Physics of a nuclear explosion
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- Опубліковано 4 чер 2024
- Physics of a nuclear explosion. Calculations proving that a chain reaction in Uranium would produce an colossal nuclear blast. Discussion of some of the key results of the Frisch-Pieierls Memorandum and the origins of the gun-type and implosion bomb designs.
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00:00 Introduction
01:18 What is an explosion?
02:00 Energy released
04:04 Speed of the reaction
05:50 Summary Peierls-Friesch results
06:47 Frisch-Peierls Memorandum
07:28 Origin of the implosion bomb - Наука та технологія
Thank you, impressive, and it is amazing to think that they were banned from working on what was regarded as top-secret, radar, and they were given this as a side project by Sir Mark Oliphant.
Very welcome! I found funny and quite frustrating that Peierls and Frisch were banned from the work they started. It reminds me the sad story of David Bohm, student of Oppenheimer, whose career got ruined when he got was banned from the Manhattan Project but also of talking about his own thesis.
new video posted, Mark Oliphant gets some exposure to the general public
Amazing, not many people out there explain this concept with graphics. We need more of such videos 👍👍👍
Thanks for the feedback, make sure to check the rest of the video in the channel.
Another great video. The calculations are super complex but you manage to explain everything without getting bogged down in the maths behind them. Nice.
Glad it was helpful! More math coming and also some dedicated videos to more advanced topics because some nerds have requested deep walk-through solving the neutron diffusion equation so stay tuned. Happy to be in nerd team and respond to this kind of requests.
Another excellent video! Thanks Jorge👍
My pleasure! A follow-up video on the consequences of the Frisch-Peierls memorandum coming soon, stay tuned
Hi! Glad I found your channel. There's not much content for people unsatisfied by math free 'science' youtube, but can't commit to watch a bone dry university lecture series on nuclear physics. I don't mind a little calculus or algebra, if the derivation is insightful or a neat trick involved. Cheers!
I am curious to know what brings viewers to the channel, were you searching for something in particular or did the 'mighty algorithm' find you?
An amazing series of videos, the best explained I've seen on YT (even a biologist like me can understand it 😃). Thank you Dr Diaz.
Thanks for the positive feedback. I am glad you found the content of interest and clearly explained, new videos already in the pipeline. Thanks for watching and welcome to the channel.
Another great video. Lucid explanation of the theoretical work of Frisch and Pierles with some heavy duty numbers crunching to show the fission bomb was a practical and achievable goal . Their concern for security takes an ironic twist when Pierles finally working on the British A-Bomb research recruits a brilliant young mathematical physicist and student of Max Born-- Klaus Fuchs.
glad you liked it; I wanted to show more of the work by Peierls and Frisch but decided to split it into two videos (the last one and this); otherwise, it would have been too heavy. Peierls brought in Klaus Fuchs as his assistant but lived with him in the same room used by Frisch who moved to Liverpool to work with Chadwick. This is a tragic story, the Peierls really treated Fuchs as a son; Rudolf Peierls even wrote a letter to Fuchs when he was released from prison offering help and support but Fuchs never replied. There is a great lecture on UA-cam by Frank Close, author of "Trinity: The Treachery and Pursuit of the Most Dangerous Spy in History"
@@jkzero thanks for the great reply. I’ll check out the lecture now
Frank Close did a brilliant detective work checking the notes on Peierls' diary and letters to pinpoint even the dates when Fuchs was meeting his Soviet contacts during the early days of the Tube Alloys project.
@jsdiaz I just watched his lecture on this. Brilliant. Brings lots of new facts to light on th story. Amazing archival research. More like an archeological dig through the files.
@@johnned4848glad that you liked it; I am not much into the espionage topic but Frank Close presents the story with such a level of detail that it is captivating
Great stuff. By chance do you use some form of LaTeX to make your videos? The serif font looks a lot like CMU Serif.
