The physics

Splitting the atom

At the centre of every atom is a tiny, dense nucleus. In fission a free neutron strikes a heavy nucleus, such as uranium-235, and the nucleus splits into two new, lighter nuclei. ^{Sources: 9, 10}

Each fission of uranium-235 also throws out two or three more neutrons, and each of those may go on to split another nucleus. ^{Sources: 1, 10}

Each fission releases about 200 million electron volts of energy. More than 80 per cent of it goes into the speed of the two flying fragments; the rest is carried by neutrons and radioactivity. ^{Sources: 1, 10, 11}

That is a great deal for one atom. Robert Serber’s 1943 lectures to the new scientists at Los Alamos put it at more than ten million times the heat that one atom gives off in ordinary burning. ^{Sources: 4}

The energy comes from mass. Einstein’s equation, E = mc², says that mass and energy are equivalent, and because the speed of light is so large, a little mass stands for a great deal of energy. Nuclear explosions release energy from the nucleus; ordinary explosives draw theirs from chemical reactions. ^{Sources: 12}

The complete fission of one pound of uranium or plutonium releases as much energy as about 8,000 tons of TNT. A 20-kiloton bomb splits only about 2.5 pounds of material. ^{Sources: 1, 13}

The chain reaction

Because each fission frees more neutrons than it takes in, the reaction can feed itself. One fission leads to several, those to many more, and the numbers grow at each step. This is the chain reaction.

With fast neutrons each step, or generation, takes about a hundred-millionth of a second. Physicists call that unit a shake. ^{Sources: 1, 4}

Starting from a single neutron, about 58 generations are enough to release 100 kilotons. Almost all of it comes at the very end: 99.9 per cent of the energy is released in the last 7 generations, in roughly 0.07 microsecond. ^{Sources: 1}

A reactor and a bomb use the chain reaction in opposite ways. A reactor slows its neutrons with a moderator, a light material such as graphite or heavy water, because uranium-235 splits far more readily when a slow neutron strikes it. ^{Sources: 14, 15, 16}

A bomb cannot wait. Slowing a neutron takes about a microsecond, and by then the explosion is over, so a bomb has to run on fast neutrons. ^{Sources: 4}

Critical mass

Some neutrons escape through the surface of the metal before they can split anything, while new ones are made all through it. So a bigger lump loses a smaller share of its neutrons, and so does the same lump squeezed smaller. ^{Sources: 1}

The critical mass is the smallest amount that will keep a chain reaction going on its own. Below it, too many neutrons escape and the reaction dies away. ^{Sources: 17, 18}

A tamper, a heavy shell around the core, reflects escaping neutrons back in and holds the core together a little longer, so less material is needed. Both the gun and the implosion designs used one. ^{Sources: 1, 17, 19}

Nobody knew the true figure at first. In March 1940 Otto Frisch and Rudolf Peierls estimated the critical size of pure uranium-235 at about one pound. Early American estimates ran anywhere from one to one hundred kilograms. ^{Sources: 2, 3, 15}

By April 1943 Serber’s best estimate, with a uranium tamper, was 15 kg of uranium-235 or 5 kg of plutonium, figures he called still quite uncertain. Fat Man’s plutonium core weighed about 6.2 kg. ^{Sources: 4, 20, 21}

The uranium problem

Natural uranium is about 0.7 per cent uranium-235. The other 99.3 per cent is uranium-238. That is about 1 in 140 atoms. ^{Sources: 1, 4, 22}

The two kinds are chemically identical, so no chemical process can pull them apart. They differ only slightly in weight, and separating them by physical means was, in the words of the official history, extremely difficult and expensive. ^{Sources: 23}

Oak Ridge used three methods. In gaseous diffusion, at K-25, uranium was made into a gas, uranium hexafluoride, and pumped through porous barriers. The lighter molecules pass through slightly more easily, but at best each barrier improves the mix by a factor of only 1.0043. ^{Sources: 24, 25}

The barriers needed billions of holes no larger than about 0.01 micron. K-25 had 2,892 stages, cost 500 million dollars and employed 12,000 workers. ^{Sources: 24, 25}

Even so, in wartime K-25 could not finish the job alone. Its product reached 1.1 per cent uranium-235 by April 1945 and nearly 7 per cent by June, and went on to Y-12 for the final step. ^{Sources: 24}

At Y-12 the calutrons sent beams of uranium through a strong magnetic field. The lighter uranium-235 curved a little further and was caught separately. The process was so wasteful that only 1 in 5,825 parts of the charge became finished product. ^{Sources: 26}

The third plant, S-50, used heat. Its 2,142 columns, each 48 feet tall, raised uranium-235 from 0.71 per cent to about 0.85 per cent, a small first step for the others. ^{Sources: 27}

Making plutonium

Plutonium was the other road to a bomb. It is made in a reactor. Uranium-238 takes in a neutron and becomes uranium-239, which decays with a half-life of 23 minutes to neptunium-239, which decays with a half-life of 2.3 days to plutonium-239. ^{Sources: 28, 29}

