Amazing, as a theoretical physicist myself, I'm looking forward to see more mathematical videos about this topic 😁 Edit: makes me wanna sit down with numerical methods and analyze more reallistic example of shrinking and expanding core (true R(t))
@pressaltf4forfreevbucks179
8 ай бұрын
Is that actually 2500 dollars?!?!? I should become a theoritical physicist too💀💀💀
@jakubstawarczyk
8 ай бұрын
@@pressaltf4forfreevbucks179 Hong Kong $ ... so only 64 US$ I'm poor too 😭😉 (and given I'm now in Philippines it shows 2500PHP... not sure why as my visa was charged 500HKD that I've selected)
@jkzero
8 ай бұрын
WOW, thank you so much for your kind support, I am grateful for the appreciation. This drives me to keep making these videos. I enjoy making them (despite the consumption of my free time) so it is very gratifying to know that the content is appreciated. Thanks again!
@Keshav-il2hp
8 ай бұрын
its pesos lol 2500 is $44 still great@@pressaltf4forfreevbucks179
@multiarray2320
8 ай бұрын
@@pressaltf4forfreevbucks179 no, its about 40 bucks.
@hypercomms2001
8 ай бұрын
Absolutely fascinating. I have always been interested how this was calculated ever since I did a school assignment on the Manhattan project when I was 14 in 1974.
@jkzero
8 ай бұрын
glad you liked it; similar story here: I read about the Manhattan Project when I was a kid and got obsessed and decided to be a physicist. That was a few decades back and here I am.
@-VinhKhang_yearsago
8 ай бұрын
@@jkzero congratulations
@MrFib112358
8 ай бұрын
This is the first time that I am excited for a homework assignment and I can't believe it came from KZitem, I really want to try to do this! Brilliant video and thanks for educating us on this fascinating topic!
@jkzero
8 ай бұрын
happy to see that some viewers have accepted the challenge, let me know what you get
@kirkhamandy
8 ай бұрын
17:15 _This will very quickly start blowing up_ LOL, I've often heard of exponentials "blowing up" but here, never a more true definition 😂
@jkzero
8 ай бұрын
glad to see that people appreciate the puns... there is a Taylor Swift joke hidden in a previous video than maybe was too subtle because only one person noticed it
@KiwiExpressCream
8 ай бұрын
Not going to lie, the maths is a bit beyond me, but I love how you worked out the critical masses. All of your videos have been amazing and I always look forward to the next one.
@jkzero
8 ай бұрын
thanks for the feedback, this video was math heavy; people seem to like these so I will make more but I will also continue with the standard video of some history sprinkled with a less-intense calculation on interesting topics, even beyond nuclear weapons; I don't want the FBI knocking on my door :D
@Hexnano
8 ай бұрын
Thank you for this video, I got stuck while working on building my atomic bomb and this was very helpful.
@jkzero
8 ай бұрын
I am glad you liked the video; however, I cannot wish you well in your endeavors :)
@footbballa1784
8 ай бұрын
This channel deserves more views and subs, one of the best Physics YT channels out there keep it up!
@jkzero
8 ай бұрын
Thanks for the endorsement; I wish I could get to wider audiences but the KZitem algorithm is driven by engagement so you can actively help the channel by liking, subscribing, and sharing. This type of support is highly appreciated so I can continue making videos.
@tomashernandez8711
8 ай бұрын
Man, this theory was taught to me by a professor the last semester, amazing the application and the smooth way this works to explain such a beauty phenomenon
@jkzero
8 ай бұрын
Awesome! 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?
@ion8264
8 ай бұрын
Shame how underrated this channel is😢
@jkzero
8 ай бұрын
thanks for that, you can support the channel by liking, commenting, and sharing the videos, that engagement drives the algorithm that gives the channel exposure. Thanks in advance.
@The_Fancy_Duck
8 ай бұрын
Very underrated KZitem channel.
@jkzero
8 ай бұрын
Thanks for the endorsement; I wish I could get to wider audiences but the KZitem algorithm is driven by engagement so you can actively help the channel by liking, subscribing, and sharing. This type of support is highly appreciated so I can continue making videos.
@fablearchitect7645
8 ай бұрын
Can you please do a video on deriving the transfer function for a nuclear reactor in terms of control rods vs output thermal power?
@terrycole472
4 ай бұрын
You could always look at KZitem channel "Nuclear Engineering Lectures" NE560, here: kzitem.info/news/bejne/yomYsol4rpOFam0 - but remember transfer function analyses are perturbative, and the full range of control rod operation is not, so you have to hope things stay linear. Also remember transfer function theory often looks at the Zero-Power state (to avoid pesky thermal feedback considerations) of a reactor at criticality. It's a useful tool but extending it to more general cases is not trivial.
@pawelbjanowski
8 ай бұрын
A coffee/beer from a nuclear colleague from Poland, with kind regards!⚛
@jkzero
8 ай бұрын
Thank you so much for your kind support, I am grateful for the appreciation, which drives me to keep making these videos. Thanks again!
