There are many books on how the atom bomb was made. They are histories of the great men who succeeded at site Y, Los Alamos, usually with a sidelight of the economics and politics in the US at the time. It’s sometimes noted that there was an equally great German group working too, and one in Japan and in Russia, that they didn’t succeed, but it’s rarely discussed what they did wrong. Nor does anyone make clear why so many US scholars were needed. What did all those great US minds to do? The design seems sort-of obvious; it appears in the note Einstein sent to Roosevelt, so what were all these people thinking about all that time, and why did the Germans fail? By way of answer, let me follow the German approach to this problem, an approach that won’t get you anywhere, or anywhere that I’ve seen.
It seems that everyone knew that making a bomb was possible, that it would be fearsomely powerful, and that it would be made using a chain reaction in uranium or plutonium. Everyone seems to have understood that there must be a critical mass: use less and there is no explosion, use more and there is one. The trick was how to bring enough uranium together make the thing go off, and as a beginning to that, there is the concept of “a barn.” A barn is a very small unit of area = 10−24 cm², and a typical atom has a cross-section of a few barns. Despite this, it is generally thought to be very easy to hit an atom at the nucleus, that is, at the right spot, as easy as hitting the board side of a barn (hence the name). The cross section of a uranium atom is 600 barnes at room temperature, or 6×10−22 cm². But each cubic centimeter of uranium holds .5 x 1023 atoms. Based on this, it comes out that a thermal neutron that enters a 1 cm cube of uranium has a virtual certainty of hitting an atom — there are 3 cm² of atoms in a 1 cm² box. You could hardly miss.
Each uranium atom gives off a lot of energy when hit with a neutron, but neutrons are hard to come by, so a practical bomb would have to involve a seed neutron that hits a uranium atom and releases two or more neutrons along with energy. The next neutron has to hit another nucleus, and it has to releases two or more. As it happens uranium atoms, when hit release on average 2.5 neutrons, so building a bomb seems awfully easy.
But things get more difficult as the neutron speeds get greater, and as the atoms of uranium get hotter. The cross-section of the uranium atom goes down as the temperature goes up. What’s more the uranium atoms start to move apart fast. The net result is that the bomb can blow itself apart before most of the uranium atoms are split. At high speed, the cross -section of a uranium atom decreases to about 5 barnes you thus need a fairly large ball of uranium if you expect that each neutron will hit something. So how do you deal with this. For their first bomb, the American scientists made a 5 kg (about) sphere of plutonium, a man-made uranium substitute, and compressed it with explosives. The explosion had to be symmetrical and very fast. Deciding how fast, and if the design would work required a room full of human “computers”. The German scientists, instead made flat plates of uranium and slowed the neutrons down using heavy water. The heavy water slowed the neutrons, and thus, increased the effective size of the uranium atoms. Though this design seems reasonable, I’m happy to say, it can not ever work well; long before the majority of the reaction takes place, the neutrons get hot, and the uranium atoms fly apart, and you get only a small fraction of the promised bang for your bomb.
How fast do you need to go to get things right? Assume you want to fusion 4 kg of uranium, or 1 x 1025 atoms. In that case, hitting atoms has to be repeated some 83 times. In tech terms, that will take 83 shakes (83 shakes of a lamb’s tail, as it were). This requires getting the ball compressed in the time it takes for a high speed neutron to go 83 x 3 cm= 250 cm. That would seem to require 1 x 10-7 seconds, impossibly fast, but it turns out, you can go somewhat slower. How much slower? It depends, and thus the need for the computers. And how much power do you get? Gram for gram, uranium releases about 10 million times more energy than TNT, but costs hardly more. That’s a lot of bang for the buck.
Robert Buxbaum, Mar 29, 2020.