Critical Mass: when the atomic bomb got real
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- Опубликовано: 27 май 2024
- Physics of critical mass for uranium, mostly the work of Rudolf Peierls on nuclear fission and how a simple question from Otto Frisch led to the realization that an atomic bomb was possible.
Follow-up video: How to calculate an atomic bomb's critical mass • How to calculate an at...
Playlist Physics of Nuclear Weapons: • Physics of Nuclear Wea...
"Critical Assembly Simulator" by Alex Wellerstein blog.nuclearsecrecy.com/misc/...
00:00 Introduction
01:01 Nuclear Fission
02:20 Critical mass: Bohr
03:25 Critical mass: Perrin
04:27 Critical mass: Peierls
08:29 Cross section & mean free path
09:59 Critical mass: Frisch-Peierls 
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Thanks!
wow, thanks to you for supporting the channel! I really appreciate the gesture, for now I can only do my best to keep producing this kind of content. Thanks so much!
Thank you so much for this very interesting video on Dr. Peierls and fission. I've read some physics history and was already familiar with the great physicists of the 20th century; I've even got a poster of the famous photo of the Solvay conference on my office wall. I was unfamiliar with the work of Dr. Peierls and now can appreciate how important a physicist he was not only from a scientific viewpoint but a historical one as well. I look forward to further videos from you and perhaps you can write a book some day.
great to know that you got sir Rudolf Peierls (he was appointed a Commander of the Order of the British Empire) into your list of important physicists of the past century, like Hans Bethe, Peierls is a legend of physics, but unfortunately his importance requires lots of concepts to appreciate and for the same reason it is unlikely to have films about them. Thanks for watching and subscribe for more content coming.
I just discovered this channel I'm in love with the visuals along with your intuitive explanations. You easily deserve 100x your current following. Awesome videos
great that the algorithm someone brought you here; I am glad you found the content of interest and clearly explained. Thanks for the positive feedback. Just curious, what were you searching that brought you here? Thanks for watching and welcome to the channel.
@@jkzero I was initally reccomended the "Math of Saving the Enola Gay" video on the RUclips homepage and decided to watch a few more of your videos. The algorithm knows all 😇
great to know that my first video is so much recommended by "the mighty algorithm" and thanks for exploring the rest of the channel. It is very quite new but quickly growing, which motivates me to keep making videos. Comments and suggestions for topics are more than welcome. I cannot guarantee to take all requests but I am collecting suggestions for the future, if there is any particular topic you are curious just let me know in the comments.
@@jkzero Ahh, I didn't realize that it was your first. Thats a high bar to set for yourself ;p. Something I am curious about is the calculations behind the arrangement of high and low speed explosives in an implosion style warhead. I've definitely heard it mentioned in several places but I don't remember the keywords to search for.
@@amelted thanks fro sharing your interests, I have watched dozens of documentaries and videos about the implosion design and I agree with you, the whole idea of how to turn the high-explosive's shockwaves inside-out for the implosion is always glanced over. I have a video about the implosion design in the pipeline because someone asked me "how much is the plutonium core compressed?" and I honestly had no idea. I did the calculation and I now know, so I plan a video for that, maybe I should create one about how the explosive lenses work. Thanks for the suggestion!
Thank you Dr Diaz. I am so glad to have found your channel. I am thoroughly enjoying the fission bomb videos. Will you be doing any fusion bomb content at any point you think? (I don't mean right away, just at some point)
I am glad that you find the content of interest, there is plenty to talk about fission and some bomb physics, but fusion could also come in the future, requests are more than welcome so I will keep it in mind.
A++ was a grade. Great presentation and well done.
appreciated, follow-up videos posted already so make sure to check them out
A very good video, I gave a thumbs up and subscribed to the channel. Thank you for the great work. And yes, I'd love to see a video on the neutron diffusion equation.
Awesome, thank you! The video walk-through solving the neutron diffusion equation has received way more support than expected, great to find more people interested in the stories but also in the calculations. Thanks for watching and welcome to the channel
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
"I could talk about Peierls for hours....." please do! There is a large and appreciative audience for your content.....formal physics education is wasted on the young 🤭
Happy to see Peierls getting some love, and thanks for watching and the positive feedback.
great video. How did they know they made Barium? It seems like the amount of Barium would be too small to detect.
Hahn and Strassmann found short-lived radioactivity that could be percipitated from uranium salt solution using barium as carrier. That indicated that the trace-amount isotope was radium or barium, but since the active element could not be separated from barium via any chemical method, the implication was that this was in fact barium. Suported by findings of Curie-Savic team checked by Lise Meittner that the 3.5h half life isotope found in same uranium solution after neutron irradiation was lanthanum, Hahn and Strassman wereassured that neutron induced reaction in uranium is producing light elements contrary to Fermy's idea of transuranic elements. Few days after Hahn and Strassmann published their findings, Meittner understood that the atomic numbers of light elements produced are adding to 92 (atomic number of uranium) and after doing some liquid-drop model (model of nucleus developed by Neils Bohr) calculations she wrote back to Hahn and Strassman explaning that uranium nuclei were splitting producing light isotopes and about 200MeV of energy. Her nephew Otto Frish then improvised further experiments and in few days prooved this theory right, also giving the name to the reaction 'the fission' inspired by the name of cell-multiplying process (binary fission) in biology. In the next few months (in the spring od 1939) Joliot, Halban, Fermi, Frish and others found almost everything about uranium fission. That uranium 235 fissioned with low energy (thermal) neutrons, that uranium 238 fissioned with high energy neutrons, that the fission is producing 2 to 3 new, high energy neutrons...
