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I think most of us know about the construction of the first atomic bomb at Los Alamos, with Robert Oppenheimer (who said he became "The destroyer of worlds", which goes to show he regretted his participation; nevertheless he did participate) in charge of an enormous complex where many, many brilliant physicists (including Feynman) were offered (ordered for participating in?) a well-paid job, housing, food and drink, etc. The project was initiated by Einstein after sending a letter to Roosevelt (correct me if I'm wrong), which seems to contradict his pacifist attitude. But that's not that relevant to my question. Which is:

Why did it take such a long time (2-3 years) for all these men (and some women), working on that enormous complex, to construct an actual working device [the first test (called the Trinity nuclear test) hit the jackpot], while in principle you "just" have to smash together two masses of Plutonium below the critical mass, which after the smash have a mass above that mass? That was known (i.e. in theory) at the time. Was it because it was the beginning of the atomic era, and there was still much to learn? Was it to prevent failure? I've read many times the Nazis were on the verge of constructing one too, and I suppose the Americans knew that too. So why not hurry a bit more? "Luckily", the Americans were first, though there were two dropped on Japan since Germany had already surrendered. Even a third was planned to be thrown because there could be used three different elements in the bomb, and the Americans wanted to see how all three exploded. The second one, dropped on Nagasaki, was i.m.o. totally superfluous. By the way, the only relevant tag I could find was "nuclear physics".

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    $\begingroup$ From what I recall when reading about this in various sources (biographies of some of the physicists involved, The Day of Trinity, which I read many years ago, and other things), I think the problem was the rapidity of the fission process and the difficulty in getting nearly all the atoms split before the energy from the earlier splitting atoms blew away the remaining atoms. Also, any kind of asymmetry in bringing the atoms together would ruin the attempt, maybe like trying to symmetrically squeeze a blown up balloon with your hands. $\endgroup$ – Dave L Renfro Dec 25 '17 at 8:12
  • $\begingroup$ That last sentence is a very nice way to visualize the point of symmetry! $\endgroup$ – descheleschilder Dec 25 '17 at 13:24
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    $\begingroup$ The picture you seem to have formed of the Manhattan project isn't accurate. WP says 90% of the cost was in the production of the fissile materials. That took place at Hanford and Oak Ridge, not Los Alamos. It was basically a big industrial effort, with a relatively small scientific effort to support it. $\endgroup$ – Ben Crowell Dec 26 '17 at 16:02
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    $\begingroup$ "In theory, there is NO difference between the theory and practice. In practice, there IS" Wikipedia has plenty of reading about the industrial challenges to overcome. $\endgroup$ – Peter M. - stands for Monica Dec 27 '17 at 18:30
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    $\begingroup$ One does not just smash together two pieces of plutonium: such a bomb would go critical prematurely, and blow apart in a relatively small explosion. For plutonium, the much more complex implosion technique was Invented. It requires starting with a very nearly critical assembly, the precise timing of multiple explosive lenses, and an initiator to provide a burst of neutrons, among other things. $\endgroup$ – sdenham Dec 29 '17 at 17:56
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Some of the most critical numbers needed are the reaction cross sections. There was basically no serious way of calculating those beyond orders of magnitude. The cross-sections had to be measured, and this is a tedious process, even with good sources and pure samples.

Next, understanding (in an age where all computers were human) the hydrodynamics of the shock wave propagation in plasma bounded by a medium that is about to be blown to bits was a big headache, never mind the reflection of the shock waves to produce spherical compression. The precise timings of the various physical phenomena, and how one step in the sequence affected later steps had to be understood. The thermodynamics alone is not exactly equilibrium stuff. Indeed, the actual compression design was rather controversial as it required machining precision that was, at that time, exquisite. Working out the actual geometry of the lenses, and getting rid of the imperfections, were also necessary breakthroughs.

As an aside, you can get a good survey of the math involved in thermonuclear (i.e. fusion) devices from the book The physical principles of themonuclear explosive devices by F. Winterberg. This is not what you’re asking for but it will give you a sense that the ideas might not be so complicated, but the math remains challenging and the engineering to make it work is even more sophisticated.

