Talk:Critical mass

Merged article

Article merged: See old talk-page talk:Critical size

Symbol for critical mass

Is there a common or standardized symbol for the critical mass of an element? For example, μ_U-233 if "μ" was the appropriate symbol and U-233 was the element in question.

Honestly I am not sure there is any symbol

Does anybody know the critical mass for a gas-core "nuclear lightbulb" reactor?

I did a calculation with MCNP5 two years ago using UF6 as a solid, which is about half as dense as H2O.... I found a phase diagram for UF6 that showed at what temperatures/pressures the compound was solid/gas. If I recall correctly, the critical size was between 1-3 meters for a right cylinder in the solid state (~room temperature).—Preceding unsigned comment added by 72.81.90.108 (talk • contribs) 03:06, 8 July 2007

The critical mass is certainly dependant on the material, rather than what device it is being used in. I have no idea what the critical mass of uranium hexaflouride is (the NLB propellant), but Im guessing it's irrelevant as the mixture is heated to a plasma when used and the resulting increase in pressure generated will allow a higher rate of fission. So unless you deliberately compress the gas too much during transport you shouldn't get into any problems with it going fissile.

Also, I think critical mass is a but of a bad name, it should really be critical density

Critically depends on mass and density, so that term is imperfect too. However, for a given mass critical density makes sense; similarly, for a given density, the critical mass is meaningful. --Patrick 15:21, 16 December 2005 (UTC)

Californium-251 bare-sphere critical mass

The article says Californium-251 bare-sphere critical mass is 9kg, based on an incidental comment in this article. But the Nuclear Weapons FAQ (section 6.2.4.4) estimates it to be 1.94kg. Does anyone know of another source for this info? - Rwendland 11:24, 2 December 2005 (UTC)

As no-one has offered a third source, and I strongly suspect the 9kg is wrong, I'll delete Californium-251 from the table. Better no info than possible wrong info I think. -- Rwendland 14:08, 17 December 2005 (UTC)

Copyediting

The paragraph:

The realisation that a supercritical assembly is not necessarily prompt critical is attributed to Enrico Fermi, and made the construction of a nuclear reactor using a fission chain reaction possible. Any prompt critical assembly will explode if not rapidly brought below prompt criticality.

seems to need some editing for clarity, however, I don't know the original meaning and I am not a nuclear physicist so, rather than introducing new errors of terminology, if someone else would like to fix it ... Alex.tan 03:16, 9 December 2005 (UTC)

Alex, the meaning of this passage hinges on the words "supercritical" and "prompt critical". An assembly is prompt critical when only the neutrons resulting from fissioning nuclei are sufficient to sustain the chain reaction (supercriticality). The neutrons released after fissioning from the fission fragments (daughter nuclei) are not necessary to sustain the chain reaction. Yet I have to agree the final sentence is a bit mysterious!Wikkileaker (talk) 17:09, 23 January 2019 (UTC)

Re: Criticality pathways tutorial

This passage is just out of place here both in content and style. Also I suspect that it was not originally written for this article, but comes from someplace else unattributed. In my opinion it should be deleted outright. DV8 2XL 19:39, 16 December 2005 (UTC)

• I agree. Something along these lines might be useful for people who are new to the subject and not well-versed in physics, though. One has to take into account that people reading these articles come to them with all manner of levels of expertise. Still, I don't really like the style of this. Petwil 03:48, 17 December 2005 (UTC)

Article name

I think this physical concept is the primary "critical mass" and the page should be at critical mass. How do others feel about that? --Yath 05:07, 18 December 2005 (UTC)

Wikimedia is being too finicky to move the page over the current redirect for some reason, so I listed it at Wikipedia:Requested moves. --Yath 20:37, 21 December 2005 (UTC)

The first paragraph in the section titled, "Criticality via additional mass" is not accurate; this is why I added the second paragraph and three enumerated points regarding thermal feedback. The statements are not quoted from any particular source. I did not wish to delete the previous entry regarding the marbles.

Move from Critical mass (nuclear) to Critical mass

Votes

• Support.--Patrick 12:26, 18 December 2005 (UTC)
• OPPOSE, I don't think it's the most overwhelming meaning. 132.205.45.148 18:29, 22 December 2005 (UTC)
• OPPOSE, The term is used now in many other domains. 70.51.178.2 19:29, 22 December 2005 (UTC)
• OPPOSE, term is used is many other domains (right, what 70.51.178.2 said!) - Tedernst | talk 19:41, 22 December 2005 (UTC)
• Support - since the physical concept is the primary meaning, and for other reasons given in the discussion section. --Yath 19:45, 22 December 2005 (UTC)
• Support. The physics term is the original meaning, upon which all the other uses are based. --Srleffler 20:19, 22 December 2005 (UTC)
• Support. All derived uses of this phrase are meaningless without its original physical definition. Femto 20:49, 22 December 2005 (UTC)
• Support. See discussion. Jitse Niesen (talk) 21:56, 22 December 2005 (UTC)
• Support. I guess that a user searching for "critical mass" will almost certainly want to read about the physics concept. For the occasional exception, there is Critical mass (disambiguation).---CH 11:32, 23 December 2005 (UTC)
• Support. Other meaning are relatively marginal. Karol 16:05, 23 December 2005 (UTC)
• Support. Other meaning are 100% derived from core concept. (And BTW, Critical Mass for the self-organized cycling, etc. human-powered mobility events is always capitalized (both words)ericbritton 18:18, 23 December 2005 (UTC)
• Support. Obviously. The other meanings on Critical mass (disambiguation) don't even come close to the importance or predominance of the concept in physics. This should never have been moved in the first place. — Knowledge Seeker দ 04:03, 26 December 2005 (UTC)

