Need vaues for critical conditions of Uranium 235

[swansont]

 

One U-235 after fission will produce new 3 free neutrons. At least one of them must collide with yet another U-235 to sustain reaction.

 

2.43. One reason Plutonium is used is that it releases more neutrons on average (around 2.7), so you have a smaller critical mass.

 

 

Another thing I'm confused about is the mechanism, because I see different examples like in a nuclear reactor and theoretical or in a bomb and it seems like they have different mechanisms for triggering fission. It seems like for the sake of a theoretical situation where ideal conditions are assumed, I don't need to calculate more math about a neutron gun right? If I have critical mass at critical volume, that's it, the decay from the high specific activity optizes the probability of the reaction triggers on its own right? Or no?

 

You can add neutrons if you have an alpha emitter and something that releases neutrons when bombarded, such as Polonium and Beryllium. That will help trigger the reaction and give you extra neutrons at the outset.

[MWresearch]

"You can add neutrons if you have an alpha emitter and something that releases neutrons when bombarded, such as Polonium and Beryllium. That will help trigger the reaction and give you extra neutrons at the outset."

 

I'm not really sure what you mean. But, what about the mechanism for which the process triggers? Another thing I'm confused about is the mechanism by which the reaction triggers at critical mass. If enough mass is collected, the mass goes critical on it's own, and neutron guns are just for moderation reactions in nuclear reactors? And what about the equation that uses the factors? Specifically, I need something I can use in different frames of reference in a space environment, and space is really big, I can assume a four factor formula in an infinite environment where neutron reflection and the temperature of the medium is negligible. But, is that something that will even show the probability of a chain reaction in different frames? I'm not sure, I don't know what the actual equations are for determining fission probability based on like, nuclear density, material volume, temperature, some cross section thing, criticality, specific activity or ect.

[swansont]

"You can add neutrons if you have an alpha emitter and something that releases neutrons when bombarded, such as Polonium and Beryllium. That will help trigger the reaction and give you extra neutrons at the outset."

 

I'm not really sure what you mean. But, what about the mechanism for which the process triggers? Another thing I'm confused about is the mechanism by which the reaction triggers at critical mass. If enough mass is collected, the mass goes critical on it's own, and neutron guns are just for moderation reactions in nuclear reactors? And what about the equation that uses the factors? Specifically, I need something I can use in different frames of reference in a space environment, and space is really big, I can assume a four factor formula in an infinite environment where neutron reflection and the temperature of the medium is negligible. But, is that something that will even show the probability of a chain reaction in different frames? I'm not sure, I don't know what the actual equations are for determining fission probability based on like, nuclear density, material volume, temperature, some cross section thing, criticality, specific activity or ect.

Polonium is an alpha emitter. Beryllium releases neutrons when bombarded by alphas.

 

http://en.wikipedia.org/wiki/Modulated_neutron_initiator

 

One crucial aspect of detonation is that the reaction ramp up in a short amount of time. If it ramps too slowly or is initiated at the wrong time you don't get a very good explosion (known as a "fizzle", as mentioned in the link)

[MWresearch]

Ok, I see. But, is neutron bombardment from some special event the only mechanism by which the chain reaction initiates? Because if I could simply the problem if 100% pure U235 on its own causes itself to undergo a chain reaction once critical conditions are met without any sort of neutron bombardment gun, it would make the situation less unnecessarily complicated. Although, since neutron velocity and mass and energy aren't really the focus of the theoretical experiment, perhaps I can just assume a situation after detonation.

 

That equation mentioned in another link about prompt critical, it says the number of fissions per unit of time is modeled with an exponential equation which is what I mentioned before. In that equation, if I know the number of moles of U235 and thus the number of U235 atoms, I can calculate how many fission events are necessary to use up all of the fissile material. In relativistic frames of reference, can I easily substitute the temporal or time-aspect of the equations with simply modified lengths of time that are affected by time dilation, using the equation t'=to/sqrt(1-v^2/c^2)?