@danieleambrosini1681
8 ай бұрын
Awesome! Make a lot of videos on physics because you are really talented! :) Love from Italy
@jkzero
8 ай бұрын
thanks, I appreciate the feedback. I hope to keep making videos, I really enjoy this and the interaction with the community. 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?
@ion8264
8 ай бұрын
@@jkzeroI searched relaxing physics video and found you😂
@jkzero
8 ай бұрын
@@ion8264 nothing more relaxing than taking time off and spending free time solving partial differential equations 😃
@danieleambrosini1681
8 ай бұрын
@@jkzero i really love physic and math, i study engineering so i really like to Watch videos about what i like, i found you about 5 months ago when you did the video about the Enola Gay, today i opened KZitem and in the home i found your video, i really enjoyed It!😊
@jkzero
8 ай бұрын
@@danieleambrosini1681 the Enola Gay video was my official debut with the channel and having a community of nerds interested in physics stories and that don't shy away from some math is just great. Thanks for returning for more!
@paulm1241
8 ай бұрын
Excellent! Could you make a video on the implosion physics ? For example, it is often said that although it was known that hollow cores would have a much better yield, the original bomb used a "conservative" design based on a solid core ("Christy core") because the maths of hollow core implosion was too difficult to solve at the time (but it was finally implemented in all designs a few years later). I could not find any more detailed info on that on the web.
@jkzero
8 ай бұрын
did you check my "Nuclear Weapons Q&A" video? I don't go into the details of the solid vs. hollow core but I do calculate how much the core is compressed because somebody asked about it.
@gaHuJIa_Macmep
8 ай бұрын
Read the NWFAQ by Carey Sublette.
@Isaac-mt9hx
8 ай бұрын
This is an amazing video! Made me even more excited to learn DPEs next semester!
@jkzero
8 ай бұрын
If anything in my videos can make people excited about physics and math, I can say: mission accomplished! Thanks for sharing
@billynomates920
8 ай бұрын
clicked on your video just as the cider i'd had earlier informed me that actually, it has not yet fully diffused through my system and that perhaps i'd get more from your video if i delayed watching it until tomorrow. til then! thank you.
@jkzero
8 ай бұрын
stay safe and enjoy the video later
@dylangabriel2703
8 ай бұрын
Thank you I was trying to find this for a long long time
@ytashu33
8 ай бұрын
My kind of YT video, just at the right intersection of math and physics, delivered at the right cadence, not too fast, not too slow, loved it. One question, if sin(kR) = 0, wouldn't that give us multiple solutions? ie, kR = n * pi? Any particular physical constraint that we must consider only the lowest numbered "harmonic", n = 1?
@1995error
8 ай бұрын
If you used solutions with multiples of pi you would have areas with negative neutron density which I guess would not make much physical sense, but I am kinda guessing. The reason why you can use multiple solutions in QM is that you multiply the function with it’s complex conjugate before you get the probability, which means that it will always be positive:)
@jkzero
8 ай бұрын
nice catch, that is a very nice observation; you are right, the general solution is kappa*R=n*pi; however, the higher "harmonics" will only make the bomb core bigger, we are searching for the minimum radius. Also, a solution for n>1 can lead to a negative density, which is also a non-physical solution. Mathematically, your point is 100% correct; however, here is when physics guides the final solution. Just like setting B=0 to remove the non-physical cos(kappa*r) term.
@ytashu33
8 ай бұрын
Thank you Prof, that makes sense. You did proactively point out all other, non-valid, solutions and explained why they are not applicable. So this stuck with me. This was the only point, everything else i was able to follow-up rather clearly. These are not easy thing to communicate, you struck absolutely the right balance between explaining the points in sufficient detail, without getting bogged down. That balance is hard to get right, you hit the ball out of the park. Thank you!
@jkzero
8 ай бұрын
@@ytashu33 in the video at 14:20 I refer to the solution used as "the simplest solution" this is precisely to address your question. I could have explained more details but the video was already 25 min long. Thanks for your appreciation, I love teaching and created this channel mostly because I wanted to share fun and education stuff, I just never thought that a video only about solving a hard equation would produce this level of interest, which I find great. Welcome to the channel and make sure to check the other videos.
@MisterTutor2010
8 ай бұрын
The Differential Equation of DOOM :)
@jkzero
8 ай бұрын
I read this as "The Differential Equation of BOOM" but yeah, both work, I guess
@spencerwenzel7381
7 ай бұрын
I really appreciate that in every formula you describe what each variable represents and how it relates to the physical interpretation. Even if I don't completely understand the math, the implications are not completely lost and I am still learning. Thanks for making these.
@jkzero
7 ай бұрын
Thanks, 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?
@spencerwenzel7381
7 ай бұрын
@@jkzero Your video about Planck caught my interest initially and then I started looking through your other videos. However I initially saw it on my feed.
@jkzero
7 ай бұрын
@@spencerwenzel7381 Thanks for sharing and I am glad the algorithm has been showing my video to so many people, I hope you find the other videos of interest too and welcome to the channel.