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    $\begingroup$ in an age where all computers were human. I like that! Best (most informative) answer of all! $\endgroup$ – descheleschilder Dec 26 '17 at 4:50
  • $\begingroup$ "Best (most informative) answer of all!" I agree. $\endgroup$ – Dave L Renfro Dec 26 '17 at 10:57
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    $\begingroup$ @descheleschilder FYI Feynman made an early very positive impression with the bigshots by organizing the computations, i.e. segmenting the tasks in doable chunks and managing the humans in charge of the calculations. (I believe the human computers were in many cases wifes of scientists working more directly on the design, but I could be wrong.) In a different direction, Chandrasekhar apparently "solved" the various stellar structure equations by having chains of women in long rows manually integrating one step of a calculation and physically passing their result to the person in the row. $\endgroup$ – user6552 Dec 26 '17 at 15:44
  • $\begingroup$ Wow, man! That also very nice to know!.Especially when I try to visualize the chains of women in long rows manually integrating one step of a calculation and physically passing their result to the person in the row. $\endgroup$ – descheleschilder Dec 26 '17 at 16:30
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    $\begingroup$ @descheleschilder They were (apparently) physically and manually integrating using the Runge-Kutta scheme one step at the time. $\endgroup$ – user6552 Dec 26 '17 at 18:08
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One of the big issues was isotope separation. Extracting uranium 235 from uranite was a huge problem that took quite an effort to overcome. In fact, just before the war started Niels Bohr believed that extracting enough uranium 235 to build a bomb would be an impossible task (see Margaret Gowing's Niels Bohr and Nuclear Weapons, in Niels Bohr: A Centenary Volume (Harvard University Press, 1987)).

I suggest that you read Richard Rhodes' The Making of the Atomic Bomb.

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(1) Weapon-grade uranium is hard to make - it took almost a year to separate 64 kg of weapon-grade uranium for the bomb, so "Little boy" bomb was not even tested (they had no spare). And because of the bomb design, most of that expensive uranium was NOT involved in the nuclear explosion (bomb exploded into sub-critical mass before most of the uranium was involved in the chain reaction).

How hard is to make the weapon-grade uranium: in Y-12 complex in Oak Ridge electromagnetic isotope separation, they used 12 300 tonnes (1 tonne = 1000 kg = 2204 lb, $300 million worth) of silver (copper as strategic material was not available in necessary quantities) converted to wires for the coils. After manufacturing the wires, facility was burned down to extract spilled silver from the ashes. Less than 0.036% was lost.

But to have feasible nuclear bomb, you need plutonium, which has to be first isolated (in 1940) and researched, then, industrial amounts of sufficiently pure isotopes of plutonium has to be manufactured in a breeder nuclear reactor, which is also an easy to bomb target (and extremely expensive to build).

Scientist were well aware of the inefficiency of the "Little boy" design, therefore they used shaped explosion to create superctitical mass of 11 kg of Plutonium - which has to be created from industry-grade (not weapon-grade) uranium in a breeder reactors, so it is much cheaper and faster process (it took about 1 month to breed enough Plutonium for 1 bomb). But you need to build also breeder reactors to manufacture the plutonium.

Because scientists were not sure if plutonium bomb would even work (decision could not be made based on the minute amount of the plutonium isotopes available), Manhattan Projects decided to invest in both approaches to save time and halve the risk.

(2) Explosion-shaped charge used in Fat Man design is substantially more complex design (as compared to just two pieces of metal hitting each other as in Little boy): requires precise synchronization of multiple explosions (to shape explosion inward: hundred nanoseconds difference can make it or break it), therefore it was tested - Trinity - and they could not use computer simulation for explosion because computers were not invented yet, all calculation were made by hand.

(3) Bomb delivery is another big problem: Developing B-29 "strategic" bomber was even more expensive than the Manhattan project. It was about twice heavier than "standard" heavy bomber, B-17 and so substantially more complex. Getting enough power from just 4 engines, and fully pressurized cabin (to be able of long flights in high altitude, where enemy fighters cannot reach it), was especially hard.

