How much "yellowcake" to make a Bomb?

[elucidator]

Question came up in another thread. How much uranium ore or “yellowcake” would need to be processed in order to build an A-Bomb?

[Q.E.D]

From here:

Uranium-235 is very difficult to extract. In fact, for every 25,000 tons of Uranium ore that is mined from the earth, only 50 tons of Uranium metal can be refined from that, and 99.3% of that metal is U-238 which is too stable to be used as an active agent in an atomic detonation. To make matters even more complicated, no ordinary chemical extraction can separate the two isotopes since both U-235 and U-238 possess precisely identical chemical characteristics. The only methods that can effectively separate U-235 from U-238 are mechanical methods.

So, to get 110 pounds of fissionable U-325, you would need to process about 4000 tons of raw ore.

[Ale]

That´s a big piece of yellowcake.

[zigaretten]

Yellowcake is what you get after you treat the ore. It is concentrated U[sub]3[/sub]O[sub]8[/sub].

1 kg of U[sub]3[/sub]O[sub]8[/sub] contains 848g of uranium which is about 0.7% U-235.

So 1 kg of yellowcake contains about 5.936g of U-235.

A bomb requires about 5kg of 90% enriched uranium or 4,500g of U-235.

So one bomb would require about 760kg (or 1,670 lbs) of yellowcake.

Of course, yellowcake can’t be converted to enriched uranium with 100% efficiency, so considerably more would actually be required.

Data from here.

[Q.E.D]

*Originally posted by zigaretten *
A bomb requires about 5kg of 90% enriched uranium or 4,500g of U-235.

Where did you get your information from? From every source I can find online, it says the minimum mass of pure fissionable U-235 is 50 kilograms, or 110 pounds.

[zigaretten]

From here:

To build a bomb, one must have a mass larger than the critical mass (supercritical mass) and must hold it together long enough for the desired energy release to occur. About 5 kilograms of enriched uranium are needed to achieve critical mass.

………and here:

An atomic bomb must contain a critical mass of fissile material that is, material that can undergo fission. Two types of fissile material have been used in atomic bombs up to the present type:
– Uranium-235 (235U), the rare isotope of uranium, critical mass about 5 kg

[Desmostylus]

Note, zigaretten, that this sentence:

A bomb requires about 5kg of 90% enriched uranium or 4,500g of U-235.

is incorrect. A critical mass is the minimum required for a self-sustaining chain reaction, e.g. in a nuclear reactor. As your own cite notes, more than this is required for a bomb. All the stuff I’ve seen indicates that Q.E.D.'s mass requirement is the correct one for a bomb.

[zigaretten]

Hmmmm…

The more I read about this the less I know, but…

50kg of U-235 is approximately what was used in the Hiroshima bomb and I have found several sites that state that this is “defined” to be the supercritical mass for uranium, but I don’t pretend to know what the exact significance of "defined is here.

At the same time, it occurs to me that we can probably make “better” bombs today than in 1945. And, indeed, Jane’s Defense Weekly says the following:

The amount of 90% pure plutonium (Pu239) required to make one 20kT nuclear bomb, known as a “bare” critical mass, is known to be 10kg. The most basic plutonium-based atom bombs, however, surround the plutonium sphere with a beryllium neutron reflector to enhance the nuclear reaction. As a result, they can use less Pu239.

Because the design is so basic and beryllium is so easy to acquire, most defence analysts now use the reflected critical mass figure, 5kg, as the minimum reaction mass in a nuclear device.

The same is true for a uranium device. It takes 52kg of pure U235 to make one 20kT atom bomb. The reflected critical mass surrounded by beryllium is only around a third as much, or 15kg.

Note that 20kT is approximately the size of the Hiroshima bomb and I’ve seen a couple of sites that state that the Hiroshima bomb was only the size it was because the physicists involved wanted a 20kT device (in other words, perhaps they could have made it smaller).

So…this suggests to me that we can now make a bomb which is equivalent to the Hiroshima bomb using only 15kg of U-235. Is it possible to make a smaller bomb with only 5kg? I confess that I don’t know.

[elucidator]

Well, I read all that to mean that you gotta have 55kg of uranium 235, period. Hence, it is impossible to make boom with anything less, no matter what you do to 1kg of uranium, it doesnt have critical mass.

