Frisch-Peierls Memorandum • 1940
On the Construction of a "Super-bomb"
(based on a Nuclear Chain Reaction in Uranium)
 The possible construction of "super-bombs' based on a nuclear chain reaction in uranium has been discussed a great deal and arguments have been brought forward which seemed to exclude this possibility. We wish here to point out and discuss a possibility which seems to have been overlooked in these earlier discussions.
Uranium consists essentially of two isotopes, 238U (99.3%) and 235U (0.7%). If a uranium nucleus is hit by a neutron, three processes are possible: (1) scattering, whereby the neutron changes directions and if its energy is above 0.1 MeV, loses energy; (2) capture, when the neutron is taken up by the nucleus; and (3) fission, i.e. the nucleus breaks up into two nuclei of comparable size, with the liberation of an energy of about 200 MeV.
The possibility of chain reaction is given by the fact that neutrons are emitted in the fission and that the number of these neutrons per fission is greater than 1. The most probable value for this figure seems to be 2.3, from two independent determinations.
However, it has been shown that even in a large block of ordinary uranium no chain reaction would take place since too many neutrons would be slowed down by inelastic scattering into the energy region where they are strongly absorbed by 238U.
Several people have tried to make chain reactions possible by mixing the uranium with water, which reduces the energy of the neutrons still further and thereby increases their efficiency again. It seems fairly certain however that even then it is impossible to sustain a chain reaction.
In any case, no arrangement containing hydrogen and based on the action of slow neutrons could act as an effective super-bomb, because the reaction would be too slow. The time required to slow down a neutron is about 10-5 sec and the average time loss before a neutron hits a uranium nucleus is even 10-4. In the reaction, the number of neutrons would increase exponentially, like  where  would be at least 10-4 sec. When the temperature reaches several thousand degrees the container of the bomb will break and within 10-4 sec the uranium would have expanded sufficiently to let the neutrons escape and so to stop the reaction. The energy liberated would, therefore, be only a few times the energy required to break the container, i.e. of the same order of magnitude as with ordinary high explosives.
Bohr has put forward strong arguments for the suggestion that the fission observed with slow neutrons is to be ascribed to the rare isotope 235U, and that this isotope has, on the whole, a much greater fission probability than the common isotope 238U. Effective methods for the separation of isotopes have been developed recently, of which the method of thermal diffusion is simple enough to permit separation on a fairly large scale.
This permits, in principle, the use of nearly pure 235U in such a bomb, a possibility which apparently has not so far been seriously considered. We have discussed this possibility and come to the conclusion that a moderate amount of 235U would indeed constitute an extremely efficient explosive.
The behavior of 235U under bombardment with fast neutrons is not experimentally, but from rather simple theoretical arguments it can be concluded that almost every collision produces fission and that neutrons of any energy are effective. Therefore it is not necessary to add hydrogen, and the reaction, depending on the action of fast neutrons, develops with very great rapidity so that a considerable part of the total energy is liberated before the reaction gets stopped on account of the expansion of the material.
The critical radius  - i.e. the radius of sphere in which the surplus of neutrons created by the fission is just equal to the loss of neutrons by escape through the surface-is, for a material with a given composition, in a fixed ration to the mean free path of neutrons, and this in turn is inversely proportional to the density . It therefore pays to bring the material into the densest possible form, i.e. the metallic state, probably sintered or hammered. If we assume for 235, no appreciable scattering, and 2.3 neutrons emitted per fission, then the critical radius is found to be 0.8 time the mean free path. In the metallic state (density 15), and assuming a fission cross-section of 10-23 cm2, the mean free path would be 2.6 cm and would be 2.1 cm, corresponding to a mass of 600 grams. A sphere of metallic 235U of a radius greater than would be explosive, and one might think of about 1 kg as suitable size for a bomb.
The speed of the reaction is easy to estimate. The neutrons emitted in the fission have velocities of about 10-9 cm/sec and they have to travel 2.6 cm before hitting a uranium nucleus. For a sphere well above the critical size the loss through neutron escape would be small, so we may assume that each neutron after a life of 2.6 x 10-9 sec, produces fission, giving birth to two neutrons. In the expression for the increase of neutron density with time, it would be about 4 x 10-9 sec, very much shorter than in the case of a chain reaction depending on slow neutrons.