Discussion

The term, "critical mass", was invented in the 20th century (OED dates it 1941, Femto) specifically to describe the concept of the amount of mass required for a sustained nuclear chain reaction. It has had primarily that (or no other) meaning for many decades. If you use the term with anyone, if they happen to know what it means, they think of nuclear reactions first and foremost.

The mere fact that it has other meanings as well is not enough to make a disambiguation page the primary page for the term. Since the physical concept is the primary meaning (by far), it belongs at the main page, with a link to the disambiguation for other meanings of the term. For example, there are about 9 articles about various concepts associated with the word "ruby", but since the gemstone is the main meaning, it is at ruby rather than a disambiguation page. (This is in response to 70.51.178.2 and Tedernst: your reasoning is incorrect.)

I hope more people will vote for this page move, since giving the primary meaning of a term the proper prominence has a definite effect on readers' understanding of the term and its more modern derivatives. --Yath 19:45, 22 December 2005 (UTC)

You have the history correct, yet your reasoning about "primary use" is unsubstantiated. Words and terms change meanings over time. People often now use the word "xerox" to mean any photocopier, or the act of making copies, for example. The encylopedia is here to describe the world, not decide how it should be. Do you have anything to backup your claim of the physical concept as the primary meaning by far? Tedernst | talk 20:02, 22 December 2005 (UTC)

[1] (dictionary.com). In google, the critical Mass (bicycle) concept has the first hit, though the number of hits for "critical mass" physics outnumbers "critical mass" bicycle by about 30%. --Yath 20:15, 22 December 2005 (UTC)

Not to forget the "critical mass media" hits. Google schmoogle, you could prove anything either way. Repeat after me, Google is not a linguistic tool. Femto 20:49, 22 December 2005 (UTC)

Yath your reasoning would have some validity were this a dictionary, where of course this meaning would have the first position. However this is an encyclopedia and thus we are obligated to sort meanings of the same term into separate articles, routing the reader through a disambiguation page is simply the easiest way when usages split or drift from the original meaning. 70.51.178.2 20:23, 22 December 2005 (UTC)

I understand that you are addressing two separate concepts here. By saying "we are obligated to sort meanings of the same term into separate articles" you assert that a disambiguation page must exist; however, everyone agrees that there will be one, so it is unnecessary to argue that point. You also don't feel that the physical concept has sufficient prominence to be given the primary article name; on that point we certainly disagree. --Yath 20:34, 22 December 2005 (UTC)

The way I understand our mission here (and how I read WP:DAB#Page naming), the only time one article should have the main title over another, is if it's by far the more common usage of the title. Rome, for example. Your data showing 30% more does not seem to indicate that one use is far more than the others. Tedernst | talk 20:45, 22 December 2005 (UTC)

What exactly are those other uses of equal importance? All I see on the disambiguation page are things or groups that evidently borrowed the concept. A dictionary might give equal weight to various uses of words in describing the world, but an encyclopedia should give priority to the basic definitions. Femto 20:49, 22 December 2005 (UTC)

It seems to me that the physical meaning is indeed the primary one. Not only because I had never heard of the other meanings (which is a personal thing), but more importantly, all other meanings are clearly derived from the physical meaning. -- Jitse Niesen (talk) 21:56, 22 December 2005 (UTC)

List of Critical Mass Rides - look at all those rides! There are tens of thousands, perhaps hundreds of thousands of people riding in Critical Mass bicycle rides every month around the world. Of course the name is derivative. That doesn't mean it's necessarily a less-important meaning. - Tedernst

Granted, though some of those people call it Masa Krytyczna, Kritinė Masė, or Критическая Масса. In French however, this very same event is called Vélorution, which is neither in name nor in meaning related to nuclear physics. It's a borrowed name that is used in some languages, unlike the physical concept whose encyclopedic meaning is universal.