The amount of barium produced indeed must have been fantastically small, I'd offhandedly guess a few nanograms at the absolute most, but maybe the video author can do some simple calculations to find the true range. The physical amount of Ba140 is immaterial though, since it has a tiny half-life of a dozen days it is screamingly radioactive and so all that is needed is to detect its radioactivity in a sample which was chemically obtained by a means previously known to isolate only barium. This method was a fractional recrystallization technique.
@@Muonium1 Ba140 yield in U235 fission is about 6%. Since Hahn and Strassmann were working with thermal neutrons only U235 fissioned, also, their sample was of natural uranium (first enriched uranium plant is still about 5yrs in future, the moment they discovered fission) total concentration of U235 was only about 0.72%. To know the real yield of Ba140 in mass one must know the burnup rate of uranium in their experiment, and that is extremly hard to calculate because very little original data are available. But to make educated guess, the burnup of uranium sample in Hahn and Strassmann experiment, I imagine, was in order of uWhr range. One Whr of burnup is 1.13x10^14 fissions. One uWhr burnup is 1.13x10^8 fissions. And that adds to ~6.75x10^6 Ba140 atoms per h. In one half life of Ba140 of burnup (13days od irradiation of uranium sample) there will be about 1.5x10^9 Ba140 atoms and that adds to about 50 p grams of Ba140. And the total produced Ba140 activity would be about 85kBq. That is more than enough activity to be measured nicely. As an ex nuke, the number feels about ok but, since I done the calculations in my head I'm almost sure I made mistake somewhere, so be free to check the numbers up. :D
the comments above provide a very complete picture. Yes, the amounts of Barium were small but very precise chemical measurements were possible and Hahn was recognized as the best radio-chemist of his time. If you want hard-core details, my suggestion is "The Making of the Atomic Bomb" by Richard Rhodes, it has a full chapter dedicated to the letters that Hahn wrote to Lise Meitner asking for her advice to understand his measurements. In the back and forth, it is possible to read how Hahn starts convinced that he observes "Radium-like Barium" but states that obviously it is not Barium (note that Radium is below Barium in the periodic table, so they share many chemical properties), to "it really looks like Barium but it cannot be Barium," but then goes into desperate mode to "we have done everything many times and we cannot separate it from Barium, please help" and finally to acceptance. He change the wording of his paper several times because he knew that he could ruin his reputation but he accepts that Barium is the only explanation. In the paper he even says that despite the report of Barium, some experimental error could be causing this "Barium fantasy."
@@glenliesegang233 It is impossible. Quantities of barium in experiments that lead to discovery of fission were so small that it is impossible to trace them via modern spectrometers. Even AAS spectrometer would struggle. They could be measured (and are) via gamma spectrocscopy but first usable gamma spectrometers were made during project Manhattan, and actually worked with conversion of gamma rays to photoelectrons and then measuring the energy spectra of those photoelectrons via magnetic sector speed separator, so to measure gamma spectra you would need really high activity of your sample. In conclusion, during 1930s only method of detecting trace amounts of radioelements was half-life measurement. And if You read papes by Curie, Fermi, Hahn, you will see that they used ONLY half life measurement for identifying. Please, do not write about something You clearely dont know a thing about... To be fair, percipitation methods of chemical microanalysis combined with half life measurements were quite sensitive qualitatively speaking as long as you had less than 3 radioistopes of the same element and as long as their half-lifes were quite different (about order of magnitude different).
Another great video. Thanks for the upload!
Glad you enjoyed it! There is a follow-up video already posted
This video is so great 😍, I love it.
PS: Can you do the video about the neutron diffusion equation please😁, I would love to see that
I am glad that you liked the video, I already see 4 votes for the solution of the neutron diffusion equation, I think it is a fantastic exercise for any student of differential equations. I will add it to my list of future videos.
As a nuclear engineering student, we were first introduced to calculating criticality using what was called the four-factor formula which had several terms relating to probabilities of fission, resonance escape, leakage etc.Then we moved on to the diffusion equation and the limitations of its assumptions. More exact answers are obtained using what is called neutron transport or monte carlo methods.
I’d like to see the diffusion equation video. Another difficult concept to grasp is neutron kinetics, the time rate of change of neutron population in subcritical or supercritical systems and effects of delayed neutrons.