And, I guess it also matters that the nuclei aren't moving near the speed of light, because then there might be even more time dilation I would need to account for. Would the speed that the nuclei and neutrons move at be negligible for calculating addition special relativistic speeds?

[swansont]

You can figure the population of neutrons from the spontaneous fission rate, or find where someone has done it for you.

 

http://en.wikipedia.org/wiki/Spontaneous_fission#Spontaneous_fission_rates

[MWresearch]

Ok, but what about all the other stuff I said? Or could you elaborate more on how that link answers all of my questions?

[MWresearch]

Here's what I need: An equation which gives me the probability of a chain reaction as a function of mass, the size of individual atoms, the probability of neutrons being absorbed into a nuclei to further a chain reaction, and something to do with the resting specific activity which on its own would cause a chain reaction, assuming that mechanism is correct. But to be frank, I can't really pinpoint the point of what you are saying. If I have two piece of Uranium 235 that has a mass of 52kg in a sphere 17cm in diameter, will that alone detonate itself? Because otherwise I cannot think of why they would need to separate subcritical mass pieces in that gun bomb model.

As for the special relativity aspects, I'll just assume that since it's a simpler or ideal situation that is being assumed that the time dilation and length contraction happen normally according to the square root equations with v^2/c^2. But, as I said, I don't really even know what to research. Even if I assume values of critical conditions, I still don't know the grand equation that determines the probability of a critical or supercritical mass creating a chain reaction in itself.

[ajb]

At the risk of being off topic... I was told not so long ago that UK teachers and lectures are expected to watch out for extremism and potential terrorism from our students. Part of this would involve me reporting if any students ask strange off subject questions; for example nuclear weapons when we are not studying nuclear physics! My reply to this request was that I could not tell them anything that they could not find in a standard nuclear physics textbook or even Wikipedia. I have no specialist knowledge in that subject. But of course I am to some extent obliged to report things like this from students.

 

I will be clear that I am not accusing anyone of actually preparing to make weapons, all I am doing is pointing out the paranoia we live with.

[StringJunky]

At the risk of being off topic... I was told not so long ago that UK teachers and lectures are expected to watch out for extremism and potential terrorism from our students. Part of this would involve me reporting if any students ask strange off subject questions; for example nuclear weapons when we are not studying nuclear physics! My reply to this request was that I could not tell them anything that they could not find in a standard nuclear physics textbook or even Wikipedia. I have no specialist knowledge in that subject. But of course I am to some extent obliged to report things like this from students.

 

I will be clear that I am not accusing anyone of actually preparing to make weapons, all I am doing is pointing out the paranoia we live with.

The level of conversation and information here is vastly less than has been publically released by NATO government departments. Nuclear acquisition and capability is a state-level endeavour. Short of nicking an actual warhead I don't think any non-state group has sufficient means, logistical capability or nous to be a credible risk. As far as nuclear weapons goes, paranoia is just that ...paranoia. I like reading about all things nuclear and shall continue to do so. Ironically, even though it is by far the most dangerous form of 'pyrotechnics' it is safest to converse about, in a general way, because it is so practically and technically inaccessible to anyone but government-level entities.

 

That's my 2p's worth anyway.

[Sensei]

because it is so practically and technically inaccessible to anyone but government-level entities.

 

IMHO it's myth.

There are even people building their own fusion reactors at home f.e.

http://www.bbc.co.uk/news/10385853

People with knowledge, don't find reason for building their own fission reactors or nuclear bombs. Without purpose, there is little sense building them. And danger of ending up radiated.

 

Real extremists are plain stupid. How many hours per day they are spending on praying? The last thing they would be doing is reading (in foreign language) "decadent" western science books, every day for 8+ hours, every book, and making experiments..

They would have to spend 10-20 years on learning quantum physics to build working bomb and they would in mean time lost all their extremisms..

 

Marie Curie-Sklodowska was processing uranium ore in hovel..

 

Tons of ore..