But wait, since "Critical Mass" (as opposed to "critical mass") is a proper noun, there is no page name conflict! We could have Critical mass (nuclear) at critical mass and Critical Mass (bicycle) at Critical Mass. There already are some articles disambiguated in this way. And, seeing that the proper noun Critical Mass already redirects to Critical Mass (bicycle), it only seems fair to redirect the 'non-proper' noun critical mass to Critical mass (nuclear). Each page would have a link to the full Critical mass (disambiguation). Then we could just sit back and watch the sociodynamicists fight it out with the hardcore band... :) Femto 12:12, 23 December 2005 (UTC)

In my experience, people are not so nuanced when they search wikipedia. Tedernst | talk 17:58, 23 December 2005 (UTC)

The disambiguation system is not intended as a search tool and should only be used sparingly to resolve page naming conflicts. As such, there is none between "critical mass" (nuclear) and "Critical Mass" (bicycle), which clearly are the primary topics between the other meanings, within their own capitalization variant. The disambiguation notes will be there in any case. Femto 20:29, 23 December 2005 (UTC)

What do you mean? When people search wikipedia, unless they choose the exact same naming conventions used by editors, they will end up in the disambiguation system. No where else on the internet, that I know of, is case sensitive. On google, for example, "critical mass" and "Critical Mass" are the same. Even here, "critical mass" and "Critical mass" are the same. Why should we expect readers looking for Critical Mass to know that capitalization is important? What is the harm in sending everyone to the dab page first, and letting them choose from there? Unless we know that the vast majority are looking for one of those available options, it seems foolish to me to pick one over the others. Tedernst | talk 20:35, 23 December 2005 (UTC)

The harm lies in that if we allow any ol' derived trademark, band name, organization name, company name etc. to impose a disambiguation on a page, Wikipedia would consist of nothing but disambiguation pages. It seems more foolish to send a not unsubstantial number of people through a dab page when they don't need to. Femto 21:04, 23 December 2005 (UTC)

It's not any old trademark or brand name. It's a monthly event all over the world with hundreds of thousands of participants. For all we know, it's accessed as often as the physical concept. No one yet has attempted to show otherwise. Tedernst | talk 21:11, 23 December 2005 (UTC)

On the other hand there may be hundreds of millions of people who never heard of one of these derived names and who expect to find a physics article first and foremost. Femto 21:38, 23 December 2005 (UTC)

Yes, of course there may. But this discussion is about taking one use among many and elevating it to a primary position, based on just the feelings of some editors here. I'm suggesting that unless we have some actual data, it may just as easily be appropriate to elevate one of the other meanings to the primary position. All these pages and pages of discussion have gotten us no closer to knowing which meaning is actually most likely to be meant by a person typing "critical mass" into the wikipedia search box, or a person clicking a bad link to critical mass. Tedernst | talk 21:47, 23 December 2005 (UTC)

These discussions so far have gotten us a poll with eight supports and three opposes, even if you count the anonymous IPs. Absent of any actual data or standards, the gut feeling of our (public) editors is what best defines the (public) needs. It seems inappropriate not to elevate what is assumed the primary topic. Femto 22:10, 23 December 2005 (UTC)

All of the discussion and support votes assert that the physical concept is primary, either because it came first, or just because it obviously is more important. Do we have any evidence that it's vastly more important? I do not have any evidence either way, which is why I ask. We should not be giving supremacy to one concept over another because "it's obvious" to some people that this is the way it should be. Tedernst | talk 17:58, 23 December 2005 (UTC)

Wikipedia editors happen to be fairly astute, and their opinions are regularly used to decide such matters in the absence of more authoritative data. --Yath 18:16, 23 December 2005 (UTC)

It's all right to rely on our judgment when making decisions, although if data are available they should definitely be considered. In general, it is difficult to find these sorts of data, though different searches are occasionally used. A good question might be "Which is more likely to have an article in a standard encyclopedia?" It's not always clear-cut, and there are sometimes controversial proposals, such as for Plasma (disambiguation), Venus (planet), or Georgia (disambiugation). Significant discussion might be necessary to find a good consensus. In this case, however, it is pretty clear that the physics concept has precedence. Remember that Wikipedia is still an encyclopedia, and academic or scholarly topics will often receive more importance. — Knowledge Seeker দ 02:35, 28 December 2005 (UTC)

• Support. I was surprised to find that the cycling Critical Mass was the main article, even though that was what I was looking for. I agree with ericbritton that the idea of a cycling/vehicular critical mass is derived from the physical one. I think that the main article being this one would also instruct some readers as to the derivation of the phrase. Ooooooooo 20:28, 7 February 2006 (UTC)

Result

Moved. WhiteNight ^{T | @ | C} 01:16, 28 December 2005 (UTC)

Prompt supercritical assemblies

In discussions on the A-bomb, there is generally an argument being made that one has to use high explosives to get the prompt supercritical mass for explosion, otherwise the excursion will be terminated before a huge amount of energy is released. Indeed, when one looks at cases like the SL-1 reactor, which became prompt supercritical, there wasn't an atomic explosion (though there was a steam explosion, which had the good effects of removing the moderator).

The time constants for neutron propagation and fission look very small compared to the time constants for, say, vaporizing the moderator water. So what exactly are the mechanism that prevent a "simple" prompt supercritical mass from exploding?