@@KevinBalch-dt8ot great to have someone with nuclear engineering expertise around, thanks for stopping by and welcome to the channel. You are right, early methods are quite crude, in fact Frisch and Peierls did several approximations, like ignoring the scattering cross-section, which significantly simplifies calculations because all the transport terms reduce to just fission terms. The four-factor formula is intended for reactor criticality but not for bomb criticality. In a bomb the goal is to let the neutron multiplication go wild as much as possible, contrary to the conditions in a reactor where you try control the neutron multiplication. Monte Carlo methods formally didn't exist when Peierls and Frisch did their calculations. Monte Carlo method was created during the development of thermonuclear bombs.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
Great vídeo. Thank you so mucho for your explanations
Thanks for watching and welcome to the channel, there are already new videos and more coming soon. Subscription is highly appreciated ;)
Wonderful video!! Thank you so much!
Thank you too for watching and leaving a comment. The latest video in the channel is about what came next, so check it out!
@@jkzero oooo, I certainly will! Thanks!😁
My God, what an interesting great video! I am so sorry I didn't know about your youtube channel until now.
No worries that I am just getting started with the channel. Glad you liked it and that the mighty algorithm brought you here. Thanks for watching and welcome to the channel. Make sure to check the other videos.
An complete and honestly the most embrancing, yet clear explanation about nuclear fisson qualitative machanics i've seen! Also... That part of neutron diffusion got my attention... It would be nice to have the proper video for it!
thanks fro the kind comment; I am glad that you found the video so valuable. I feel that I am making the videos that I wished I could have watched as a kid. The video walk-through solving the neutron diffusion equation has received way more support than expected, great to find more people interested in the stories but also in the calculations. It is in the pipeline, coming soon. 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 To be honest, the encounter with this video specificaly was made via recomendations! I don't have the most clean searching reference, as I usually research about scientific themes, but your playlist about nuclear physics poped up at the collum aside a video (specificaly, one from a non-scientifical topic), and so I was here! But, honestly, I find myself lucky for have been lead here... there's some serious work being done, and in a so good explanation, that I agree with fellow comments: there is less viwers/subscriptions than it should have
@@juliofaria4503 thanks for sharing and for the feedback, I appreciate the kind words of support. I hope to keep growing, I will keep making videos but in the end what keeps a channel alive is the interaction with viewers so thanks for commenting and sharing. I am glad that the mighty algorithm found you.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
Subscribed, didn't expect to learn anything new but I did. My old university is where Lise Meitner studied. Kinda sad there isn't any memorial. There is one for Boltzmann of course but she deserves one too and as an enthusiast of nuclear weapons design it is a bit cool that the place I studied was part of the story, even if only in a small way.
BTW no silent letters in German, so it's appeoximately pronounced Lisey Meitner. Same as Porsche. Every letter is pronounced, German is a very consistent language, which I like. It's still horribly complicated though.
A discussion of Krytrons or high voltage spark gap switches could be fun too, another piece of the puzzle. Today you can buy them but they only ship to the US :) I suppose modern bombs synchronise the detonators in a different way.
Thanks for watching and subscribing, that really helps the channel. I am glad that you found something new in the video, you are more than welcome to check out the other videos of the series.
Thanks for the comment on the pronunciation of Lise Meitner's name, I struggle with it because I learned it as "Lisa" in my home country, then I moved to the US and I had to learn the American pronunciation, which stuck with me. You would be shocked by how the name of Karl Schwarzschild is pronounced in those others parts of the world. At least my students here in Germany were when I was teaching General Relativity and I said "Schwarzschild" out loud for the first time. You are so right, German is very consistent but also very hard, I have been for years in Germany and my German is still not even basic.
Wonderful explanation of the history and science. Thanks.
Glad you liked it! Thanks for watching, for the support, and welcome to the channel.
An excellent and descriptive video.
Many thanks! The follow-up video is already posted, enjoy.
You were wise to include the short summary about fission circa 1938 because that chapter as well as most everything else discussed in this video was either completely missing or, at best, poorly understood by the parts of my brain apportioned to understanding the development of science. Kudos to the RUclips algorithm for bringing my attention to this video. Hamlet could well have been speaking directly to me,
"There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy."
I had an unfortunate aversion to math and science when I was in school which I am now determined to change. The story of atomic weapons, despite the unsettling reality of their use, is nevertheless a fascinating revelation of the world of the very small made discernable only by intricate mathematical equations and the application of logic and reason. It can also be seen as a spectacular success for the theory of science and the Calculus. What can be achieved by the greatest minds in physics teaming up for a common purpose is pretty amazing.
I am glad that the quick summary was useful, I wanted to go quickly over the story found in many other channels because I wanted to get to the part that most popular science channels or documentaries leave out. The story of nuclear physics and weapons is fascinating, despite, as you say, their unsettling reality. Every time watch footage of nuclear tests I can only think of them as terrifying beauty. Thanks for watching and welcome to the channel.
Thanks for making and sharing this video. And yes, I'd appreciate a video on the neutron diffusion equation.
I am glad you liked the video and the video solving the neutron diffusion equation is now published, check the most recent video on the channel
@@jkzero Thanks. Just a suggestion, you might want to add a note to this video about the neutron diffusion equation being publishes.
@@rmandra good suggestion, thanks! And done!