[zigaretten]

Well, the Federation of American Scientists appears to disagree:

The minimum mass of fissile material that can sustain a nuclear chain reaction is called a critical mass and depends on the density, shape, and type of fissile material, as well as the effectiveness of any surrounding material (called a reflector or tamper) at reflecting neutrons back into the fissioning mass. Critical masses in spherical geometry for weapon-grade materials are as follows:
Uranium-235 Plutonium-239

Bare sphere:		56 kg	 	11 kg
Thick Tamper:		15 kg		 5 kg

The critical mass of compressed fissile material decreases as the inverse square of the density achieved. Since critical mass decreases rapidly as density increases, the implosion technique can make do with substantially less nuclear material than the gun-assembly method. The “Fat Man” atomic bomb that destroyed Nagasaki in 1945 used 6.2 kilograms of plutonium and produced an explosive yield of 21-23 kilotons [a 1987 reassessment of the Japanese bombings placed the yield at 21 Kt]. Until January 1994, the Department of Energy (DOE) estimated that 8 kilograms would typically be needed to make a small nuclear weapon. Subsequently, however, DOE reduced the estimate of the amount of plutonium needed to 4 kilograms. Some US scientists believe that 1 kilogram of plutonium will suffice.
If any more material is added to a critical mass a condition of supercriticality results. The chain reaction in a supercritical mass increases rapidly in intensity until the heat generated by the nuclear reactions causes the mass to expand so greatly that the assembly is no longer critical.

So does the Wiscon Project on Nuclear Arms Control:

Uranium-235 needed to make a bomb:

….15 kilograms: Weight of a solid sphere of 100 percent uranium-235 just large enough to achieve a critical mass with a beryllium reflector. Diameter of such a sphere: 4.48 in (11.4 cm). Diameter of a regulation softball: 3.82 in (9.7 cm).
….16 kilograms: Amount needed for an Iraqi bomb design found by UN inspectors.
….50 kilograms: Weight of a solid sphere of 100 percent uranium-235 just large enough to achieve a critical mass without a reflector. Diameter of such a sphere: 6.74 in (17.2 cm), comparable to an average honeydew melon.
….60 kilograms: Reported amount used in Hiroshima bomb “Little Boy.”

16 kg would require 5,900 lbs of yellowcake, or about 3 tons.

But you’ve still got to consider that Iraq could never extract the U-235 with 100% efficiency, so a more realistic estmate might even be as much as 100 times that amount, assuming that their technology isn’t the best.

[Spiny_Norman]

• according to chapter 4.1.7.1 of the handy-dandy Nuclear weapons FAQ, the critical masses for a Uranium-based bomb with a Beryllium reflector are dependent on the enrichment as follows

Enrichment / Kg Uranium
(% U-235)
93.5 / 14.1
90.0 / 15.5
80.0 / 19.3
70.0 / 24.1
60.0 / 32.0
50.0 / 45.0
40.0 / 70
30.0 / 130
20.0 / 245

Of course, enriching to even 20% is a non-trivial exercise - seeing as the Uranium in Yellowcake will have about 0.8% U-235. The NWFAQ claims that US bomb designs have used 80-93.5% enrichment.

The NWFAQ can be found here:

http://gawain.membrane.com/hew/

[Hari_Seldon]

Looking at the question behind the question, I think you have to realize that to start from the beginning, you should realize that it cost the US a couple billion 1942 dollars. Ok, you wouldn’t really have to start from the beginning (you wouldn’t have to invent teflon, for example). But unless you began with atomic scientists who were highly trained (and there aren’t many of those around, although I guess former Soviets might be available), you would first have to extract the U-235, which is damnedly difficult, then design the bomb, then figure out how to deliver it. And remember, the ingredients are highly radioactive. I guess if you were using volunteer martyrs it might simplfy life somewhat but you would always have to be training new ones. While Ted Taylor may be able to build a bomb in his garage, I think that it would require a major effort and enormous expense to do it.

[3waygeek]

*Originally posted by Hari Seldon *
**While Ted Taylor may be able to build a bomb in his garage, I think that it would require a major effort and enormous expense to do it. **

Ted Taylor himself would seem to disagree with you – read The Curve of Binding Energy sometime. Granted, the book’s 30 years old, but it’s still quite relevant.