If the reaction proceeds until most of the uranium is used up, temperatures of the order of 1010 degrees and pressure of about 1013 atmospheres are produced. It is difficult to predict accurately the behavior of matter under there extreme conditions, and the mathematical difficulties of the problem are considerable. By a rough calculation we get the following expression for the energy liberated before the mass expands so much that the reaction is interrupted:
(M, total mass of uranium;  , radius of sphere; , critical radius; , time required for neutron density to multiply by a factor e). For a sphere of radius 4.2 cm ( = 2.1 cm), M = 4700 grams, = 4 x 10-9 sec, we find E = 4 x 1020 ergs, which is about one-tenth of the total fission energy. For a radius of about 8 cm (m = 32 kg) the whole fission energy is liberated, according to the formula (1). For small radii the efficiency falls off even faster than indicated by formula (1) because goes up as approaches . The energy liberated by a 5 kg bomb would be equivalent to that of several thousand tons of dynamite, while that of a 1 kg bomb, though about 500 times less, would still be formidable.
It is necessary that such a sphere should be made in two (or more) parts which are brought together first when the explosion is wanted. Once assembled, the bomb would explode within a second or less, since one neutron is sufficient to start the reaction and there are several neutrons passing through the bomb every second, from the cosmic radiation. ( Neutrons originating from the action of uranium alpha rays on light-element impurities would be negligible provided the uranium is reasonably pure.) A sphere with a radius of less than about 3 cm could be made up in two hemispheres, which are pulled together by springs and kept separated by a suitable structure which is removed at the desired moment. A larger sphere would have to be composed of more than two parts, if the parts, taken separately, are to be stable.
It is important that the assembling of the parts should be done as rapidly as possible, in order to minimize the chance of a reaction getting started at a moment when the critical conditions have only just been reached. If this happened, the reaction rate would be much slower and the energy liberation would be considerably reduced; it would, however, always be sufficient to destroy the bomb.
For the separation of the 235U, the method of thermal diffusion, developed by Clusius and others, seems to be the only one which can cope with the large amounts required. A gaseous uranium compound, for example uranium hexafluoride, is placed between two vertical surfaces which are kept at a different temperature. The light isotope tends to get more concentrated near the hot surface, where it is carried upwards by the convection current. Exchange with the current moving downwards along the cold surface produces a fractionating effect, and after some time a state of equilibrium is reached when the gas near the upper end contains markedly more of the light isotope than near the lower end.
For example, a system of two concentric tubes, of 2mm separation and 3 cm diameter, 150 cm long, would produce a difference of about 40% in the concentration of the rare isotope between its end without unduly upsetting the equilibrium.
In order to produce large amounts of highly concentrated 235U, a great number of these separating units will have to be used, being arranged in parallel as well as in series. For a daily production of 100 grams of 235U of 90% purity, we estimate that about 100,000 of these tubes would be required. This seems a large number, but it would undoubtedly be possible to design some kind of a system which would have the same effective area in a more compact and less expensive form.
In addition to the destructive effect of the explosion itself, the whole material of the bomb would be transformed into a highly radioactive stage. The energy radiated by these active substances will amount to about 20% of the energy liberated in the explosion, and the radiations would be fatal to living beings even a long time after the explosion.
The fission of uranium results in the formation of a great number of active bodies with periods between, roughly speaking, a second and a year. The resulting radiation is found to decay in such a way that the intensity is about inversely proportional to the time. Even one day after the explosion the radiation will correspond to a power expenditure of the order 1,000 kW, or to the radiation of a hundred tons of radium.
Any estimates of the effects of this radiation on human beings must be rather uncertain because it is difficult to tell what will happen to the radioactive material after the explosion. Most of it will probably be blown into the air and carried away by the wind. This cloud of radioactive material will kill everybody within a strip estimate to be several miles long. If it rained the danger would be even worse because the active material would be carried down to the ground and stick to it, and persons entering the contaminated area would be subjected to dangerous radiations even after days. If 1% of the active material sticks to the debris in the vicinity of the explosion and if the debris is spread over an area of, say, a square mile, any person entering this area would be in serious danger, even several days after the explosion.
In estimates, the lethal dose penetrating radiation was assumed to be 1,000 Roentgen; consultation of a medical specialist on X-ray treatment and perhaps further biological research may enable one to fix the danger limit more accurately. The main source of uncertainty is our lack of knowledge as to the behavior of materials in such a super-explosion, an expert on high explosives may be able to clarify some of these problems.
Effective protection is hardly possible. Houses would offer protection only at the margins of the danger zone. Deep cellar or tunnels may be comparatively safe from the effects of radiation, provided air can be supplied from an uncontaminated area (some of the active substance would be noble gases which are not stop by ordinary filters)
The irradiation is not felt until hours later when it may become too late. Therefore it would be very important to have an organization which determines the exact extent of the danger area, by means of ionization measurements, so that people can be warned from entering it.
O. R. Frisch
R. Peierls
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