Unexpected part that it at the end, nuclear bombing not only saved lives (it prevented expected 500K US casualties and tens of millions expected Japanese casualties during the planned invasion Operation Downfall - bigger than D-Day), but also saved money: because it shortened war by several months, war cost were about 1 Billion per week, and cost of B-29 and Manhattan Project were in total only about $4B.

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  • $\begingroup$ I like your answer (what amazes me is that the development of the B-29 was even more expensive than the Manhattan project) though I find it a bit strange to say that the bomb "saved" many lives. Of course I understand what you mean by that, but nevertheless; ask the people on who this weapon of mass destruction was dropped. I don't think they agree..(the people that survived). And why a second one had to be dropped? $\endgroup$ – descheleschilder Dec 27 '17 at 0:36
  • $\begingroup$ Second bomb was dropped because Japanese did not surrender after first one. When fighting a war, your mission is NOT to die for your country, but to make the other guy to die for his. $\endgroup$ – Peter M. - stands for Monica Dec 27 '17 at 14:56
  • $\begingroup$ Your mission when fighting a war is not to make the other guys dying for their country. That would mean mass suicide (which it actually is, after some thinking, but not in the normal sense of the word). Your mission is simply to kill (which is not the same as making them die for their country) the other poor guys who went to war (non-voluntarily, for the biggest part, although the people in power can manipulate guys to go to war voluntarily; maybe by saying that's the greatest virtue of all, it's an honor, etc. and especially the younger guys are sensitive for this kind of rhetoric). $\endgroup$ – descheleschilder Dec 27 '17 at 15:16
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    $\begingroup$ @descheleschilder - Facts are not on your side. Nagasaki bomb was dropped on Aug 9. Japan surrender was announced Aug 15. In the night Aug 14-15, there was attempt of military coup d'état to prevent the surrender. Japan knew that making the bomb is slow process. USA had only one more produced and ready, and as I said it took a month to make new one. BTW facts are stubborn: they do not care how you personally feel about the issue. $\endgroup$ – Peter M. - stands for Monica Dec 27 '17 at 15:39
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    $\begingroup$ @descheleschilder - Not sure what are you trying to dispute: Dates of bombing? Date of surrender? BTW many historians consider Soviet invasion of Manchuria on Aug 9 a strong contributing factor to Japanese surrender, but how much would be always a matter of debate, because in history, we cannot have controlled experiments like in what you call "exact sciences". $\endgroup$ – Peter M. - stands for Monica Dec 27 '17 at 16:14
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You should do some preliminary research before asking such a question. It was not so easy, even in theory. They did not know anything about Plutonium when they started, it simply did not exist. They had to make it, and study its properties etc. This was a slow process. The first bomb was based on Urainum rather then Plutonium, and again there was a huge problem to obtain the correct isotope of Uranium. There were many other difficult problems, or example how exactly you compress a piece of Plutonium to achieve critical mass. This is done with ordinary explosives, and the technology which does this (called implosion) had to be developed both in theory and in practice. These are only some of the most difficult problems they had. And it is actually amazing that they were able to do all of this so quickly.

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    $\begingroup$ My grandmother, Lilli Hornig, who worked in a minor role on plutonium chemistry at Los Alamos, sometimes privately made jokes that they knew so little about plutonium that they used it for paperweights on their desks. She made some related comments about the isotope issue in this interview: manhattanprojectvoices.org/oral-histories/… $\endgroup$ – Dan Fox Dec 28 '17 at 10:27
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    $\begingroup$ @Dan Fox: pretty expensive paperweights:-) $\endgroup$ – Alexandre Eremenko Dec 28 '17 at 12:32
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I can only recommend R. Rhodes, The Making of the Atomic Bomb once more and very strongly. It is also instructive to note that although Leo Szilard [sp] was inspired to understand and fight for the chain reaction concept and also held the patent it was years before he or anyone else could figure out what material could be used to demonstrate the concept. Now, of course, there is a whole declension of what elements turn into other elements as a sun burn through its life.

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