How to calculate critical mass for fissionable materials?

[Xanax]

Yes, anyone who knows how to calculate critical mass for fissionable materials?

And also, what is the critical mass for Uranium-235 & Plutonium-239. A search on the net, every page gives a different value for it. Someone who knows a thrustable source?

[fubar]

I don´t know how to calculate the critical mass of U-235 or Pltutonium-239; but i know from an (i think thrustable) source that the critical mass of U-235 is officially 15 kg (probably lower), and from Plutonium-239 it is 10 kg.

[thrall]

I don't know how this question belongs to battle feild chemistry and ....well,The critical mass of fissionable meterial depands on the probability of chain reaction continuing and so it depends on Density,Area exposed and shape of material.Now minimum critical mass is calculated for ,of course, spherical shape but density is not a constant.So different sourses say different values.When I did a course in nuclear technology(long ago) I roughly remember I was told that for tightly moulded U-235 in normal air(no pressure) it is 25 kg. but again even temperature is a variable involved.
BTW considering the density of U-235 what will be the size of the "Ball of crotical mass U-235";)?

[vulture]

Usually, for maximum density, plutonium critical mass is a oversized tennisbal and for uranium a size 4 soccer ball IIRC.

[thrall]

I knew about uranium.Here comes something interesting for people who wants to do something "good".I always wondered "how about "assembling" a Nuke in enemy country?50 kg of meterial can be smuggled easily and so are the high explosives and triggers and shields.The outer shell is triky but that can be "Improted legally in the enemy country as hollow shell(nothing threatening) in the name of some antique(just color is wieredly,damn I've seen a shop where very large hemispherical metal pots with all those oil paintings on them at sell).so you have got everything right in the city of target.Now.................................;):)

[simply RED]

50 kg of meterial can be smuggled easily

Bullshit!

[matjaz]

For a trivial geometry, like a sphere, it might be possible to do it analytically, solving the neutron transport equations. For anything fancier, one would resort to a sort of a Monte-Carlo calculation. You describe the geometry of the system in a computer program, put in a few seeds for the avalanche, then follow them numerically thru the matter. Some of the behaviour, such as scattering angles, are chosen randomly (hence the name Monte-Carlo), conforming to the appropriate distributions for each. Each daughter neutron is then followed thru its life in the same way... If your code chews on happily, you're below critical mass. If you get a stack overflow, having to follow too many daughter reactions, you're above critical.:D

The hard part is to get the reaction cross-sections right. These are considered "sensitive" data and would be hard to aquire.

[Mike76251]

There are satelites in orbit that can "see" radioactive sources.
Those gamma rays will give you away real quick and you cannot shield them very easily.
A nuke core that I dreamed of sent gamma rays through 100 ft. of concrete when it was operating.
As a interesting side note............this reactor that I dreamed of made $$1 million USD a day worth of electricity.

[Bert]

1. This isn't exactly chemistry. Why post it in chemistry related?
2. It seems more than a bit speculative and kewl
3. Everyone should read the nuclear weapons FAQ by Carey Sublette (http://nuclearweaponarchive.org/Nwfaq/Nfaq4-1.html#Nfaq4.1.2) as it lists unreflected critical masses for the common nuclear fuels.

(edit) And once again- this is a first post asking a question. Used to be a guaranteed kick.

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We cleared the last point by email, didn't we?

Rhadon

[firebreether]

matjaz: the reaction cross sections are not "sensitive data" and are in fact easily obtainable in graphical and text format here:

http://www2.bnl.gov/ton/

You simply input the desired nuclide, say U, hit enter. Then select which isotope you want, say 235. Then click on "XS graphs", then which library you want ususally the first, and select which cross section you want, probably "total fission cross section" and then go to plot, and it gives you graphically and text file. Its pretty sweet.

and another handy link for cross sections, not just neutron cross sections is here:

http://www.nndc.bnl.gov/%7Ekinsey/endf/

[matjaz]

firebreether,
Usually, the ENDF, the Firestone's Table of Isotopes, Nuclides.net, published articles are more or less consistent for exotic reactions far from the valley of stability. They need to be, since that's where the game is in research. For classical reactions of "tactical" interest ;), you will find many discrepancies. Also, a lot of data differs systematically from very careful measurements and I cannot but think of "conspiration theory" sometimes.

Moreover, "total fission cross section" is not all there is. Neutrons and gammas produced have nontrivial energy, spin and angular distributions, which can depend on geometry, capture resonances in impurities... You cannot just multiply that by the total cross section, since the cross sections are functions of all this parameters... as well. Namely, you need a lot of data which is indeed difficult to get and will trigger questions if you try.

Another problem is getting good computer codes. MCNP, Geant... etc are good, but to use them well, tricky variance-reducing techniques need to be used since Monte-Carlo gives huge statistical error if you just go brute-force.

[matjaz]

There are satelites in orbit that can "see" radioactive sources. Those gamma rays will give you away real quick and you cannot shield them very easily. A nuke core that I dreamed of sent gamma rays through 100 ft. of concrete when it was operating.
- In my estimate, satellites could not even see awfully hot (in the multi-Ci range) unshielded sources. It's just too far and shielded too well by the air to work.
- Any gamma source can send gamma rays through any thickness of concrete. It's the probability that gets sort of... low. 100ft of concrete is A LOT. Yes, you do get a photon every now and then. But detectable from the background? No. I don't think any fission reactor has more than a couple of feet total shielding.

Getting really OT... Can some senior open a thread on this?