Building a good bomb is harder.
In 1938, Lise Meitner and collaborators discovered that the nuclei of certain heavy metallic elements, most notably uranium, are subject to fission: when bombarded with neutrons, they will sometimes absorb the neutron, becoming unstable and splitting into two smaller nuclei, releasing more neutrons, and much miscellaneous radiation, in the process. It was quickly realized that those new neutrons could trigger more fissions, and so start a chain reaction, which would grow exponentially until its fuel began to be exhausted, developing a tremendous amount of energy in moments. But stray neutrons are relatively common, and uranium, while rare, is still around, not having long since vanished in a puff of gamma rays. Why not?
Well, for two reasons. First: not all uranium nuclei are fissile. The two principle sorts are the lighter U-235, and the heavier, much more common U-238. Only U-235 will fission at low energies; U-238 is more stable. Second: even if you got together purified U-235 and started fission going, not all the neutrons produced would hit another nucleus before they lost so much energy they couldn't split it, or decayed themselves (neutrons do not make good pets), or wandered away. To a first approximation, neutrons get shot off in all directions, so fissions near the edge of the lump of uranium will spray the surroundings with neutrons but not lead to many new fissions. The fraction of fast neutrons lost to the chain reaction from this cause will (roughly) vary as the ratio of the surface area of the material to its volume, so the loses will become proportionally smaller as one increases the bulk of the material. Thus the concept of critical mass: the minimum mass of fissile material, in a given shape, the chain reaction needs to take off.
In the simplest case, the critical mass can be calculated using a little diffusion theory and a few experimental parameters. It amounts to some two hundred kilograms of uranium: utterly impractical as a weapon. The first key to unlocking the nuclear armory is reducing the critical mass. One begins by using something a bit better than elementary diffusion theory, and getting a better estimate of the critical mass at sixty kilograms; but merely fiddling with one's math doesn't go far enough. The most effective way of reducing the critical mass is to keep those neutrons at the edge of the mass from straying, to redirect them back into the chain reaction. This calls for a "tamper," a thick casing of a dense metal, like U-238 or gold. ("The active materials seemed so precious that everything else in contrast seemed cheap. The notion of vaporizing a few hundred pounds of gold in the explosion did not strike us as odd." [pp. 29--30]) At the relevant temperature and pressure, there is no significant difference between such metal and an equally dense gas, which greatly facilitates the calculation of the new critical mass: fifteen kilograms of U-235. (The artificial element plutonium has an isotope, Pu-239, which is more fissile than U-235, and consequently has a lower critical mass.)
The second key is to increase the amount of energy coaxed out of the reaction. The obvious way to do this is to give the chain reaction more than just the critical mass to feed upon. The problem with this is that, in assembling twice the critical mass, there is usually a stage where just the critical mass has been assembled: but then the reaction starts, and it very quickly blows everything to hell. The problem of critical assembly is one of the great technical challenges confronting the bomb-builder. The other, also related to increasing the yield, is the physical limitation imposed by the Stefan-Boltzmann law for black-body radiation: the energy density of the radiation goes up as the fourth power of its temperature, so (once the gas has come to mechanical equilibrium with its radiation field, i.e., once the pressure of the gas equals the pressure of the light) pumping more energy in only increases the temperature, and so the yield, very slowly. The problem of critical assembly was solved, as was the problem of producing enough fissile material, whether through the "enrichment" of uranium or the synthesis of plutonium; that of efficiency was eventually to be evaded by the hydrogen bomb.
The Los Alamos Primer originated as a series of five lectures, delivered by Robert Serber, Oppenheimer's theoretical lieutenant, to the physicists of the Manhattan Project at its commencement, covering roughly the subjects I have just sketched, only with the real physics, i.e., the equations. This is not especially esoteric material: relativity does not enter into it at all, not even E=mc^2 (all that's needed is the knowledge that fission releases energy, and how much), quantum mechanics just barely. The core of the physical problem, the calculation of the critical mass and the course of the chain reaction, uses no more than old-fashioned kinetic theory of the sort known to Boltzmann a hundred years ago. Presented well, as Serber presents it, it can (here I speak from personal experience) be taught successfully to second-year undergraduate physics students. It is in fact a paradigm (in the original sense) of physical modeling, and the complications induced by aiming at more realism only add to the technical charm. (The methods of increasing yield and achieving a sufficiently rapid critical assembly are quite properly not described in any detail.)
For the present edition (the first declassified one), the late Dr. Serber (Wisconsin, Ph.D. '34) annotated his original notes, explaining the code terms which were used even in Los Alamos (thus "material 25" for "uranium-235"), amplifying the reasoning, patching a few mistakes, and deriving some results (like the diffusion law) and explaining some concepts (like cross-sections) in appendices. To this Serber added a memoir of his own career through the beginning of the Los Alamos phase of the project, and Rhodes, the celebrated author of The Making of the Atomic Bomb, an introduction on the historical background of the project. The result is an exposition of the elementary physics of the atomic bomb adapted, if not to the meanest understanding, then to that of almost all with a good grasp of calculus. Anyone with such qualifications and an interest in how we came to live with the possibility of instant and total destruction would do well to read this book, if only to see how easy it is to start.