(We have exchanged ideas but none seem very convincing.) David.Monniaux 21:06, 30 May 2006 (UTC)

Probably a bit late for your question, but anyway... To my understanding there are several effects that take place on different time-scales. Doppler broadening and thermal expansion of the fissile material kick in very rapidly, and limit the criticality excursion, after that the void-coefficient of the surrounding material may be important, in certain cases ( like the Chernobyl reactor ) increased formation of gas voids in the coolant increased the reaction rate. Finally the explosion itself will rip the fissile material apart. The main reason nuclear weapons release so much more energy than a reactor criticality accident is simply that they reach much higher levels of criticality. While even a k = 1.01 will cause a reactor to blow up, weapons typically achieve k exceeding 2 or 3, or even higher. Thus simply the time required for the explosion to overcome the inertia of the fissile material and tamper is enough to release a high yield, while in a reactor only a small amount of the fuel would fission before it is blown apart, since the chain reaction proceeds much more slowly. 85.230.199.154 03:11, 10 September 2007 (UTC)

There are two types of fission reaction - fast fission, and moderated. Reactors use moderated reactions, for the most part. Critical mass is far lower for moderated reactions, because cross sections for lower energy neutrons are higher, but the timescale is longer (neutrons are moving slower and are reflected many times between fissile nucleus encounters, etc). The timescale for doubling for moderated reactions is slow enough that for practical sized finite assemblies, the energy it can generate in the core before it dissassembles is only on the order of the same energy that conventional explosives generate. It simply blows itself apart at (by atomic standards) very low energy output. Depending on the details of the assembly, the yield may be negligible, or approach that of high explosives, or somewhere in between. The dissassembly may be a steam explosion, or the fissile elements may melt or partly vaporize as well. Georgewilliamherbert 20:48, 11 September 2007 (UTC)

Moved from Ref desk: science

by--Light current 02:06, 13 September 2006 (UTC)

THe critical mass of pure U235 is about 50kg so how do you get this business of only 100ml to make a bomb? Density (solid) at 20.7 °C 5.09 g/cm3. So 100cc would weigh 509g -- far short of the 50kg required even if Pakistan could make 100% pure U235. Yes?--Light current 01:02, 13 September 2006 (UTC)

How have you come to the conclusion of 50Kg. I guess this figure is for 80% enriched version.nids(♂) 01:13, 13 September 2006 (UTC)

Look at critical mass page under Uranium 235 in the table--Light current 01:33, 13 September 2006 (UTC)

It is not clear if these figures are for higher enriched versions. and most likely, they are not. We know about little boy that it contained just about 60Kg. of U-235 with average 80% enrichment.nids(♂) 01:38, 13 September 2006 (UTC)

We also know that only 0.7Kg of 64 Kg. underwent fission in that bomb. So there is no reason to believe that we will be needing any more than 0.65 Kg. of Pure element, if we can enrich to 99.9% levels.nids(♂) 01:40, 13 September 2006 (UTC)

Im not an expert, but I dont think it works like that. You need critical mass to get fission (by definition). After that the thing blows apart and complete fission of all the material may not occur (unless its designed very well), But youve still made a bomb! I think it is false logic to assume that since only 0.65 kg fissioned, this is equal to the critical mass of 235. Any way if you want to continue this discussion, it should be moved to an appropriate page as i thikn we have now answered your questions.--Light current 01:48, 13 September 2006 (UTC)

Even i am not an expert and so i asked the experienced editors to give a better figure. But 50 Kg. is absolutely wrong. That would mean that we havent done anything in last 60 years. Moreover, there has to be a big difference between 80% enriched versions and 99.9% ones.nids(♂) 01:56, 13 September 2006 (UTC)

We have given you a figure based on the information here and in other reliable sources. If you choose not to accept it, so be it 8-)--Light current 02:12, 13 September 2006 (UTC)

Seek an expert and ye shall find. Sometimes.

There are several confusions about fission and critical mass in play here. Let me try and clarify.

First, critical mass is (almost) completely unrelated to the amount of material which fissions when a nuclear bomb detonates. Critical mass is defined as the minimum mass required to support an ongoing fission reaction. With exactly one critical mass of material, you have a reaction which keeps on going but does not increase in power. With less than one critical mass, any neutrons you inject may cause a reaction, but it dies out over time. The time for it to die out increases the closer it gets to exactly critical mass.

There's a specific number, k, used to refer to criticality. k = 1.0 is exactly critical. k less than 1 is subcritical, k greater than 1 is supercritical.

There are also two different types of fission reaction happening. One is fast fission, where neutrons hit another fissile (uranium, plutonium) atom at the speed that they were ejected from their parent fission reaction. The other is moderated fission, where neutrons bounce off other light elements (hydrogen in water, carbon, etc) and slow down before they are absorbed. The cross sections, or chance that a given neutron will actually cause a fission when it encounters another atom, are higher for moderated fission than for fast fission. So to assemble a critical mass of moderated material takes less material. A water solution of highly enriched uranium or plutonium can literally be only a few liters of volume and reach criticality.