Excellent video
Thanks for watching and welcome to the channel, there are already new videos and more coming soon. Subscription is highly appreciated ;)
This is really fascinating!
I'm amazed they could determine these parameters with any degree of accuracy considering the crude equipment available then.
I am glad you liked it. I have always been fascinated by this story and, just like you said, all what they could do with so little tools available back then. In case you are interested, I posted a video with the full calculation that Peierls and Frisch did to calculate the critical mass here ruclips.net/video/DIuoFAW9H3E/видео.html
Great video - thsnk you! It fills in some gaps that some of us want to know.
Glad you enjoyed it! There are many channels describing the general and qualitative aspects of nuclear physics but I thought that a more quantitative description was missing. I love solving equations and I have now found out that in addition to interesting stories many people really want to see calculations too for solving applied problems so I intend to fill that gap. Moreover, I wanted to tell the stories of less-known but crucial characters, like Frisch and Peierls in this video, and many others in future videos. Thanks for watching and welcome to the channel.
I would loooove a video on solving the neutron diffusion equation!
oh, it is done, enjoy: ruclips.net/video/DIuoFAW9H3E/видео.html
Pretty cool how bits of history are intertwined with the physics
I find these stories fun and illuminating, they give a more human perspective. Textbooks present many ideas and, unless super famous, leave the protagonists aside. These stories, the people and the science, deserve to be shared
an excellent video. i think the pacing is perfect.
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.
You are a great story teller!
thanks, I appreciate the appraisal; I do what I can with the narration but I take a long time and many iterations to complete a script so I am glad that it gets appreciated. Welcome to the channel.
I just discovered your videos, Congratulations and thanks for shearing your big knowledge your explanations are very clear.. there are a lot of super transcendental experiments but they are nor well explained like the oil droplet that you explained very clear and deep,etc. where can I find a list of your videos?
Thanks for watching and welcome to the channel. You can find a list with all the videos here: www.youtube.com/@jkzero/videos
Very good video !
Merci
Glad you liked it! Thanks to you for watching and welcome to the channel
Wow, what a great video, subscribed! Now to watch your others 🙂
Thanks for subscribing! I am glad you found the content of interest, all the videos of this series in the playlist linked in the description above. Thanks for watching and welcome to the channel
Dang. Facinating. Tell me that you are going to do a follow up video.
great that you liked it. The follow-up video is about Peierls and Frisch demonstrating that the nuclear chain reaction produces an explosion, check out the full playlist and let me know your impressions ruclips.net/p/PL_UV-wQj1lvUhNttvv4_KsYrQxHygj3Ey
So this is something I have often wondered about. The basic model of fission is that neutrons fly out and split other atoms, but in order to get fission, you have to slow the neutrons down. This changes the whole idea does it not? It goes from a bullet hitting an target to one of a particle being attracted to and captured by the target atom.
the need of slowing down neutrons is only relevant for fissioning U-238 in a controlled manner, such as a nuclear reactor, this is the role of the moderator. Please check the follow-up video for Peierls & Frisch calculation of the heating and expansion of the nuclear core, which would stop the chain reaction. The process is so fast that slow neutrons cannot be used for a bomb; a bomb can only work with fast neutrons.
Hello! Great video. Small thing to 3:01 - uranium has 92 protons, 94 is plutonium, I bet you know this properly but some missnumbering happened :) Cheers!
oh nooooooooooooooo... the curse of copy+paste! How could this happen! Thank for notifying it, I really missed that. I try to be as careful as possible and for each video I watch the final version a dozen times looking for minor details but things still slip through. Yes, I know that uranium has 92 protons, this is a typo. Thanks again for watching with such attention.
Very interesting especially about the "unknowns" in developing nuclear theory.
And don't worry about the geneology slide.
Pianists also want to brag about their lineage. My college piano instructor studied with someone who studied with someone who studied someone who studied with Liszt who studied with Czerny who studied with Beethoven! So there!
The rule of thumb for every tonne of uranium fissioned 8kg of plutonium is produced or put it the longer you cook uranium in a reactor the more plutonium. Plutonium is easily separated by chemical means the yellow uranium at the top and blue plutonium at the bottom. The spent uranium can be used in fast breeder reactors to produce further plutonium to extend fissile material. Enrichment of uranium is expensive and centrifuge technology is used and energy used is between 40kw and 110kw the Urenco TC21 centrifuge has a rotor length of 5m and 100 SWU per annum and AC100M centrifuge has a rotor length of 16.5m and is rated at 350 SWU . The SILEX process is new and the separative power index is unknown.
SILEX: About 10-20% enrichment per pass.
Prolonged irradiation in the reactor poisons Pu with by-products. So there is a balance
Up until that point they thought they would be so big that they would have to be delivered by boat, it must have been enlightening and somewhat terrifying to know the critical mass was much smaller than originally thought.
Also there is a plaque on the University that shows that Frisch and Peierls first showed the feasibility of an airborne atomic weapon there
yeah, the mention of a bomb carried by boat shows the naive ideas about the size of the bomb.