Glad you liked it. And yeah, I create my videos with Manim, which, in addition to the opportunity to mathematically animate graphics, let's you render LaTeX formulas docs.manim.community/en/stable/guides/using_text.html#text-with-latex
Great videos! Really appreciate you going into some of the underlying physics and math. Your video references the time involved with the fission energy release...somewhat related to that, the timing of a thermonuclear device seems improbable. How does X-ray emission, X-ray absorption by aerogel, physical implosion of the secondary, lithium deuteride reactions and fusion and finally secondary tamper fission all occur before the primary vaporizes everything? Perhaps you could cover this in a future video
Thanks for the positive feedback. Thermonuclear weapons are quite complex in the sense that they are three bombs into one: a high-explosives explosion that compresses a plutonium core (Fat Man style), whose X-rays trigger the secondary thermonuclear component. All this is very fast because X-rays travel at the speed of light. If you want a fascinating description of H-bombs I can highly recommend the controversial article published on The Progressive magazine in 1979 by Howard Morland titled “The H‐Bomb Secret, How We Got - Why We're Telling It.” It was a very controversial 10‐page article that, at the time, revealed "way too much."
Thanks - I've come across that article before; the Nuclear Weapons archive also provides detailed design info. But even with X-rays traveling at the speed of light to reach the secondary, it's still seems amazing that the subsequent processes - implosion of secondary, fission of spark-plug, fusion reaction and fission of tamper - can all occur before the whole device disassembles.@@jkzero
Very nice production. Having been a technical writier, _("MilSpec",_ no *_tourist brochures!)_* I appreciate your eye for detail and finish!
best
Thanks for watching and the positive feedback; and welcome to the channel!
Amazing video
I am glad you found the content of interest, make sure to check the several follow-up videos. Thanks for watching and welcome to the channel.
Great stuff.
I am glad you found the content of interest, make sure to check the several new videos. Thanks for watching and welcome to the channel.
Just a small correction. Chemical explosives -- particularly high explosives -- aren't particularly about having "fuel" and oxygen within the molecule. The biggest part of the energy release is generally from combining nitrogen atoms into N2 molecules. Having said that, the video you're showing at the time is likely ANFO being used in quarrying, and that is a fuel-oxidizer reaction.
👍 thank you, great video
Thanks for watching, I am glad you liked the video. I am curious to know what brings viewers to the channel, were you searching for something in particular or did the 'mighty algorithm' find you?
@@jkzero Yeah I first saw your videos thanks to the algorithm. I expected you to have few hundreds of thousands or even millions of subs so I was quite surprised to see it was much less. But I love your videos, think I have watched all of them in a span of few days. Please keep the vids coming.
Thanks for sharing and I am glad the algorithm is working, welcome to the channel! The next video is a follow-up so make sure to watch the latest that ends on a cliffhanger.
How did you come up with average speed = 10^9 cm/s? Given that the “temperature” of a critical assembly is rising, and scattering/absorption dynamics changes, this number probably needs either a more detailed derivation, or a description of conditions, under which it holds true. Also, as you are well aware, the energy spectrum of the fission neutrons is pretty wide. Just a thought. Thank you.
Thanks for your question. The value ~10^9 cm/s is just a representative average speed and you are totally right: an appropriate (careful) treatment of the problem requires the mean energy to be calculated using the full neutron distribution. Where did I get this value? Fast neutrons produced by fission are produced with a mean kinetic energy of 2 MeV. Using K=½mv^2, the speed is ~2x10^7 m/s, which is of order 10^9 cm/s.
@@jkzeroThank you. I should have thought about mean :) As always, great video. Cheers!
@@sergeyyatskevitch3617 thanks again for watching and the interest, happy to help in case you have any question.
Done❤
Did Frisch & Peierls really find (1:10) that "one kilogram [of U-235] could produce a self-sustaining fission chain reaction"? I'm looking at my copy of the original memorandum right now, which proposes 600g as the relevant figure. But it does immediately infer that a kilogram would suffice: "one might think of about 1 kg as a suitable size for the bomb".
I referred to 1 kg as a round-up value because this is the follow-up of the video about critical mass (ua-cam.com/video/LduH7613QXw/v-deo.html), where you will see the estimate of the 600 g reported by Frisch and Peierls.