You can't practically make a moderated bomb, because moderated neutrons take about ten times longer between when they are emitted in one fission until they are absorbed by the next uranium or plutonium atom and cause another fission. Once a supercritical assembly reaches the point that it will start to boil or melt, it will dissassemble itself (fall apart, or be "blown apart" by a small physical explosion) very rapidly. With a moderated fission reaction, the time scale for melting and steam explosions is roughly the same as the rate at which the fission energy is increasing, so it just blows itself apart with about at most the same energy as you'd get out of a chemical explosive bomb of about the same size, plus a big radiation pulse. With only slightly critical configurations, even boiling of the water solution or warming of the Uranium will cause it to drop below criticality.

This is how a bunch of criticality accidents have happened in nuclear fuel fabrication labs, where they accidentally assembled a water solution of too high a concentration of uranium or plutonium. The energy releases in these accidents have been as high as roughly 1E16 fissions, but typically less (1E13 or 1E14). 1E16 fissions is 1/1E10 of a mole of material fissioning - at roughly 16 kilotons per kilogram of material which fissions, the explosive energy equivalent of a 1E16 fission criticality accident is only about 1/4E10 x 16 kilotons = .0004 kilogram of TNT energy.

Criticality of material is dependent not just on how much material is present, but the geometry (is it a sphere? a flat plate or flat pool of liquid? a cylinder? how long, how wide, etc), and whether the material is reflected (surrounded by materials that bounce some escaping neutrons back into it). It also depends on density - the criticality is equal to the square of the density of the material, so if you manufacture say highly enriched uranium metal foam, with bubbles in it which have half the normal metal density, then you need four times as much to reach criticality (about 200 kg for an unreflected or bare spherical metal assembly). Conversely, if you compress the material, the criticality increases as you compress it, with the square of the density. So if you double the density, then the criticality is four times higher. That's how implosion nuclear bombs work - they take a subcritical mass of uranium or plutonium, and compress it explosively into supercriticality.

I hope this helps explain. Please feel free to ask for further clarification or explanation if there are points which don't make sense. Georgewilliamherbert 03:04, 13 September 2006 (UTC)

Should we start an article on Moderated nuclear explosion, or is all of this already covered in Criticality accident? -- Petri Krohn 14:06, 12 September 2007 (UTC)

Absolutely not, as it's a badly mis-informing term which does not exist outside of the now-created article. I've marked it for speedy deletion, as it is patent nonsense; a steam blast caused by nuclear fission is not a "nuclear explosion" of any sort. --24.28.6.209 02:46, 18 September 2007 (UTC)

I would also like to know that what purity for enriched Uranium has been acheived. And what will be the minimum amount required in your view, if we do compress it as much as it is legitimate.nids(♂) 08:14, 13 September 2006 (UTC)

What's used practically, or the best which can be achieved? I've heard of 99% enriched, for small lab specimens, but the odds are that production for military purposes is mostly 90% to 94% enriched. The critical mass falls significantly from 80 to 90% but not so much beyond that, and the energy to enrich beyond that point is significant.

The amount of Uranium required for a moderately modern implosion bomb is widely reported as around 15 to 25 kilograms, depending on design yield and how advanced it is. The actual amounts used in compact weapons more modern than Little Boy (which was an uncompressed gun type bomb anyways) are still classified, though estimates of the Mark 18 nuclear bomb pit are that it had over 60, perhaps 75 kg of HEU Nuclear weapons FAQ sect 4.2.4, High Yield weapons.

Most modern weapons use Plutonium fission stages, though. Georgewilliamherbert 08:30, 13 September 2006 (UTC)

Please correct this statement on the Enriched Uranium page, if this is wrong.

“ The critical mass for 85 % of highly enriched uranium is about 50 kilograms. ”

nids(♂) 08:20, 13 September 2006 (UTC)

I added "for a bare sphere at normal density", see e.g. [2]. The difference with the "15 to 25 kilograms" above seems due to the density during the implosion and the neutron reflection.--Patrick 14:35, 12 September 2007 (UTC)

Diagram to add

At top: A sphere of fissile material is too small to allow the chain reaction to become self-sustaining as neutrons generated by fissions can too easily escape. In center: By increasing the mass of the sphere to a critical mass, the reaction can become self-sustaining. At bottom: By surrounding the original sphere with a neutron reflector, it can increase the efficiency of the reactions and also allow the material to become self-sustaining.

I have made a diagram. However I can't edit to the page because of some sort of idiotic spam system that has gone into place and cannot differentiate between subdomains and domains. In any case if they ever fix it, someone can perhaps add this image to the second section. (Perhaps I am being less than charitable re: the spam link system but I am frustrated because it does not seem to be something I can override even though I am an admin, and the appeal system seems quite slow.) --Fastfission 04:34, 11 December 2006 (UTC)

Critical Mass and Density

The paragraph beginning with: "The critical mass is inversely proportional to the square of the density: if the density is 1% more and the mass 2% less, then the volume is 3% less and the diameter 1% less." is not well written. It's fair enough to point out that density is a factor in critical mass, but perhaps someone could rewrite it? Volantares 17:33, 8 March 2007 (UTC)

Overly technical

for those who aren't completely acquainted with this subject, this article is a little confusing, because it is very technical.Statue2 12:11, 28 August 2007 (UTC)

concur

This is a fairly wonky bit of writing, and an intro with pictures describing the principles in plain, but technically correct, language would be welcome. --75.73.1.89 (talk) 17:53, 6 November 2013 (UTC)