Edited February 26, 2015 by Sensei

[StringJunky]

 

IMHO it's myth.

There are even people building their own fusion reactors at home f.e.

So,we'll be seeing some homemade pure-fusion weapons in the near future then?

[swansont]

Here's what I need: An equation which gives me the probability of a chain reaction as a function of mass, the size of individual atoms, the probability of neutrons being absorbed into a nuclei to further a chain reaction, and something to do with the resting specific activity which on its own would cause a chain reaction, assuming that mechanism is correct. But to be frank, I can't really pinpoint the point of what you are saying. If I have two piece of Uranium 235 that has a mass of 52kg in a sphere 17cm in diameter, will that alone detonate itself? Because otherwise I cannot think of why they would need to separate subcritical mass pieces in that gun bomb model.

As for the special relativity aspects, I'll just assume that since it's a simpler or ideal situation that is being assumed that the time dilation and length contraction happen normally according to the square root equations with v^2/c^2. But, as I said, I don't really even know what to research. Even if I assume values of critical conditions, I still don't know the grand equation that determines the probability of a critical or supercritical mass creating a chain reaction in itself.

 

Well, there's this formula

http://en.wikipedia.org/wiki/Six_factor_formula

 

You need to separate the masses because criticality will just lead to reactions that are much too slow for detonation. The final mass in a bomb is above critical mass; you want; something that is prompt supercritical.

 

Frankly, I don't see anything in this discussion that leads one to consider relativity in any way.

The level of conversation and information here is vastly less than has been publically released by NATO government departments.

 

I am in complete agreement. This information is easily Googled anyway, or by reading a Fredrick Forsyth novel (Go forth and use the Google protocol to find out which. Pretty sure Tom Clancy wrote one too, but with a thermonuclear device, and there are surely more out there.). Doing any kind of experimental/technical work is harder than reading the stuff anyway — there's always a whole host of lab skills required, and the people with such skills are going to have more knowledge than is being displayed here.

[Enthalpy]

[] Short of nicking an actual warhead I don't think any non-state group has sufficient means, logistical capability or nous to be a credible risk. As far as nuclear weapons goes |...] it is so practically and technically inaccessible to anyone but government-level entities.

 

Nukes were difficult 70 years ago. Technology has progressed meanwhile, as well as the general knowledge, and worse, materials are available. Who knows what Daesh finds in Syria and Iraq, as accumulated by Saddam and the others? They have already found combat gas and components to make them, and Iraq had acquired nuclear materials. In addition, nuclear material can be purchased presently - fundamental difference with 1940.

 

As for Daesh, they are capable of making Internet attacks, and after months of bombing by the US and allies, they stay and gain terrain occasionally.

 

What information is available from the best sources to the best specialists isn't neither what tinkerers know or can find, especially in a country destroyed by war, under embargo and from which the scientists have fled. The questions raised on a chemistry forum were obvious for any student, yet they related closely to the combat gas later used by Assad's regime, and would improbably have been needed for an other use. So information even far below the best knowledge can make a difference.

 

Then you should distinguish between the sought effect of nuclear weapons. One that fits is a rocket transported by a small combat aircraft and destroys a city is difficult, one that fizzles where a group has placed it is far easier, and is enough to terrorize a city and deter a government.

 

In fact, I'd like nuke scientists to think at ways to prevent such an attack. Government programs try to intercept incoming missiles, which is irrelevant. The two bombs that destroyed cities did not travel on missiles, the next one may well travel by container ship.

 

Notice I'm by no means suggesting this is the intent here. But remember that many people read forum discussions, not just identified forum members.

