[syhprum (OP)]

I am always surprised by how much U235 was in the "small boy" bomb as this was extremely expensive to produce and in such short supply that no test detonations were made.
Was it due to the uncertainty of exactly how much was required or for political reasons playing safe ?
I understand that one of the reasons for the abandonment of the German U235 bomb project was that they badly miscalculated the quantity required although I have seen it published that the calculation is relatively easy !
The use of a Polonium trigger was supposed to be a big secret just after the War but I would be surprised if both the German and Japanese scientist did not understand this.
.

[alancalverd]

Trinity was the code name of the first detonation of a nuclear device. It was conducted by the United States Army at 5:29 a.m. on July 16, 1945, as part of the Manhattan Project. The test was conducted in the Jornada del Muerto desert about 35 miles southeast of Socorro, New Mexico, on what was then the USAAF Alamogordo Bombing and Gunnery Range, now part of White Sands Missile Range.

The physics of explosive chain reaction was well established by 1943 but the engineering requirement to manufacture sufficient fissile material and assemble it in a reliable bomb was orders of magnitude more difficult.

German progress was hampered by a false start, basing reactor technology on heavy water rather than graphite. It is conceivable that Heisenberg (not known for Nazi enthusiasm) actually encouraged this as a diversionary tactic, knowing that the only source of sufficient D2O, the Rjukan plant, could be bombed or sabotaged once the Allies got wind of the project - and it was. 

[syhprum (OP)]

Trinity was of course the result of a compressed Plutonium core ,weapons grade Plutonium being much cheaper to produce, the critical masses were determined in crude experiments which resulted in the deaths of technicians on two occasions.
Thanks Alan but it is really U235 in which I am interested why so profligate with this Rare materiel ?
The Germans tried to use Graphite but the Graphite they were supplied with was not of adequate purity     

[evan_au]

I understand that the uranium bomb design was tested with sub-critical masses.

By measuring the growth in neutron emission over time, they could extrapolate the amount of material they would need for a critical mass, and how long they had to assemble the critical mass.

The critical mass can be reduced by reflecting neutrons back into the core, and the chain reaction can be accelerated by a pulse of neutrons at the right time. I am sure many optimisations of the basic design took place after WW2.

But to end WW2, the USA wanted something that they were confident would work.

[syhprum (OP)]

Why were the Germans so far out in their calculations of the amount of U235 required did they have too little for experimentation or was their theory wrong, Did Heisenberg give any explanation after the war ?

[Bored chemist]

I have seen it published that the calculation is relatively easy !

Yes, as long as you know the neutron yield of uranium fission.
That's not an easy thing to measure.

[syhprum (OP)]

For long after the war the Neutron yield from a fission event was considered a military secret.

[Petrochemicals]

I am always surprised by how much U235 was in the "small boy" bomb as this was extremely expensive to produce and in such short supply that no test detonations were made.
Was it due to the uncertainty of exactly how much was required or for political reasons playing safe ?
I understand that one of the reasons for the abandonment of the German U235 bomb project was that they badly miscalculated the quantity required although I have seen it published that the calculation is relatively easy !
The use of a Polonium trigger was supposed to be a big secret just after the War but I would be surprised if both the German and Japanese scientist did not understand this.
.

The trinity test was of a fat man ngasaki plutonium type, little boy was virtually a dirty bomb, the Americans did not understand it. Basically it was the test of another weapon, but the us did not wish to waste the bomb. They expected far more from the bomb in all honesty, most of the uranium was wasted. Given that, you have to think that physicists estimated a very low conversion ratio when calculating. The nagasaki fat man became the go too bomb not only for cost, but for efficiency. I believe the little boy was a stand in for the thin man design that was scrapped.

https://en.m.wikipedia.org/wiki/Thin_Man_(nuclear_bomb)

https://en.m.wikipedia.org/wiki/Little_Boy

[alancalverd]

U235 isn't particularly rare. It accounts for about 0.7% of natural uranium, which has been mined and refined in tonne quantities for many years as the basis for pottery glazes. Separation by differential diffusion of the hexafluoride was well established in WWII.

A couple of years ago  I was called out to investigate the radiation badge dose of one man who worked with electron beam welding. Turned out that the foreman, who rarely operated the machine, had a much larger dose than either of the technicians who did most of the work. We couldn't find any leakage from the EBW unit, but when they weren't using it, the guys left their badges on a Victorian-tiled windowsill that fairly crackled with uranium beta emission and bremsstrahlung. Previous  findings in a "contaminated" hospital x-ray room - glazed sink and toilet - led me to suspect the tiles.

[Bored chemist]

U235 isn't particularly rare. It accounts for about 0.7% of natural uranium,

Isolated 235 U is very rare, and rather expensive.

[syhprum (OP)]

The 50 Kg or so used in the WWII bomb probably cost about $25 billion in modern money to produce.
Can I buy nano gram quantities for research ?

[Bored chemist]

It's also important to realise that "the quantity of U235 required for an explosion" is poorly defined to the extent that you can hardly answer the question today.
In principle, you can calculate a minimum, but when did the army ever want a "minimum" size bomb?

[syhprum (OP)]

It seems that the further we get from events the more the truth leaks out, the Hiroshima bomb was almost a technical failure as well as a political one at the time we were told how scientific the Americans were calculating the required amount of U235 to the nearest milligram but it know seems they scrapped the bottom of the barrel to use every bit of U235 they could  to get a bang of some sort.
The use of two bombs in rapid succession was meant to convince the USSR that they had a large supply of them but Stalin knew better.
The rapid surrender of Japan was attributed to the new wonder weapons not the entry of the USSR into the war or the easing of the surrender terms to allow the Emperor to remain in power.