The amounts are tiny. Hanford’s T Plant was designed to recover about 250 grams of plutonium from each ton of uranium that had been through a reactor. ^{Sources: 30}

So the reactors were huge. Each Hanford reactor was a 1,200-ton graphite cylinder lying on its side, pierced by 2,004 aluminium tubes, loaded with 200 tons of uranium slugs and designed to run at 250,000 kilowatts. ^{Sources: 31}

Plutonium is a different element from uranium, so unlike uranium-235 it can be separated by chemistry. The difficulty was the radiation: the separation plants had to be run by remote control, behind thick shielding. ^{Sources: 28, 32}

Coming together in time

A lump below the critical mass is safe. To explode, the material has to be made supercritical, and so quickly that it cannot melt or change shape first. ^{Sources: 1}

There are always stray neutrons about. If one starts the chain before the pieces are fully together, the bomb will fizzle. ^{Sources: 33}

Serber reckoned that even a gun firing at 3,000 feet per second would take about a ten-thousandth of a second to bring the pieces together, thousands of times longer than the explosion itself. So stray neutrons had to be kept as few as possible. ^{Sources: 4, 19}

Uranium-235 helped. In December 1943 Segrè found that it split on its own so rarely that the pieces did not need to meet as fast as feared. The uranium gun could fire more slowly, and be shorter and lighter. That became Little Boy. ^{Sources: 5}

Plutonium did not. In April 1944 Emilio Segrè’s group found that reactor plutonium contains plutonium-240, which splits on its own far too often. A plutonium gun would have fizzled, and on 17 July 1944 work on Thin Man, the plutonium gun, stopped. ^{Sources: 6, 7}

Implosion

Implosion was the answer. Explosives around a ball of plutonium below the critical mass send a shock wave inward that squeezes it into a denser, supercritical ball. It works because the denser the metal, the smaller its critical mass. ^{Sources: 1, 17, 34}

The squeeze had to be almost perfectly even, or the core would deform and the bomb would fizzle. Explosive lenses shaped the blast, much as a glass lens focuses light, so that it reached the core as a smooth, shrinking sphere. ^{Sources: 35}

The Trinity device was built of 32 lenses, hexagons and pentagons fitted together like the panels of a football, each made of two different high explosives. Fat Man was the same design as the Trinity device. ^{Sources: 36, 37, 38, 39}

Every lens had to fire at the same instant. Luis Alvarez and Lawrence Johnston developed the exploding-bridgewire detonator, in which a pulse of electricity heats a very thin wire. Properly wired, the detonators all fired within a few hundredths of a microsecond. ^{Sources: 8, 35, 38}

At the centre sat an initiator of polonium and beryllium. Its job was to start the chain reaction at the right moment, rather than leaving it to a stray neutron. ^{Sources: 19, 40}

In September 1944 Robert Christy suggested a solid core rather than a hollow shell. It was less efficient but kept its shape better under the squeeze, and with a sensitive initiator it worked. ^{Sources: 34}

How much of the fuel was used

Once the chain starts, the bomb begins to destroy itself. Within about half a microsecond the core is so hot that it expands in spite of the tamper. Neutrons then escape more easily and the chain stops. ^{Sources: 1, 4}

Only about 1.4 per cent of Little Boy’s uranium split. Its yield is put at about 15 kilotons, with an uncertainty of about 20 per cent. ^{Sources: 21, 41, 42}

Fat Man did far better. About 1 kilogram of its plutonium core of about 6.2 kg split, roughly one sixth, for a yield of about 21 kilotons, with an uncertainty of about 10 per cent. ^{Sources: 20, 21, 41}

That is why the designers worked so hard on fast assembly, tampers and initiators. Each one let more of the fuel split before the bomb blew itself apart. ^{Sources: 13}

Why it was so hard

Much of the basic data did not exist. Los Alamos had to measure cross sections, the chances that a neutron will cause fission, be captured or bounce off, before it could calculate a critical mass or a bomb’s efficiency. ^{Sources: 5, 19}

In the middle of 1943 nobody yet knew for certain that plutonium gave off neutrons when it split. The first experiment at Los Alamos, in July 1943, used a sample of less than 200 micrograms that Glenn Seaborg had carried from Chicago in his suitcase. ^{Sources: 5}

The sums were done first by teams working mechanical calculators, many of them scientists’ wives, and then also by IBM punched-card machines. Their main wartime work was the design of the explosive lenses. ^{Sources: 43, 44}

Oppenheimer judged implosion the hardest problem of all. It required very new experimental techniques, he said, in a branch of physics few people knew well. ^{Sources: 37}

Above all, the fuel was hard to make. To the end of 1945 Oak Ridge cost about 1.19 billion dollars and Hanford about 390 million, more than four-fifths of the project’s 1.89 billion. Los Alamos, where the bombs were designed, cost about 74 million. ^{Sources: 45}

Germany discovered fission and started first, but never came close to making either fuel in quantity. How far it got is told on The German bomb.