U-238. The Advisory Committee initially reported to the National Bureau of Standards, but in June, 1940, it came under the administration of the National Defense Research Committee (NDRC), an agency Roosevelt established to organize research which might have military applications. The NDRC was directed by Vannevar Bush, a Massachusetts Institute of Technology electrical engineer. In June 1941, the NDRC was absorbed into a successor agency, the Office of Scientific Research and Development (OSRD), also directed by Bush. By the time of the Japanese attack at Pearl Harbor, the NDRC/OSRD had funded contracts totaling some $300 000 for research on fission and isotope separation.
When the NDRC inherited the uranium issue, Bush appointed University of Chicago physics Nobel laureate Arthur Compton to chair a separate committee, the ‘National Academy of Sciences Committee on Atomic Fission’. From the spring through the late fall of 1941, Compton’s committee prepared three reports on the feasibility of reactors and bombs; their final report, which Bush took to Roosevelt just before Pearl Harbor, laid out the prospects for fission bombs in considerable detail. This last Compton report was heavily influenced by a report prepared by a parallel group in Britain. In March, 1940, Otto Frisch and Rudolf Peierls, respectively Austrian and German émigré physicists then working at Birmingham University, prepared a memorandum in which they estimated the critical mass of U-235 to be about a pound. This was an underestimate, but their document reached the government’s Scientific Survey of Air Warfare, whose chairman, Sir Henry Tizard, asked physicist George P Thomson to investigate the issue. (Thomson was the son of J J Thomson, discoverer of the electron.) This resulted in the formation of the so-called MAUD committee, which in July, 1941, produced an extensive report on the feasibility of fission bombs and isotope-separation methods. This report reached American officials that October, at which time Bush briefed Roosevelt on its conclusions. About a month later, Bush used the third Compton
report to bolster the case for proceeding with an all-out project to construct fission weapons.
In summary, by late 1941, physicists in both America and Britain had converged on the conclusion that there looked to be two possible means of creating nuclear explosives. These were: (i) isolate tens of kilograms of U-235 by some isotope enrichment method and use it to create a fast-neutron chain-reaction bomb, and/or (ii) develop reactors and use them to breed plutonium (specifically, Pu-239) via U-238 slow-neutron capture, extract the plutonium, and use it to build a bomb. U-235 was predicted to be almost certain to make an excellent nuclear explosive, but the kilograms would have to be extracted one atom at a time from a mass of uranium ore. On the up-side, various isotope enrichment methods looked promising, even if they would be difficult to put into practice on large scales. Regarding plutonium, nobody had ever built an operating reactor; also, an unknown element might well prove to have some property that obviated its value as an explosive. Bush made the only recommendation he could in the circumstances of wartime: both methods should be pursued. However, it was clear that such a dual effort would require building enormous factories to enrich uranium, and a vast research and development effort to build reactors. The only organization which possessed the budget and resources necessary to carry out such an operation with the requisite secrecy was the Corps of Engineers of the United States Army, and Bush began lobbying Roosevelt to turn the project over to the Corps. The President approved the transfer in March, 1942, and the Army formally established the ‘Manhattan Engineer District’ (MED) on August 13, 1942. The name came from the fact that the MED’s first commander, Colonel James Marshall, established his headquarters in Manhattan. In September, 1942, the MED was placed under the command of Brigadier General Leslie Groves (figure 1.2), then in charge of all domestic military construction; his most recent large project had been the building of the Pentagon. Groves wasted no time in getting to work on his new responsibility, acquiring sites at which to locate factories to isolate U-235 (Oak Ridge, Tennessee), reactors to synthesize plutonium (Hanford, Washington), and set up a highly-secret bomb design laboratory (Los Alamos, New Mexico); see figure 1.3. And with this, it is time for us to explore some of the physics of Manhattan.
Figure 1.2. General Leslie Richard Groves (1896–1970) http://commons.wikimedia.org/wiki/File:Leslie_Groves.jpg.
Figure 1.3. Locations of major Manhattan Project sites. From [2].
References
[1] Reed B C 2015 Atomic bomb: the story of the Manhattan Project (San Rafael, CA: Morgan & Claypool)
[2] Reed B C 2014 The Manhattan Project Physica Scripta 89 108003 (figure 10)
IOP Concise Physics
The Manhattan Project
A very brief introduction to the physics of nuclear weapons
B Cameron Reed
* * *
Chapter 2
Nuclear fission
In the process of fission, nuclei break up into two or occasionally three lighter nuclei. Hahn and Strassmann stumbled upon uranium fission when they realized that neutron bombardment of uranium was producing nuclei of barium and krypton. Within a few weeks, it was further realized that two or three neutrons are also simultaneously released when a nucleus of uranium fissions. In notation conventionally used by nuclear physicists, the Hahn–Strassmann reaction can be written (assuming three neutrons released) as:
Notice that this reaction involves U-235, not the more common isotope of uranium, U-238. This is a crucial part of the story that will be discussed in more detail in the following sections.
2.1 Energy release in fission
In this section, the energy released in uranium fission is estimated by two different means: directly from the masses of the nuclei involved in equation (2.1), and a more theoretical approach that can be applied to ‘target nuclei’ other than uranium in order to make quick estimates.