Critical mass versus criticality accident images

The image used is about a criticality accident-that maybe would be better off on the criticality accident page (there is a picture of Godiva-difficult to understand the point of the article there as well). Anyway, perhaps a subcritical bare sphere of plutonium, then a critical sphere (with or without surrounding reflective hemispheres), as well as a supercritical mass would show the concept better? I feel that using an accident recreation seems to show a "negative view" rather than an encyclopedic description of critical mass. What do you think?--Read-write-services 23:43, 7 October 2007 (UTC)

Temperature

Is criticality really dependent on temperature itself (seems unlikely) or just in the sense that density decreases with temperature?--Patrick 13:16, 6 November 2007 (UTC)

Good point Patrick, however, an increase in temperature will cause a mass to expand-resulting in a larger volume/less dense mass-I think this is why (as I understand it). hope that kind of helps.--Read-write-services 23:03, 6 November 2007 (UTC)

OK, I adapted it.--Patrick 01:23, 7 November 2007 (UTC)

critical mass of mixtures

Is there a simple and approximately correct formula for the bare critical mass of a material that is a homogeneous mixture (an alloy, say) of other materials that have bare critical masses? I assume this would depend on the relative densities, but are there any other significant complicating factors (e.g. differences in neutron energy spectra)? NPguy (talk) 00:40, 9 May 2008 (UTC)

I don't know of one. This comes up a bit when considering different Plutonium grades (reactor grade in its mnay flavors, "weapons grade" in its many flavors, "supergrade", etc). But other than that, I don't know that anyone has any use for mixtures of Pu and HEU, or Neptunium and HEU or so forth, so I don't know if anyone's looked at trying to come up with a simplified formula.

Most of the criticality analysis stuff is working on avoiding accidents, which mostly has to do with non-homogenous configurations (complex geometries, reflected, moderated, etc). Weapons research is the only area where such things would be directly relevant, but I can't think of why you'd need to do that for weapons either. When fissile materials are mixed they tend to be layered not homogenous, and the configurations are usually well below a critical mass unless explosively compressed, which requires numerical analysis of the critical configuration to analyze. So a simple formula for bare critical masses doesn't seem particularly relevant.

Maybe I'm missing something, though. I don't do it for a living all the time.

You might ask Carey Sublette and see if he knows of one. Georgewilliamherbert (talk) 01:32, 9 May 2008 (UTC)

First equation is right?

I'm only a humble engineer without knowledge on this subject. However, reading the beginning of the article...

"A numerical measure of a critical mass is dependent on the neutron multiplication factor, k, where:

   k = f − l

where f is the average number of neutrons released per fission event and l is the average number of neutrons lost by either leaving the system or being captured in a non-fission event. When k = 1 the mass is critical."

...doesn't have a right ring to me.

How about k = f / l instead? —Preceding unsigned comment added by 201.210.220.78 (talk) 19:35, 18 July 2008 (UTC)

If e.g. f = l all neutrons released per fission event are lost, so none trigger a new fission, so that is far from critical.--Patrick (talk) 23:03, 18 July 2008 (UTC)

Note also that is says "per fission event" ( fission event = fission of a single nucleus ), so k, f, and l are all ratios.--Patrick (talk) 23:13, 18 July 2008 (UTC)

While that equation and reasoning behind it are okay, it has a problem of units and does not follow the standard method of thinking about criticality within Nuclear Engineering. The unit problem arises from the fact that k is supposed to be a ratio of n/n (albeit on different time steps); however, the equation puts k in units of n/fission. As such, the equation proposed by 201.210.220.78 is more correct and closer to the standard practice. That practice being k is the (rate of neutron production)/(rate of neutron loss). As such, the section is in need a some clean up and clarification. THaskin (talk) 05:42, 20 August 2008 (UTC)

The equation probably came from the Nuclear Weapons design side - It's effectively the one you find on The Nuclear Weapons FAQ 2.1.2, k = f - (lc + le). I've seen both used in weapons literature and reactor literature and textbooks, though reactor people seem to predominantly define it as the ratio ( [3] [4] [5] ). I wish I could find my nuclear engineering intro text and reactor design texts, but they're hiding somewhere behind my nuclear proliferation collection and a bunch of aerospace books (and / or in a box, not sure).

I don't think that I put it there, but there are signs whoever did most of the article was operating off that reference site.

The equation formulation given, k = f - l, ends up reducing to the same thing as the ratios. There's the implicit 1 neutron to start with ("per event"). The standard ratio is:

k = # neutrons second generation / # neutrons first generation

This simplifies a bit, as if expressed in "per fission event" terms the divisor is 1:

k = # neutrons second generation = # produced per fission event (f) - # lost (l)

You can't use the four factor formula (per se) for nuclear weapons, as three of the four factors are for moderated rather than fast fission.