@@jkzero : Makes sense. It also links well with Bernstein's article a decade back, "A memorandum that changed the world" where he leaves several yield calculations as "an exercise for the reader", including "that of a 1 kg bomb, though 500 times less, [which] would still be formidable". He also does the first calculation of the 1kg reaction time I can recall seeing, and gets a comparable number, "t equal to about a microsecond".
Yield and reaction time would make another good 'homework'. For example, a reason Bernstein used 1kg was it corresponds to actual mass fissioned in Little Boy (only 1.5% efficient). But there are gotchas in such exercises. I absolutely agree that Peierls and Frisch were really ahead of their time. Unfortunately their1kg case is particularly problematic.
F&P don't explicitly calculate the yield but had in mind a yield energy of 1/500 that for 4700g (~5kg) - so about 8.5 x 10^17 ergs. But this can't be right. Given F&P's value for density, the corresponding radius (for 1kg mass of metallic U-235) is about 2.52cm. Their formula then yields energy from a 1kg U-235 sphere as about 7.5 x 10^18 ergs, an order of magnitude too high.
Did Bernstein actually check this? His words could be taken that way. Regardless,
I would tend to ascribe "1/500" to numerical fatigue. Peierls had to type this memo
under time pressure, in wartime conditions, using constants and approximations which made low-mass estimates dodgy in the extreme. It is easy to understand why he might have elided figures which would take too long to pin down.
On a related matter, Bernstein gives up on trying to explain why F&P chose 4700g as their crucial yield case: "Choice of 4700 g of 235U of Frisch and Peierls seems inexplicable".
But it's not hard to see Frisch & Peierls' real point. Think about their agenda; find values not just of yield E but of reaction efficiency, with 8kg being maximally efficient, 4700g being a suitable intermediate mass for production, and 403g being minimal. To me the memo's focus on a production case is understandable.
Addressing Jeremy Bernstein's comment on F&P's "inexplicable" choice of M=4700g; that means 4.2cm as initial radius, exactly twice their critical radius, so a good place to start. I get E=4.2517(10²º) ergs, supposedly about 10% efficient. This is F&P's "5kg" case with yield "equivalent to several thousand tons of dynamite". Bernstein doesn't seem to understand why they leaned heavily on that case, but that was a dozen years ago and I'm sure he has thought about it since.
Bernstein's other bugbear is the F&P memo's remark that "τ goes up as r approches r_o"; he insists that " I do not understand the remark about τ because this time seems to be fixed by the mean free path."
I have my own notions about that, but enough on this for today. Suffice to say I had to recapitulate F&P's 4700g calculations myself because two major references (that of the Atomic Archive, and Stanford University's web page) get it wrong. The former correctly declares 4700g to yield E=4(10²º) ergs, F&P's result. But it wrongly displays the square root term. So does the Stanford web page which also finds E=4(10²²) ergs, a couple of orders of magnitude off.
It always amazes me how low the actal yield of usable fissile material is when it goes boom. The earliest creations Fat Man and Little Boy being only around 2-4% of the fissile material being used before it all vaporises
yeah, and despite those inefficiencies these early weapons were still terrifying
@@jkzero oh I absolutely agree!
A nuclear explosion has 2 blast waves that radiate outward from the critical mass , the first is the light that instantly vaporizes the paint that's on a test house that might be set up near ground zero and a few seconds later the blast wave of compressed air hits the house blowing it to smithereens . The light energy travels much faster than the heat energy that follows behind it due to the heats induction that stirs up or excites the atoms that make up the air . Why does light travel away from it's source unrestrained while heat energy gets drug behind and takes time to try to follow the light ?
the first wave that you mention is just electromagnetic radiation (visible light, UV, X rays, gamma ray) and for this reason it propagates at the speed of light. What you call the thermal wave is slower because this depends on heat transfer. The equation that describes the propagation of heat (the heat equation) is just another diffusion equation, whose speed depends on thermal properties of the medium, in this case, the air.
Just doing the math in my head this means that to get 1 kg of U235 to chain react in a low yield bomb you have to compress it enough to raise it's density by 6 times if you don't have a neutron reflector?
