# Formula for critical mass? Critical mass of polonium?

I'm looking for the critical mass of Polonium; is there a formula? E.g.:$$\text{Neutrons / Protons}\cdot\text{ Constant = X kg}$$

There is a little table in the Wikipedia. E.g.:

$\begin{array}{ccccr} \text{Name}&\text{Symbol}&\text{Neutrons}&\text{Protons}&\text{Crit. mass} \\\hline \text{Uranium-233}&{}^{233}\text{U}&141&92&15\:\mathrm{kg} \\\text{Plutonium-238}&{}^{238}\text{Pu}&144&94&9\text{–}10\:\mathrm{kg} \\\text{Plutonium-240}&{}^{240}\text{Pu}&146&94&40\:\mathrm{kg} \end{array}$

I'm wondering, is there any dependence? What about with a neutron reflector?

What is the critical mass of Polonium?

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You cannot have critical mass assembly if it has a short half-life, for its enormous decay heat/time. Plutonium-238 alpha-decay heat is used in radioisotope thermoelectric generators. Champion fissile nuclei are odd-numbered atomic weights. U-233, U-235, Pu-239. Polonium isotopes are useless as critical masses for their very short half-lives. – Uncle Al Mar 6 '14 at 23:04

In order to answer this question for a fissionable material, you need to know the cross section for neutron-induced fission, the number of free neutrons released in a typical fission event, and the energies that the neutrons are born with. For instance, the evaluated nuclear data file for uranium-235 lists a fission cross section of 1 barn for 10 MeV neutrons. You can change the critical mass by changing the behavior of the neutrons: for instance by surrounding the fissionable assembly with a neutron reflector, or using some "moderator" to change the average neutron energy to something more favorable for fission.

There is no measured cross section for neutron-induced fission on polonium, and polonium-209 and -210 do not have decay modes which emit neutrons. Both of these reactions are required for a uranium-like spontaneous chain reaction, so I'm prepared to assert that polonium does not have a critical mass.

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Apparently not. For Polonium in particular, see

If calculating critical mass were easy, we'd have a lot of physicists out of work :-( -- or alternatively, the Nazis would have had a working bomb long before 1944.

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I'm not sure I'd cite answers.yahoo.com if I wanted an authoritative source (though in this case I agree with the answers there). – John Rennie Feb 4 '14 at 16:00
I'll wait for answer with precise in kg. See answer from suitti answered 6 months ago from answers.yahoo.com. – user2496 Feb 4 '14 at 16:08
@user2496: you can only have a critical mass if a chain reaction is possible. This isn't possible for polonium hence you can't define a critical mass for it. – John Rennie Feb 4 '14 at 17:58
The scientists at Los Alamos were able to make calculations of the amount of U-235 required for a critical mass. This is detailed in Serber's "The Los Alamos Primer". The German atomic program foundered on several different technical points, none of which involved calculation of the critical mass of uranium. – user16622 Jun 18 at 14:31

If you have neutron-absorption cross-section/neutron energy, average neutrons/fission emitted within a shake or two of the event, and density of the material, all else is number crunching. Note the world is a dirty place (impurities, multiple isotopes, phase transitions, structural disorder and voids, atmospheric neutrons from cosmic ray atom spallation, increasing temperature plus disassembly in the interval...) so there will be slop in the gears.

Look at isotope half-lives. Assembling a subcritical spherical few kg of polonium is a not insignificant cooling problem. Is polonium fissile at all? No. Also see "tickling the dragon's tail." A Manhattan project engineer sought to assemble an exponentially sub-critical mass of fissile material within neutron-reflecting blocks. As he leaned over, his bodily wealth of neutron-reflecting hydrogen and carbon set it supercritical.

"Layer-cake" cores have been tried. If you simultaneously D-T fusion (lots of 14.1 MeV neutrons) your fission critical mass decreases. However, reaction requires time versus the imploded fissile body rebounding, heating, expanding, and disassembling. An H-bomb has a thick non-fissile U-238 bomb jacket. The blast of neutrons from the fusion secondary are all well in excess of 1 Mev, the (nonpropagating) fission threshold for U-238. It all fissions anyway.

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