[MWresearch]

I have no issue with clearing my name. But this level of talk actually is part of standard physics, its actually all introductory lecture notes on nuclear engineering which I was thinking about going into if not mechanical engineering or physics, from googling stuff I see things like "introduction to nuclear engineering. By the end of this course students are expected to calculate fission rates, give critical mass...etc." which I tried studying on my own, but without any guidance I became lost and could not even figure out what I'm looking for. If you must know prematurely, I'm doing a theoretical research on the conservation of probability in different frames of reference. When I was talking about relativity with a physics professor, we stumbled upon the issue about what would happen if a nuclear bomb was going near the speed light which might have been on this very website. Since its density would appear to increase it might detonate in one frame but not in the other. I know from relativity that causality must be upheld. If the bomb doesn't explode in one frame especially the rest frame, it cannot explode in the other, and I'm trying to prove it mathematically since we obviously can't do that type of experiment in real life.

With reference to Swansont, I did actually find the six and four factor formulas, but I guess in my ignorance I still do not see how to use that formula. From what I see, that formula only calculates the neutron multiplication factor. Is that what I need? I don't know, it seems like there's more to probability than a neutron multiplication factor.

Edited February 26, 2015 by MWresearch

[Endy0816]

 

Nukes were difficult 70 years ago. Technology has progressed meanwhile, as well as the general knowledge, and worse, materials are available. Who knows what Daesh finds in Syria and Iraq, as accumulated by Saddam and the others? They have already found combat gas and components to make them, and Iraq had acquired nuclear materials. In addition, nuclear material can be purchased presently - fundamental difference with 1940.

 

As for Daesh, they are capable of making Internet attacks, and after months of bombing by the US and allies, they stay and gain terrain occasionally.

 

What information is available from the best sources to the best specialists isn't neither what tinkerers know or can find, especially in a country destroyed by war, under embargo and from which the scientists have fled. The questions raised on a chemistry forum were obvious for any student, yet they related closely to the combat gas later used by Assad's regime, and would improbably have been needed for an other use. So information even far below the best knowledge can make a difference.

 

Then you should distinguish between the sought effect of nuclear weapons. One that fits is a rocket transported by a small combat aircraft and destroys a city is difficult, one that fizzles where a group has placed it is far easier, and is enough to terrorize a city and deter a government.

 

In fact, I'd like nuke scientists to think at ways to prevent such an attack. Government programs try to intercept incoming missiles, which is irrelevant. The two bombs that destroyed cities did not travel on missiles, the next one may well travel by container ship.

 

Notice I'm by no means suggesting this is the intent here. But remember that many people read forum discussions, not just identified forum members.

 

They do have the radiation detectors scattered around.

 

http://en.wikipedia.org/wiki/Radiation_Portal_Monitor

 

There are probably more in our major cities that have not been made public knowledge.

 

 

I have no issue with clearing my name. But this level of talk actually is part of standard physics, its actually all introductory lecture notes on nuclear engineering which I was thinking about going into if not mechanical engineering or physics, from googling stuff I see things like introduction to nuclear engineering. By the end of this course students are expected to calculate fission rates, give critical mass...etc." which I tried studying on my own, but without any guidance I became lost and could not even figure out what I'm looking for. If you must know prematurely, I'm doing a theoretical research on the conservation of probability in different frames of reference. When I was talking about relativity with a physics professor, we stumbled upon the issue about what would happen if a nuclear bomb was going near the speed light which might have been on this very website. Since its density would appear to increase it might detonate in one frame but not in the other. I know from relativity that causality must be upheld. If the bomb doesn't explode in one frame especially the rest frame, it cannot explode in the other, and I'm trying to prove it mathematically since we obviously can't do that type of experiment in real life.

With reference to Swansont, I did actually find the six and four factor formulas, but I guess in my ignorance I still do not see how to use that formula. From what I see, that formula only calculates the neutron multiplication factor. Is that what I need? I don't know, it seems like there's more to probability than a neutron multiplication factor.

 

Besides the change in density, would any other factors be impacted at the same time?

[MWresearch]

Once again this website is really glitch for some reason. It never lets me use the quote feature and my entire paragraph just got erased.