Some time ago I posted a picture of the plaque at U. of Birmingham ruclips.net/user/postUgkxeLp25z0xKqPBLU_rH9lhjILeDXEPcmuv
Lise Meitner was ripped off by Otto Hann, as she was the one who interpreted the even as nuclear fission. He got all the credit. I digressed, this was an excellent presentation.
Lise Meitner is one of those terrible cases of neglect by the Nobel committee, she was nominated 19 times to the Nobel Prize in chemistry and 30 times to the Nobel Prize in physics.
She should have emigrated to the US or Britain. Unfortunately for her, she settled in Sweden - antisemitic and misogenistic at the time. She had no chances for the Nobel prize...
What must it have been like to arrive at these calculations -- in the end, simply arithmetical ones -- and to realize what in these numbers had been discovered and unleashed? I've occasionally been shocked by disappointing calculations concerning my checking-account balance, bad enough. But this?
Solving the diffusion equation is not trivial task, it requires calculus plus some clever approximations that go beyond the simple arithmetic manipulation shown in the video; however, it is something that any science or engineering undergrad could easily do. I can barely imagine how shocking and scary it must have been for Frisch and Peierls to find out that instead of tons of material only a few kilograms of U235 would be enough for a bomb; they probably checked and double-checked several times.
@@jkzeroYou're quite right, of course; I didn't mean to trivialize the calculation. But reliable approximations were soon within reach. There really is something spine-chilling about that image of the golf ball...
@@worldnotworld I am pretty sure that Frisch and Peierls got a shiver when they got R_c = 2.1 cm
@@worldnotworldI loved that mention the "spine-chilling image of the golf ball" that was precisely what I wanted to transmit, that is how I felt it too. Even when I recorded the audio I said "2.1 cm... 2.1 cm!!!" twice in the voice of Doc Brown saying "1.21 GW" but I removed it because I sounded almost silly.
@@jkzero You did just the right thing by not playing up the melodrama _at all._ It makes the image even more striking, really.
🙏🙏🙏🙏🙏 love it…., I understand just enough to hold the edge of the conversation and imagine our Quantum world 🙏🙏🙏
Clever people eh
Thanks
Thanks to you for watching and welcome to the channel
We still don't know a lot about an atom. There is still more potential in it than we can imagine.
I think the "Fat Man" bomb casing was not a "Soccer Ball" A soccer ball is a "Truncated Icosahedron" It has 12 pentagons and 20 hexagons. In this object the "dihedral angels" are different at the intersection of the Pentagons and the Hexagons and the intersection of hexagon on hexagon. Where the pentagon is adjacent to a hexagon the dihedral angle is 142,62 degrees. Where the hexagon is adjacent to a hexagon the angle is 138.18 Secondly, the area of each polygon is different. Hence you would have different quantities of explosives arranged around the core at different angles. This also means the dihedral angle planes do not split the center of the objects circumscribing sphere. All in all this says that a soccer ball would not work.
I think and I saw once a picture of the bombs casing. It was a "Deltoidal Hexecontahedron". This is an object with 60 kite shaped polygons. They form a sorta stellated dodecahedron. This would avoid the problems described above.
I think the movie got it wrong. Let me know your thoughs.. Thanks, Hamp Stevens
wow, you really made me think deep here, thanks for that! I am not sure when/where in the video I said that the explosive lenses had the shape of a soccer ball, I used the soccer ball only as a reference of the size of a bare uranium core not the shape of the high explosives. Could you point out where this was inferred from in the video?
I've often wondered whether criticality can be attained with less than the conventional "critical mass" of U-235. Could it be that a critical density is the true trigger for the reaction?
In essence, what is the minimal mass requirement for initiating a nuclear fission chain reaction using U-235 or plutonium? I would greatly appreciate insightful responses.
For those curious, my pondering was sparked by the first Predator movie. The scene where Arnold Schwarzenegger evades an explosion resembling a nuclear blast led me to consider this. However, it's implausible for him to have outrun an explosion comparable to the yield of "Little Boy" in such a brief span. Your input is valued. Thank you.
as described in the video, using modern values for density and fission cross-sections, the bare critical mass for pure U-235 is ~46 kg; however, you can push this down using a heavy metal around the uranium core called a tamper. The tamper helps in two ways: first, it reflects escaping neutrons back inside the core so they can produce more fission, and second, being heavy its inertia holds the exploding and expanding core for a few extra microseconds, which allows a few extra generations of neutron multiplication, and in an exponential growth the last few generations are the more crucial. How much you can push the critical mass down depends on the mass of the tamper, for instance, for a ~15 kg tamper the U-235 critical mass drops to ~30 kg, whereas for a 400 kg tamper the uranium core necessary for a bomb drops to ~18 kg.