I think it's reasonable and arguable that we should include both formulations, the reactor engineering standard and the one from nuclear weapons designers, as they are in real terms equivalent (just formulated differently) and both topics expand out from this general one that they share... Georgewilliamherbert (talk) 08:47, 20 August 2008 (UTC)

Really? I've never heard/read that before. Too buried in power engineering. If that is the case, I would have to agree. I'll pull out my Duderstadt and add in the power perspective in a bit. THaskin (talk) 13:31, 20 August 2008 (UTC)

Prompt critical

I know prompt critical has its own article and it is also linked in the last sentence of this one. However I think either the link should be made more prominent or some core information from that article should be included here as well, as it is not so obvious to the casual reader of this one that a critical mass doesn't simply equal a nuclear explosion. -- 77.21.99.8 (talk) 11:49, 6 February 2012 (UTC)

Definition of 'Critical mass'

I came across this 'definition' from the the Swords of Armageddon work of Chuck Hansen

“ The minimum mass of a fissionable material that will just maintain a fission chain reaction under precisely specified conditions. These conditions include the particular material and its purity, the amount and type of tamper or neutron reflector used, the density or degree of compression of the fissionable material, and its physical shape and geometry. The critical mass of a bare, untamped and unreflected sphere of oralloy (uranium enriched to contain 93.5% or more of the uranium-235 isotope) is 112 lbs. (51 kg). A critical mass is the quantity of fissionable material within which the average number of neutrons remains constant over time, i.e., the number of neutrons lost by leakage and capture by nuclei is equal to the number of neutrons spawned by nuclei division. A neutron inserted into it will always exist, either as the original neutron or as a replacement neutron spawned by a fission reaction. At Los Alamos, an early measurement of criticality was the "Christy Crit," which was the amount of fissionable material required to sustain a critical mass when it was immediately surrounded by an effectively infinite tuballoy tamper. A critical mass is also sometimes called a "crit." ”

Source @ Swords of Armageddon: The Development of U.S. Nuclear Weapons Volume 1- Glossary, Weapons Physics, Postwar Fission Weapons Development , page 1-11, PDF- 5.66 Mb via http://www.usna.edu/ 220 of ^Borg 02:55, 28 August 2015 (UTC)

Spontaneous fission

Hello NPguy. Let's discuss this issue here, rather than in edit comments. I added the following paragraph, which you then deleted:

Due to spontaneous fission a supercritical mass will undergo a chain reaction. For example, a spherical critical mass of pure uranium-235 will have a mass of 52 kg and will experience around 15 spontaneous fission events per second (see Spontaneous fission rates). The probability that one such event will cause a chain reaction depends on how much the mass exceeds the critical mass. If there is uranium-238 present, the rate of spontaneous fission will be much higher.

Let me start by asking, if what I say is correct, do you think it would be a known fact that can be found in some book or article somewhere?

Eric Kvaalen (talk) 07:42, 25 September 2017 (UTC)

It seems that if true it would be one of those well-known facts that was in basic textbooks and articles. I am skeptical because I remember hearing about the role of cosmic rays in triggering a fission chain reaction in a supercritical assembly. NPguy (talk) 01:10, 26 September 2017 (UTC)

@NPguy: Yes, that's true. It's mentioned at Spontaneous fission#History. We can add something about that. But if you read my paragraph carefully, you'll see that I do not say that a chain reaction will not start unless there is spontaneous fission.

I agree with you that if true, what I wrote must be in the books. In other words, if true, it is also verifiable and a source can be found. But I do not have any such books, so it would not be easy for me to find a source. Nevertheless, if it's true then a source can be found. Do you have any doubt about the truth of what I wrote? The part about uranium-238 is from Spontaneous fission#Spontaneous fission rates and Gun-type fission weapon#Little Boy (which mentions that it was the U-238 that would most likely trigger the chain reaction in the U-235). Eric Kvaalen (talk) 13:18, 26 September 2017 (UTC)

Wikipedia itself is not a reliable source, but the sources in those articles (refs 1 and 2 in Gun-type fission weapon) do support the claim you've been making. NPguy (talk) 01:51, 28 September 2017 (UTC)

I know that Wikipedia is not allowed as a source, but what I'm saying is that things which are well known are verifiable even if we don't put in a reference. I mean, someone theoretically has the right to demand a reference or else he will remove the statement, but if he realizes that the statement is true, and that there must be references saying so, then I consider that to be unwarranted.

It's quite an interesting mathematical problem to try to figure out what the probability of a chain reaction is for a given amount of supercriticality. I've been thinking about this problem, but of course I can't put in my conclusions because I can't be sure that they are well known and in the books.