Considering the 1kg case goes back to Frisch and Peierls who found that yield to be only 1/500 the fission power from a 5kg sphere, so smaller but nonetheless "formidable".
Interest in the calculation was revived back in May 2011 by Jeremy Bernstein who did the reaction time estimate of 1 microsecond presented here.
I'd like to know how they knew so much about U235 given that
it was almost impossible to separate from U238?
How could they get measurements without a reasonable quantity of U235?
Then - how did they find out about P239?
That was always mixed with other isotopes like P240.
There must have been dozens of fission candidates to consider?
These are all great question, let me give it a try to answer them here:
U235 was discovered by Arthur J. Dempster in 1935; Dempster was a Canadian physicist who built the most precise mass spectrometers, this is how he found that natural uranium contains 0.7% U235. Mass spectrometers allow isotope separation, even for ridiculously small amounts. This is how U235 could be studied.
Plutonium was different, is was not discovered but synthesized, it was produced by Glenn Seaborg in 1940 bombarding uranium with deuterons using a particle accelerator. Again, this allows an exquisite level of precision in the measurements. Pu-240 was produced later in nuclear reactors, together with Pu-239, and yes, Pu-240 is a problem because it can make the bomb predetonate.
Having an element that can fission is not enough for a bomb, you also need to be fissile (it can sustain a chain reaction) to make a bomb. Here the list is short: naturally occurring only U235 is fissile, and later Pu239 was added. These are the only elements that can make a bomb. Other can fission too but there cannot sustain a chain reaction. They knew all this from the Bohr-Wheeler theory, it is almost just counting protons and neutrons to check if the total number is even or odd.
Let me know if this helps.
@@jkzero - thanks for your reply - much appreciated.
It's amazing that they knew all that back in 1935 before a lump of U235
had even been separated and then so much info about P239 in 1940.
I wonder if you would do a video on mass spectrometers and how all of that was done?
There is also U233 which has been used in a bomb.
A video explaining the Bohr-Wheeler theory would be good too?
@@Bobby-fj8mk great that it helped and thanks for the suggestions, I cannot guarantee to take all requests but I am creating a list collecting suggestions for the future, if there is any particular topic you are curious just let me know in the comments of the respective videos, past and future.
@@jkzero - thank you - your videos are great - top notch.
Read or audiobook "A History of the Atomic Bomb" Richard Rhodes - it covers a lot of this material and the underlying scaffolding of discoveries that lead to the bomb.
So if i'am right, 10(9) cm sec = 10,000 KPH, speed of the reaction
No, 10,000km per _second_ -- 36,000,000 km/h. About 1/30 the speed of light.
You make me more proud of my Alma Mater (I.U. at Bloomigton)
I appreciate your kind words. What a great surprise to find another Hoosier here. I had some of my best years in B-town. If I may ask, what did you study at IU?
@@jkzero I graduated in History and Philosophy of Science. At that time -in the seventies- this department had very outstanding teachers, and Bloo...a Paradise. I live in Manizales (Colombia)B Very best regards.
Lol You guys of physics always have a great explanation of the physics, but in reality, the power of a nuclear explosion comes from "Overpressure". Lol. Any pressure over the normal 14.6 psi of atmospheric pressure is overpressure.
Nephew: "Grandpa, how come we got the bomb before the gerries did?"
Grandpa: "Because our German scientists were better than the ones that stayed in Germany!"
ouch! But yeah, it is true that many of the best German scientists moved out. It doesn't mean that the ones that remained were not good.
Please don't say "point seventy two". The word "seventy" means seven times ten, so putting it after a decimal point makes no sense at all. The conventional approach is to read the digits after the decimal point individually, so 72.72 is read as seventy two point seven two.
point taken, constructive feedback is highly appreciated.
Bull
I have doubts. And after 3 years of research, I came to the conclusion that a lot of fear is generated by the nuclear threat. Whether atomic bombs were dropped on Hiroshima and Nagasaki at all is still more than questionable today.