@@jkzero As far as I understand, pure uranium has bad compressibility in a solid core, so probably very hard to do
@@nehorlavazapalka in my comment above, I was not referring to compression but only to the reduction of the necessary core mass by using a tamper surrounding the core
Pls, explain the diffusion theory and neutron diffusion equation
thanks for your interest, the promised video explaining the details and solution of the neutron diffusion equation is already published, enjoy: ruclips.net/video/DIuoFAW9H3E/видео.html
Excellent article. I do wonder however if Bohrs actually identified U235 as the key low speed neutron fissile material. Had he done so in any sort of public or published document the Manhatten project would have started in 1939. It did not start until 1942 because only then did Britain reveal the key document by Peierls and Frisch which definately identified U235 as the cirital isatope and they also predicted size of a critical mass and yield. This was the bomb. As you say a lot of people tried to claim credit that didn't deserve much; and I really don't believe Bohr knew about U235. If he did he kept his mouth shut and didn't reveal his knowlege until after the war.
Which makes it irrellavent.
Bohr did identified U-235 as the key component of natural uranium responsible of the fission reactions with slow neutrons. He published two crucial papers in 1939, the first one alone in which he uses the differences between uranium and thorium as the key insight for the identification of U-235 titled "Resonance in Uranium and Thorium Disintegration and the Phenomenon of Nuclear Fission." The second paper, "Mechanism of Nuclear Fission," is the one mentioned at the 04:00 mark in the video. This paper co-authored with Wheeler shows all the gory calculations. Your comment about the British push to the bomb program is in fact the topic of the next video, stay tuned.
...thank you for this infomrative video. I've always thought of critical mass in terms of neutron flux and suprisingly Netron Diffusion Equation models just that. :D
If neutron flux is not hight enough to reach criticality, just decrease fuels volume (cross section) so that the probability of neutrons to fission the atomic cores can increase. On the other hand if volume is constant, just increase fuels purity so the ratio of fissable and non fissable atomic cores is higher (relative cross section is higher)...
reaching criticality is tricky, but it can be done if we can find the relevant variables driving the criticality condition. cross-sections cannot be modified, they are fundamental properties of a material like uranium 235 or plutonium 239, but other properties can be controlled like the material density (critical mass is proportional to the inverse squared of the density) and enrichment ratio. The next video is a complete walk-through on how to solve the neutron diffusion equation to derive a general formula to calculate the critical mass in general of any pure fissile material so you might like that. It will be math heavy.
@@jkzero ..."relative cross section" was a rather choice of words on my side as cross-sections you are reffering in the video are fundamental properties.
To me whole Neutron Diffusion Equation is like Bernoulli's Equation but instead of measuring fluid velocities and pressures we are measuring neutron flux and fissability. Either you change spatial dimension to increase flux or you increase density. Either ways it all comes down to how probbable is for a neutron and an atom to find themselves in a certain point of space and time for fission to occure.
To me most amazing part in your video this time is historical aspect. In a matter of mere 5 years, someting that seemed theoretically impossible (a bomb) by Bohr's initail calculation for critical mass, was turned upside down and made possible (Trinity test)...:)
@@t850I see your point, in fact the derivation of the neutron diffusion equation involves properly describing the neutron density as a current, in my new video (in preparation) I even mention the similarity with fluids and electric currents.
@@jkzero ...in the end conservation of mass and energy holds true as all this equations are just a variation of this basic physical laws.
I'm defenitely looking forward to seeing you new video...:)
@@t850 that is right, there is just a tiny but significant difference with neutrons diffusing inside a fissile material compared to an element of fluid or electric changes in a wire: the number of neutrons changes with time and position not only by diffusion but also because some neutrons are consumed by fission and new neutrons are created by fission so the continuity equation must be modified to include the corresponding source and sink terms.
Please upload a vid where you talk about Peierls for hours. Thnx!
that is an interesting challenge
@@jkzero tape begins to turn ....
_Comprehensive_ yet not *_abstruse!_* thanks so much
p.s. Frequent misuse of the term "critical mass"? I found that distracting. Such as when, for example? So many social dynamics include this notion, along with _criticality_ and _tipping point._
I was referring to the non-technical use of the term "critical mass." In the corporate world is widely used as a way to say "all you need for something to happen is a critical mass" as having more people for a task is all that matters. I think this misses the point of the meaning of the borrowed term and also misses the opportunity to use it correctly: organizations want something to happen they need the minimum number of people but that is not enough, they also need the right conditions. This is the exact definition of criticality, not critical mass. In the original script and recording I had all this explained but during the editing this sounded more like a rant than a useful comment, cutting the flow of the video, so I took it out. Does this explanation make it more clear? Sorry that it got a bit long.
@@jkzeroYes, indeed. It caught my attention because I'm pre-occupied by how _"common usage"_ can distort discourse!
So thanks for this: _" "all you need for something to happen is a critical mass"._
To be honest, I was trolling one particular sort of fish, so apologize if my question seemed cryptic and over-broad.
Addendum? I read your _" they need the minimum number of people but that is not enough, they also need the right conditions"_ with great interest!
An hour ago (quite literally!) I inserted the following into "notes to myself": _"What if there's an analogue of quantum mechanics in the domain of social cognition? What if, as light can be explored as wave and/or as particle, when observed one way a certain opinion seems perverse and illogical, while observed another way it seems antagonistic and oppositional? Then under the latter conditions, social transactions will most probably only amplify conflicts!"_
_thanks for your time!_ good of you
/bdt
p.s. grade 3 (age 9?) I pondered _"238 this, but 235 _*_that_* ... what's going on?!" 🙂
@@BenTrem42 I will need help here, I do not understand the comment
@@jkzeroApologies. But I'm sure some is clear.