Eric Kvaalen (talk) 08:06, 28 September 2017 (UTC)

From Spontaneous fission:

Spontaneous fission rates

Nu- clide	Half-life (yrs)	Fission prob. per decay (%)	Neutrons per		Spontaneous half-life (yrs)	⁠Z2/A⁠
			Fission	Gram-sec
235 U	7.04·108	2.0·10−7	1.86	000.0003	3.5·1017	36.0
238 U	4.47·109	5.4·10−5	2.07	000.0136	8.4·1015	35.6
239 Pu	24100	4.4·10−10	2.16	000.022	5.5·1015	37.0
240 Pu	06569	5.0·10−6	2.21	920	1.16·1011	36.8
250 Cm	08300	~74	3.31	01.6·1010	1.12·104	36.9
252 Cf	02.6468	3.09	3.73	02.3·1012	85.7	38.1

52000 g /(235g/mole) * (6e23 atoms/mole) / 3.5e17y / 365 d/y / 86400 s/d = 12/s. Close enough to 15 for me. Gah4 (talk) 14:09, 18 December 2021 (UTC)

References

Presence of moderating material

When I do a CTRL-F on this article I see only two instances of the word "moderator", and neither has to do with the fact that the presence of a neutron-moderating material close to a near-critical assembly can send it 'over the edge' into supercritical territory. This is abundantly clear from the literature, in particular I have in mind the book Atomic Accidents by James Mahaffey. Wikkileaker (talk) 17:13, 23 January 2019 (UTC)

Moderators are needed for low enriched material to reduce loss to U238. In the case of mentioned accidents, it is more that you get reflection from such moderators. Well, which accidents do you mean? The more famous accidents with HEU are, I believe, due to reflection. Also, HEU criticality accidents can get dangerous faster. Gah4 (talk) 02:35, 24 September 2019 (UTC)

Source for spontaneous fission in U-235?

Due to spontaneous fission a supercritical mass will undergo a chain reaction. For example, a spherical critical mass of pure uranium-235 (²³⁵U) with a mass of about 52 kilograms (115 lb) would experience around 15 spontaneous fission events per second.^{[citation needed]}

Further down this talk page there is an old version of this text with a link to https://en.wikipedia.org/wiki/Spontaneous_fission#Spontaneous_fission_rates -- multiplying the 0.0003 neutrons per (gramme Neutron) by 52000 gramme gives ~15.6 neutrons per second, which seems to roughly match the figure quoted. Though since it's given 1.86 neutrons/fission, perhaps that figure should have been 8.4 fission events per second?

I believe that's how that table should be interpreted -- though, I don't have access to the source material and there is no explanation in the surrounding article text. Also am not sure how you would quote such a calculation under Wikipedia's referencing system? Modelmat (talk) 09:27, 23 October 2021 (UTC)

p.s. Is essentially none of the textual material in this article sourced? Of the 13 references, only two are attached to text, the rest to a table, and that's just for a minor note. There's not even a list of reference books which some articles have. Modelmat (talk) 09:27, 23 October 2021 (UTC)

It is not usual, except when discussing bomb design, to indicate SF rates. Instead, and in any case where more than one decay mode is possible, (alpha and beta, for example) one gives the overall rate and the branching ratio. From the chart of the nuclides, the fraction for U235 is 7e-9. So multiply the alpha rate by 7e-9 to get the SF rate. Gah4 (talk) 07:41, 24 October 2021 (UTC)

Criticality experiment specifics

This may not be the right place but what I'm wondering about is what specifically the early criticality experiments sought to find out, especially the ones that led to the now-infamous criticality accidents of Louis Slotin and Harry K. Daghlian.

In a "normal" quantitative science experiment, what you do is keep all parameters constant except one, which you vary in order to obtain different results. These results then make it possible to arrive at formulas or algorithms to describe the interrelations between the different parameters.

For example, a simple experiment about the electrical conductivity of liquid solutions would be to dip two electrodes into a sample solution, apply a current and measure the voltage. In a series of experiments you could then vary the distance between the electrodes, or the concentration of the solution, or the current, or the voltage etc, and even do multiple series for different electrolytes to compare those to each other, and arrive at the specific conductivity of given electrolytes.

Now it is clear that in the criticality experiments, they measured neutron flux. But the variable parameter in the Daghlian experiment seems to have been the "number of reflector blocks" which seems oddly undspecific; the results would seem to be applicable only to his sepcific experimental set-up. And in the Slotin experiment, the shape of the slot between the two hemispheres is variable but there doesn't even appear to be any measurement of some distance that would allow you to calculate its geometry. Cancun (talk) 12:07, 23 November 2021 (UTC)

initiator

The section seems to indicate that the reaction is started by spontaneous fission. In real bombs, they put in a Po+Be initiator, where the two mix and generate neutrons. The goal is to get the SF rate low enough not to start too early, and then a high probability when it is time to go off. Gah4 (talk) 14:13, 18 December 2021 (UTC)

spontaneous fissions in 235 and 238

Not my area, but I found this surprising

"If there is uranium-238 (238U) present, the rate of spontaneous fission will be much higher."

I'd expect the reverse, not least because there is more 238 than 235 around.

But if it isn't a literal, might it deserve a reference or a bit more explanation somewhere? Midgley (talk) 17:25, 5 April 2024 (UTC)

The numbers are in Spontaneous fission#Spontaneous fission rates, and yes 238 is higher. Both are a small fraction of the alpha decay rate, so not much effect on the overall rate. One fun thing about nuclear physics, is that the theories aren't all that good, especially relating to decay rates. Gah4 (talk) 17:01, 10 April 2024 (UTC)