I don't know what you mean by research. Sadly, nuclear bombs were dropped over Hiroshima and Nagasaki, I do not think that is a questionable fact. Everyone is entitled to their own opinion, but not their own facts.
@@jkzero
Why do you delete every single answer I've tried to put under your comment? Within a few seconds my answer was zensored or deleted..!
@@jeito33 this is the first message that I received from you, I do not delete messages, unless they are offensive. Often UA-cam does not save messages if they include some keywords, sometimes links, and email addresses. Feel free to reach me via email, it is posted on the channel description.
@@jkzero Okay thanx. I'll do so and send my comment to your email address. Unfortunately UA-cam zensored my answer which contained two links.
I appreciate the internal communication, I will make sure to read further and get back to you.
That's all very interesting but G.N.Flerov, while being drafted as a foot soldier in the Red Army all the way back in 1941, from a literal foxhole, wrote and sent notes to the Kremlin and even a sketch of his proposed "gun-type" experiment which was by almost all comparisons identical to that of the Little Boy, complete with criticality equations of his own. What you show is very interesting but even as to the origins of the concept of criticality and actual yield calculations your historic presentation draws a very narrow picture.
you are right, my presentation is quite biased towards the British-American program. I am pretty ignorant about many of the developments on the Soviet side. The standard account is that they just copied from the information passed by Klaus Fuchs and others, but this is also probably an incomplete description. The gun design is sort of the obvious first thing to draw when designing an Uranium bomb, Oppenheimer did it just a few days after learning about the Hahn-Stranssmann and Frisch-Meitner results; even Heisenberg with his very limited knowledge of bomb physics had discussed the gun design with his German colleagues.
@@jkzero the "real" german design were the gun-and-implosion design which was a weird combo that would probably never work, the second was a bit mote sound design, the name escapes me, it featured Uranium "rings" that were supposed to collapse thus touching each other and going supercritical. A bit similar designs yet so different. Flerov however sketched up a completely vanilla gun design with one single difference; it featured two hemispheres that were supposed to be shot one into the other, as opposed to Little Boy's cylinder-and-core. In essence Flerov pretty much singlehandedly while literally serving in the armed forces away from all his scientist colleagues devised that AND endlessly warned Stalin as to the potential of this weapon, even before Kurchatov was given the final go-ahead under Beria to start the construction of the RDS-1 which was to a large degree based on the "gadget" - but was not a direct copy, rather a domestic development almost entirely except of course the actual working principle behind it which was indeed leaked from USA via all those assets that USSR either had itself or trough leaks from Oppenheimer, Fuchs etc.
The real moment of Soviet thermonuclear success came thanks to Sakharov - who first with the lithium-deuteride "sloika" concept designed the boosted implosion nuclear bomb - which later on lead to fully matured fission-fusion two stage weapons that unlike the first amrican fusion experiment were not experiments but fully field-applicable thermonuclear devices. Li-Dt became the definitive standard, with almost no significant alternations since. So yes, as you admit, your account is very one-sides. Not to deminish everyone's important work - but a broader picture can only be painted on a larger canvas with more colors.
@@LegateMalpais do you have a reference about the German gun-and-implosion design with Uranium rings that you mentioned? I don't think I know enough about this and I would be curious to read more. One of the points that feels very childish on the Frisch-Peierls memorandum is their proposal for the bomb assembly: they originally proposed bringing two sub-critical hemispheres together using springs! The first time I read this I thought "you just calculated the reaction to take a microsecond and now you want to assemble the bomb with springs?" Anyway, clearly during the MAUD days someone pointed this out and the springs were replaced by high explosives on the MAUD Report.
@@jkzero no, sorry, there was a time ago a page online about the german bomb design but it seems not operational any more. I am not too knowledgeable about that development anyway, try google.
@@jkzero but springs, lol. Well technically you COULD get a "fizzle" out of it so sure - a couple of railway car springs under tension would "work". Maybe a kiloton yield if lucky.
The accent really detracts from the message.
Dr. Diaz vocal delivery sounds fine to me. This was an excellent presentation.
You're literally complaining that a foreigner is speaking to you in your own language. Wow. Just, wow.