_"caught my attention because I'm pre-occupied by how "common usage" can distort discourse!"_
Please show neutron diffusions equations
The video walk-through solving the neutron diffusion equation has received way more support than expected, great to find more people interested in the stories but also in the calculations. It is in the pipeline, coming soon.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
The first fission of uranium was done by Fermi in 1934
true, but he didn't know it, in fact, he got the Nobel Prize for the wrong reason
@jkzero Yes, but not even Otto Hahn understood what was happening. Furthermore, Fermi paved the way for conducting the experiment. In short, someone like Fermi can not be ignored. He, also, created the first nuclear reactor.
7:22 that would be cool.
I am happily surprised by the level of support to create a video about solving an ugly partial differential equation, lots of hard-core nerds here and I am loving it. There are already several votes for this, so it is now on my to-do list.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
Awesome video. After 3 ODE classes i still dont have a real application beyond the springs on springs in a triangle pattern. Please, the derivation!
The video walk-through solving the neutron diffusion equation has received way more support than expected, great to find more people interested in the stories but also in the calculations. It is in the pipeline, coming soon.
@@jkzero 20 years after graduation, I still remember my ODE's and modern physics. But I have never really applied it to a problem that was not given to me by a prof. I want to exercise that part of my brain again, and this is interesting. I remember we solved the Schrodinger eqn (ODE version) for Hydrogen. Then we used the matrix method, then we did a numerical estimation for Hydrogen. But that is the limit of my Modern Physics II course haha.
@@YoyomaG6 glad to read about your interest on challenging yourself intellectually, that is like taking the brain to the gym. The neutron diffusion equation is a PDE, not an ODE; however, don't get intimidated, after a little quite trivial trick the PDE can be turned into two ODEs and then all the methods that you know can be applied. As I said, this is coming soon with a "calculus warning" for anybody who might want to skip it due to high level. Still, it has been great finding an audience interested in the hard stuff.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
Done❤
Please show the nuclear diffusion equationn solution
another vote for the solution of the neutron diffusion equation; I was honestly not expecting so many people asking for this so it is now in the to-do list. Coming soon so make sure to subscribe to get notified.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
So you woulda thunk that the first scientists splitting the atom and realizing it could be turned into a bomb might have just kept that to themselves.
I guess their actions have to be analyzed in their historical context: they were really afraid that Heisenberg and his club of nuclear scientists would come similar conclusions
It would be interesting to know "how was it determined that Uranium 235 and Plutonium 240(?), we're the candidates for the bomb?". Why not lead? Potassium? Etc, etc"
Also, what
several viewers have asked a similar question: out of all the elements of the periodic table, what makes Uranium 235 and Plutonium 239 special for the bomb? I will add this to my long list of videos in the pipeline, thanks for the suggestion. I am curious to know what brings viewers to the channel, were you searching for something in particular or the 'mighty algorithm' found you?
I am an electrical engineer with 40 years experience. For many years, I've been interested in the Manhattan story and certainly more interested after watching the movie Openhiemmer. Your critical mass video fascinating as you address questions that are in the realm of my grasp(barely)...and you explain who figured it out. It is amazing how those brilliant scientists used new understanding to invent the bomb(with it's horrific implications). Well, back to my questions. I've not seen any discussion "how was it discovered that Uranium and Plutonium were the candidates?". For example where there are number of research activities worldwide to analyze those elements within the periodic table for fissil properties? How is it known that fission will release large energy? How was it known, or speculated,, hydrogen fusion would release 1000(?) times more?
To your original question.... the "algorithm" found me.... but the phrase "critical mass" allows me to find you again...
@@DESERTCB1 are you familiar with The Making of the Atomic Bomb by Richard Rhodes? there you find more details than expected, it is a terrific account of many things that most documentaries would not dare to get into. There is the story of how Leo Szilard proposes a series of experiments checking all the elements of the periodic table under neutron bombardment. In parallel, Fermi and his team in Rome did exactly that. Later with the famous Bohr-Wheeler paper, the search narrows down. I should definitely make a video about this in the future
@@DESERTCB1 oh the almighty algorithm, I am glad it has reached to so many people interested in these topics beyond the classic story but accompanied with some real calculations; I am very happy with the interest in the math and physics, in addition to the cool narratives
A++
I hope this is a grade and not just a counter (sorry, I have been writing too much code lately); either way, thanks for watching and welcome to the channel
Tickeling the Dragon!
in the next video we will really be tickling the dragon's tail by solving the neutron diffusion equation and calculating the critical mass from first principles, you are welcome to join
Oh no! A nuclear chain reaction killed someone!
Umm, wait...
Odd that Nagasaki has no detectible traces of the plutonium bomb🧐
Fat Man was detonated more than half a kilometer over Nagasaki, this produced a maximally destructive blast wave over the city but also minimized radioactive fallout, I think that no detectable traces of plutonium is expected rather than odd, or are you implying something else?