Nuclear physicists tabulate masses of particles in terms of their ‘mass excesses’, which are normally designated with the symbol Δ, and which are always quoted in units of millions of electron-volts (MeV); 1 MeV = 1.602 × 10−13 J. The advantage of this approach is that the energy consumed or liberated in a reaction can be calculated very directly by subtracting the sum of the mass excesses of the particles that emerge from the reaction from the sum of those that enter the reaction. These energy values are customarily designated with the symbol Q:
If Q > 0, the reaction releases energy; if Q < 0, then the reaction consumes energy and can only be made to occur by giving the bombarding particle an amount of kinetic energy greater than Q. Δ-values for various nuclei are tabulated in a number of texts and references; the most extensive listing is published as the Nuclear Wallet Cards by the Brookhaven National Laboratory [1].
For the reaction of equation (2.1), the values are (all in MeV): , , , and . Hence,
Ordinary chemical reactions typically liberate a few electron-volts of energy per reaction; in comparison, 173 MeV is a staggering amount of energy for a single reaction, and is what makes nuclear weapons so compelling for military applications. The fission energy latent in a single kilogram of U-235 is enormous. U-235 has an atomic weight of 235 g mol−1, so a single kilogram of it contains about 4.26 moles of nuclei, that is, some 2.56 1024. At 173 MeV/reaction, the potential fission energy amounts to 4.43 1032 eV, or 7.1 1013 J. Explosion of one ton of TNT liberates about 4.2 109 J, so the energy released by fission of a single kilogram of U-235 is equivalent to nearly 17 000 tons, or 17 kilotons (kt) of TNT. (The ton meant here is a metric ton, equivalent to 1000 kg.) A sphere of U-235 of mass 1 kg would have a radius of about 2.34 cm, only a little larger than a squash ball. The ∼170 MeV released in fission goes largely into the kinetic energy of the product nuclei (about 160 MeV) and the secondary neutrons released (about 2 MeV each, on average); the balance is taken up in gamma-rays.
Exercise
The density of TNT is 1.65 g cm−3. How large a sphere of TNT would you need to have a mass of one kiloton?
Answer
Radius ∼5.25 m.
As a second approach to estimating the energy released in fission, we can appeal to a semi-empirical expression that nuclear physicists have developed to express the ‘self-energy’ of a nucleus. This expression comprises two terms, one representing a contribution to the energy from the mutual repulsion of protons within the nucleus, and one representing a ‘surface’ effect which accounts for the fact that protons and neutrons at the surface of a nucleus interact with fewer nucleons than their counterparts which reside inside the nucleus. The expression can be evaluated for an initial nucleus, and then for two product nuclei following fission; the difference between the two expressions corresponds to the energy released. If an initially spherical nucleus of atomic number Z and mass number A splits into two spherical product nuclei which then repel each other and fly off to essentially infinite distance from each other, this theory predicts an energy release of
This expression arises from empirical fits to trends in nuclear masses; its advantage is that it renders unnecessary the work of looking up mass excesses. The quantities aS and aC are fitting parameters known as the ‘areal’ and ‘Coulomb’ energy parameters; they have values of 18 MeV and 0.72 MeV, respectively. α and β are dimensionless numbers whose values depend the ratio of the masses of the fission products; for equal-mass products (a good enough approximation for our purposes), their values are α = 1.26 and β = 0.63. For U-235 (Z = 92, A = 235), you should be able to verify that this gives Q = 187 MeV, in respectable agreement with the more exact value deduced above from actual masses.
Exercise
What does equation (2.4) predict for Z = 50, A = 120? This is an isotope of tin.
Answer
Q = 21 MeV. We will see in section 2.5 that one must put in an energy of about 50 MeV to fission a nucleus of tin, so it would not be possible to sustain a fission chain reaction with tin.
Exercise
Mass numbers track atomic numbers approximately as A ∼ 1.69 Z1.09. Substit
ute this into equation (2.4), and so determine the atomic number for which Q evaluates to zero. Nuclei with greater atomic numbers than this (like uranium) will liberate energy upon fission, while lighter ones will consume energy upon fission.
Answer
Z ∼ 42. Why does this result not contradict the calculation for tin in the preceding exercise?
2.2 Chain reaction timescale
In a notation that is common in nuclear physics and that will be used throughout this book, the number of secondary neutrons liberated per fission is designated as v. Consider a kilogram of U-235 within which a chain reaction has been initiated by a single neutron. This neutron, when it causes another fission, will give rise to v ‘first-generation’ neutrons. These will each create v second-generation neutrons, and so on. The number of neutrons produced after G generations will be vG. If a bomb core contains N nuclei and if no neutrons are lost to processes other than fission, then the number of generations required to fission the entire core will be vG = N. As remarked above, one kilogram of U-235 contains N = 2.56 × 1024 nuclei; if v = 2, then G ∼ 81 generations will be required to fission the entire kilogram. (For U-235, the effective value of v is actually about 2.64, which gives G ∼ 58.)
How long does it take for these 80 generations to occur? If neutrons have average speed vneut and travel for an average distance λfiss before causing a fission, then it follows that the time τ that elapses between when a neutron is created in a fission and subsequently causes another will be