 

Anyway, the density isn't affected by time dilation, but more by length contraction and mass increase. The mass increase is kind of weird, more of an illusion since you're not actually increasing the number of atoms, and its similar with length contraction since you're not actually compressing an object, but the physical circumstance in this scenario could easily happen in something like a rock flung to near the speed of light by a black hole nonetheless.

 

Anything that travels distance over time or happens over a period of time would be affected by time dilation. The half life, the specific activity, the fission rate, and I'm hoping it's not much more complicated than that. Though calculating the relativistic values for a Lorentz boost is pretty easy, you just multiply or divide by gamma, it still makes my head hurt when I see 20 variables that I've never heard of before and I can't sort everything through.

Edited February 26, 2015 by MWresearch

[imatfaal]

Once again this website is really glitch for some reason. It never lets me use the quote feature and my entire paragraph just got erased.

 

Anyway, the density isn't affected by time dilation, but more by length contraction and mass increase. The mass increase is kind of weird, more of an illusion since you're not actually increasing the number of atoms, and its similar with length contraction since you're not actually compressing an object, but the physical circumstance in this scenario could easily happen in something like a rock flung to near the speed of light by a black hole nonetheless.

 

Anything that travels distance over time or happens over a period of time would be affected by time dilation. The half life, the specific activity, the fission rate, and I'm hoping it's not much more complicated than that. Though calculating the relativistic values for a Lorentz boost is pretty easy, you just multiply or divide by gamma, it still makes my head hurt when I see 20 variables that I've never heard of before and I can't sort everything through.

The only frame that "matters" to the neutrons and the uranium is their frame of reference - ie the frame which the bomb is at rest with respect to. The reactions happen in that frame and criticality should be judged in that frame. Obviously in the bombs inertial frame there is no length contraction and no change in energy due to motion.

 

The only time you would need to use transforms is if you had observations from your frame of a bomb moving at high speed with respect to your frame and you wanted to be able to predict what might happen. ie you "see" that the core of uranium is an oblate spheroid (flattened in the direction of relative motion) that by your untransformed sums (ie wrong) should be critical according to your observations of the mass and the volume of the oblate spheroid. But if you perform the proper transforms you can tell that in the frame of the bomb (ie the one that matters) the core of uranium is actually a perfect sphere and the oblateness was caused by length contraction. This change in volume is enough to lower the density and thus the core is non-critical

If you think about it - in the frame of reference of something moving quickly all the nukes on earth will probably be so far contracted that their density woudl mean they should be critical. Obviously they have not gone off

[MWresearch]

Right, and I'm just trying to do the mathematics to prove that the same events hold true for other frames of reference. And the college I'm at already said they'd be interested in doing a summary/story/article on the paper once its finished, so might as well finish it. I already have the shape stuff figured out if I assume that 20.21g/cm^3 is remotely accurate. Using that number I set up a system of equations and solved for the velocity necessary to create length contraction and mass increase that creates a density increase from 18.075g/cm^2 to the critical 20.21g/cm^3. Now all I need is an equation that can be used in both the rest frame and relativistic frames to show that even though the density has the illusion of being 20.21g/cm^3, the probability of a chain reaction is still close to 0. For that, I need to find an equation for the probability of a chain reaction that is a function of whatever time based stuff causes a chain reaction on its own, assuming that mechanism is correct which Swansont never cleared up, and then anything that might be affected by length contraction which will effect the cross section and probability of slow neutrons striking a nucleus, like the average radius of nuclei and neutrons. I guess I will just have to let the paper not be completely accurate and state that I made assumptions for the sake of seeing the problem through.

Edited February 26, 2015 by MWresearch

[Sensei]

If you must know prematurely, I'm doing a theoretical research on the conservation of probability in different frames of reference. When I was talking about relativity with a physics professor, we stumbled upon the issue about what would happen if a nuclear bomb was going near the speed light which might have been on this very website. Since its density would appear to increase it might detonate in one frame but not in the other. I know from relativity that causality must be upheld. If the bomb doesn't explode in one frame especially the rest frame, it cannot explode in the other, and I'm trying to prove it mathematically since we obviously can't do that type of experiment in real life.