@@jkzero And the Jesuits were out after the blast doing interviews at ground zero with no trace of radiation on the film. I call bullshit. It is all a lie.
I had a friend, John, who had a small machine shop in Southern California in the early 40s. A friend of his told him someone was looking for a machinist to create an aluminum empty ball where the two halves could slide together. John worked out how to do it. A manufacturer ordered fifty of them. But for the rest of the war more were ordered. After the war the FBI questioned him. The people he had been selling the balls to had been ripping off the government and ended up going to jail. The FBI also told John that his balls had been a part of the atomic bombs.
wow, this sounds like a hell of a story. I am not sure what halves of balls sliding together could be used for. Do you have any idea about the purpose?
@@jkzero the thickness of the wall had to be the same so there was an outer and inner lip.
@@jkzero I believe the balls contained the uranium!
@@wallymcallister5831 now I get it; what you describe sounds like the so-called "pusher" used in implosion bombs. This material compresses the plutonium (not uranium) core when the explosives lenses have turned the shockwaves from the high explosives inside out.
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Bravo Zulu!
Why did Heisenberg get it so wrong?
[insert Antonio Banderas' Laptop Reaction here] I love to get this fantastic question! You are right, Heisenberg got it very wrong. I do not know "the reason" but for the documents that I have read and the estimates he provided to the German military, he did not use the neutron diffusion equation, instead he used a very naive random-walk approach, which led him to a huge R_c, and from this a "critical mass" in the order of tons. Thanks for such a great question, I have a video dedicated to this in the pipeline, so make sure to subscribe to get notified. Welcome to the channel!
please check my latest video dedicated to Heisenberg and the German Bomb, I hope to have answered your question, if not just write in the comments there
Cross-section is not a probability and cannot be thought of as such. Probability is not being measured in the units of area!
you're a midwit if you can't see how cross sections can be a probability.
Cross section is the coefficient of proportionality between the numbers of event N in your experiment per unit time t and the incident flux of particles F that you're sending. Therefore cross section = N/(t times F). The number of events is the number of particles that you have times the probability of a single event to occur. So the cross section is directly linked to probabilities: the higher the probability, the higher the cross section. We use this idea and evaluate probabilities, using QFT and S-Matrix, to get theoretical values of cross-sections of many different processes.
@@peppescala4113 In the video he said that cross-section IS a probability, not "linked to", but "is", which is not true. And it can't be true even from dimensionality analysis.
@@gaHuJIa_Macmep If you want to be fussy, then you're winning. It's completely clear what he meant.
@@peppescala4113 I don't want anybody to be fussy. I want everyone to be precise. Is it so difficult???
yes please... Neutron Diffusion Equation!!
The video walk-through solving the neutron diffusion equation has received way more support than expected, great to find more people interested in the stories but also in the calculations. It is in the pipeline, coming soon. In the meantime make sure to check the follow-up videos and welcome to the channel.
thank you! glad to be a new subscriber.
@@lahockeyboy thanks, subscription is highly appreciated, it really helps me grow and continue making these videos. Sharing is also very helpful :)
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
I'm going to subscribe but I hope you will show the equation and solve it
Thanks for subscribing. I already made and published the video with all the gory details of solving the neutron diffusion equation and calculation of the critical mass. Enjoy it here: ruclips.net/video/DIuoFAW9H3E/видео.html
Critical Mass. Just North of Boston, right?
getting this took me more than I am willing to share :)
Are you kidding? Considering your audience of nerds, of COURSE we want to see a video on the Neutron Diffusion Equation!
Meanwhile my PhD/International Education wife is rolling her eyes and wondering what possessed her to marry a scientist… 😊
I am glad that you liked the video, I already see several votes for the solution of the neutron diffusion equation, I think it is a fantastic exercise for any student of differential equations. I will add it to my list of future videos.
promise fulfilled: solving the neutron diffusion equation step by step ruclips.net/video/DIuoFAW9H3E/видео.html
Bomb wasnt possible, some articles don't age well.
in Bohr's defense, all the calculation on his paper were correct and it gave us the modern understanding of the internal structure of nuclei, but yeah, his final remark was completely off.
Since when is a football 8.4 centimeters, you mean a softball I think
when searching for sizes of different balls to compare (yes, I had to search for this, I have no idea of sports), I found that a softball has a radius of almost 5 cm, whereas a soccer ball (football fro the rest of the world) has a radius ~11 cm. I decided to pick the higher side because, as mentioned, Peierls and Frisch underestimated the radius; also because a soccer ball is most easily recognized by viewers from all over the world. Another reason is the beautiful truncated icosahedron that foreshadows the geometry of the explosive lenses of the implosion bomb.
@@jkzero you have no idea what you are talking about a FIFA standard is 22cm wide, please don't lie to me I play football and you have your balls mixed up.
Google FIFA football size for a laugh
@@davidrobertson5700 a radius of 11 cm is the same as a diameter of 22 cm (diameter is defined as twice the radius). But you are right about the first part, when it comes to sports I usually have no idea what I am talking about so I did Google FIFA football size.
👍
thumbs up appreciated