Was it possible for Little Boy to have predetonated and fizzled? In the Manhattan project they originally planned to use plutonium for their gun-type bomb and gave the design the name "Thin Man". However it was later determined that reactor-bred Pu-239 would inevitably be contaminated with Pu-240 whose high spontaneous fission rate would have caused a gun-type bomb to predetonate and fizzle, releasing only a small portion of its energy, unless the two pieces of plutonium were to be brought together at impractically high speeds and would have required a barrel too long to fit in any bomber. As such they switched gun-type bomb development to using U-235 which would eventually result in Little Boy while the use of plutonium was confined to implosion-type weapons and was the fissile material used in Trinity and Fat Man.
The logic behind the unusability of of Thin Man was that the Pu-240 impurities had a high spontaneous fission rate and produced fast neutrons with every spontaneous fission. These neutrons could then trigger a nuclear chain reaction when the two pieces of plutonium where near enough to constitute a critical mass but before they had reached their optimal position. The energy from this reaction would blast the two pieces of plutonium apart and quickly end the reaction before more than a tiny fraction of the plutonium had undergone fission, producing a fizzle that would have released an amount of energy impressive by the standards of chemical explosives but far below the kilotons of a proper detonation.
However U-235, the material used in Little Boy, also undergoes spontaneous fission and releases neutrons, albeit at a much lower rate as it has a much lower probability of decaying by spontaneous fission and a much longer half-life making decays of any kind much less frequent than in plutonium.
My question is, was it possible for Little Boy, or for that matter any U-235 gun-type weapon, to undergo the same type of predetonation and fizzle that made Thin Man nonviable if they were unfortunate enough to have a U-235 atom undergo spontaneous fission during the window where the two masses of uranium are close enough to sustain a chain reaction but have not reached the configuration where such a reaction would split the most atoms and release the most energy?
 A: In the Little Boy, spontaneous fission within the U-235 was occurring continuously, but the two pieces of U-235 were both carefully designed to be subcritical- that is, they were deliberately shaped and set so far apart that the neutrons released by spontaneous fissions escaped the bulk of the U-235 without setting off more fissions, thereby avoiding a premature runaway chain reaction and explosion. They were also deliberately shaped so that when the gun assembled them, the resulting shape and size of the U-235 mass would assuredly be critical.
In this effort the bomb designers were aided by the fact that the U-235 which had been purified from the U-235/U-238 mixture did not have contaminants in it which had spontaneous fission rates high enough to rule out the feasibility of the gun design. They had enough confidence in their design that they felt it unnecessary to proof-test the Little Boy, and so the first time a Little Boy design exploded was when it was dropped on Hiroshima.
A: Within a given time, the probability of spontaneous fission for the isotopic composition of uranium in a weapon is very low compared to the probability of spontaneous fission for the isotopic composition of plutonium in a weapon.  The slower assembly time for a U gun-type weapon was accepted based on the low probability of pre-ignition due to spontaneous fission.  For a Pu weapon, the probability of pre-ignition is too high for the slower gun-type assembly, so the faster explosively driven implosion design was developed.  There is a small probability of a fizzle from pre-ignition from spontaneous fission for both U and Pu weapons.
The isotopic composition of plutonium in a weapon includes Pu-240 that has a relatively high rate of spontaneous fission.  The presence of Pu-240 is unavoidable for Pu produced in a nuclear reactor. Pu production reactors at Hanford and Savannah River, used relatively short exposure times for the fuel before removing it for reprocessing to recover the Pu, to avoid excessive buildup of Pu-240.
In contrast to the U in a weapon that is highly enriched- and therefore "purified"- the Pu recovered from reprocessing is not enriched, so the Pu-240 is not removed prior to use in a weapon.
A: Yes, it was indeed possible for Little Boy to have predetonated. The problem is less the spontaneous fission of the U235, but rather that almost 20% of the uranium was still U238. Quoting Carey Sublette of Nuclear Weapons Archive:
"In Little Boy a critical configuration was reached when the projectile and target were still 25 cm apart. The insertion velocity was 300 m/sec, giving an overall insertion time of 1.35 milliseconds.
Long insertion times like this place some serious constraints on the materials that can be used in the bomb since it is essential to keep neutron background levels very low. Plutonium is excluded entirely, only U-235 and U-233 may be used. Certain designs may be somewhat sensitive to the isotopic composition of the uranium also. High percentages of even-numbered isotopes may make the probability of predetonation unacceptably high.
The 64 kg of uranium in Little Boy had an isotopic purity of about 80% U-235. The 12.8 kg of U-238 and U-234 produced a neutron background of around 1 fission/14 milliseconds, giving Little Boy a predetonation probability of 8-9%. In contrast to the Fat Man bomb, predetonation in a Little Boy type bomb would result in a negligible yield in nearly every case."