 

You should start from that.

 

When you have 1 gram of water, which has 18.015 g/mol, it means there is 1 g/18.015 g/mol = 0.05551 mol

1 mol is 6.022141*10^23 particles/molecules.

0.05551 mol * 6.022141*10^23 = ~3.34285*10^22 molecules of water in 1 gram (in 1 cm^3 volume, STP).

 

Similarly when you have 52 kg = 52000 g of pure U-235, which has 235.044 g/mol, it is

52000 / 235.044 = 221.235 moles = 1.3323*10^26 U-235 atoms in such ball.

 

Quantity of molecules/particles don't change while falling into BH, nor when it's traveling with speed close to speed of light.

Instead of thinking about critical mass, you can start thinking about critical quantity of atoms.

Edited February 26, 2015 by Sensei

[MWresearch]

I think I specifically stated that the number of molecules doesn't change as a result of relative velocity and even went so far as to call it an illusion. But as I stated before, I do want an equation that considers the number of atoms if it's necessary. But, relying on that point wouldn't resolve the situation from the point of view of the person asking such a question because they you haven't actually proven that number of moles stays the same. If the mass increases then mathematically you could extrapolate the number of moles to increase even though in reality the number stays the same.

[Sensei]

If you're putting something on weight scale when you're on ground at rest, and measure mass,

and then repeat it when you're traveling with fast constant velocity,

the both measurement will show the same result,

as either you and weighting scale and measured item, has the same velocity vector,

you are all in the same frame of reference.

Edited February 26, 2015 by Sensei

[MWresearch]

I'm really not sure what you're saying. I'm not weighing anything, there's not that much gravity in space anyway. It kind of seems like you're saying things moving at the same velocity do not measure each other as being contacted or dilated, which I agree with. As I also said before, I don't think the number of atoms is actually increasing, but that doesn't change the equation m'=mo/sqrt(1-v^2/c^2). The theoretical experiment is taking place in space where a chunk of U235 has been accelerated to what becomes a constant speed at around 3% the speed of light relative to Earth, neglecting Earth's orbital motion, rotation, atmosphere and gravitational field as effects on measurements.

Edited February 26, 2015 by MWresearch

[Sensei]

I'm really not sure what you're saying. I'm not weighing anything,

 

52 kg is already weighted invariant mass of bomb. After acceleration to constant velocity it's still 52 kg invariant mass.

[MWresearch]

No, it's not. I guess I wasn't clear about the experiment. Something that's bigger than a critical sphere with less mass than critical mass is accelerated to around 3% the speed of light where it appears to take on the mass of 52kg and contract to an a=8.5, b=8.5, c=8.5 ellipsoid, also called a sphere. I'm also not really sure what you mean by "mass is weighted" because weight is different than mass. Rest mass is rest mass, I agree, but as I said, it has the illusion of changing under the equation m'=mo/sqrt(1-v^2/c^2).

Edited February 27, 2015 by MWresearch

[Sensei]

No, it's not. I guess I wasn't clear about the experiment. Something that's bigger than a critical sphere with less mass than critical mass is accelerated to around 3% the speed of light where it appears to take on the mass of 52kg and contract to a a=17, b=17, c=17 ellipsoid, also called a sphere. I'm also not really sure what you mean by "mass is weighted" because weight is different than mass. Rest mass is rest mass, I agree,

I meant "weighted" = measured.

Read it as:

"52 kg is already measured invariant mass of bomb. After acceleration to constant velocity v (whether v=0.03c or v=0.5c or v=0.866c doesn't matter) it's still 52 kg invariant mass."

 

Rest mass is rest mass, I agree, but as I said, it has the illusion of changing under the equation m'=mo/sqrt(1-v^2/c^2).

Are you aware that m0 in your equation is rest mass=invariant mass.

Then how can it change?

 

Change is in relativistic mass m' in your equation.

Edited February 27, 2015 by Sensei