@strangercydonian
8 ай бұрын
i would love to see a complete playlist about the calculus for nuclear reactions
@jkzero
8 ай бұрын
thanks for the request; I cannot guarantee to be able to fulfill all the requests but I am collecting suggestions, thanks
@paulkolodner2445
2 ай бұрын
Thanks for producing this excellent video. It answered two long-standing questions I have had: what is the uranium critical mass, and how does implosion reduce it. I have 2 comments: 1. Being too lazy to calculate, I'm guessing that putting a boundary condition on the neutron flux at the surface instead of the density means that there is a higher density of neutrons out near the boundary, producing more fissions there. Thus a lower critical mass. 2. At the end of WWII, German atomic scientists, including Werner Heisenberg, were interned at an English estate known as Farm Hall. Their conversations were bugged and translated. When they learned of the Hiroshima explosion, Heisenberg gave this lecture to the other guests. As the physicist Jeremy Bernstein pointed out, his inept presentation made it clear that he had never tried to solve this diffusion problem before. This indicates the primary reason why the Germans never got very far in making an atomic bomb: utter incompetence at the very top of a rigid, hierarchical research/development system. As Bernstein put it, Heisenberg was a great physicist (invented quantum mechanics) but not a very good one (couldn't get the units right in a simple calculation). The Manhattan project had the likes of Fermi, who was both great and good.
@jkzero
2 ай бұрын
Thanks, I am glad you liked the video and that it answer many of your questions. Regarding your follow-up questions: 1. yes, relaxing the boundary condition gives you a lower critical mass. 2. Your words echo very much Berstein's sentiment. I do not buy the narrative of the scientists' boycotting the bomb program but at the same time I disagree on Heisenberg being so inept, the evidence suggests that they simply worked on other things. His lecture at Farm Hall shows that it took him just a couple of days to correctly determine the critical mass, although the transcripts also reveal that he knew little to nothing about bomb physics. I have a full video on Heisenberg and the German bomb kzitem.info/news/bejne/l7B_sIitimSTn4o
@ukornel77
29 күн бұрын
It's ridiculous to say that Heisenberg was not a very good physicist. Heisenberg made a mistake in his first attempt to calculate the critical mass, relying on "random walk" model that resulted in need for dozens of tons of fissile material for nuclear detonation. Edward Teller admitted in an interview he made the same mistake first as well. The difference between them (Heisenberg vs Teller, or more generally, most German physicist remained in their Motherland vs Manhattan project participants) is not greatness as scientists. The reason is simply the motivation. Teller and his fellows continued relentlessly with a different approach because of the fear of the Nazis. In contrast to them, Heisenberg didn't have such phobia as a driving force against Americans. He wasn't particularly eager for building the bomb and could abandon this goal easily on one hand. On the other hand (perhaps more importantly), he could set his heart at rest, seemingly not being have to worry anymore about Germany being bombed with nuclear weapon. Teller praised Heisenberg as a "hero" for this. In a 2000 paper that summarizes and discusses Heisenberg's Farm Hall lecture, author M.S El Nachie also concluded that Heisenberg has never thought seriously about the bomb before he learned of Hiroshima bombing. Talking about scientific greatness El Nachie praises Heisenberg for his razor sharp intellect for deriving the correct result alone in couple of days, without tables, calculator, his notes etc, being de facto in captivity, knowing nothing of his family. He wrote that Heisenberg was doing what theoretical physicists do best. (Note that in the "Los Alamos Primer" -lectures based on the work of dozens of well supported scientists in the Manhattan Project- also only presented the "elementary solution" for critical mass.)
@paulkolodner2445
29 күн бұрын
@@ukornel77 Your comment, "Talking about scientific greatness El Nachie praises Heisenberg for his razor sharp intellect for deriving the correct result alone in couple of days, without tables, calculator, his notes etc, being de facto in captivity, knowing nothing of his family." is puzzling. When I was an undergraduate physics major in the 1970's, I would have been expected to be able to do this calculation off the top of my head. The mathematical techniques used therein have been part of the standard literature since the 19th century. Notes, tables, calculator are not required, although the fission cross section is required to convert the analytical result into an actual critical mass. Heisenberg most certainly should have been able to do this calculation at the beginning of the German bomb program. The physicist Jeremy Bernstein suggested that, since Heisenberg got it wrong early on, the rigid, hierarchical nature of the German research system made it very difficult for others to correct the lapse. So they all dropped the subject.
@ukornel77
28 күн бұрын
@@paulkolodner2445 You are right, calculators, tables are not needed for the correct mathematical solution. But in the Farm Hall Heisenberg wanted to answer the question: how the Americans were able to build an air transportable bomb with a reported amount of fissile material of 4 kg. For this he needed cross section data, neutron multiplication data, that were measured by a different group within the German research program and the measurement had large uncertainty. About the rigidity of the German research system: I believe Bernstein got it wrong. There were other capable scientists in the program, and they were not prohibited from reconsidering the critical mass problem. They chose freely not to reconsider it because they were not motivated enough to build the bomb. They lacked the motivation because they didn't like the Nazis, and they wear not afraid of being bombed by American nuclear weapons. As soon they learned that they were wrong, Heisenberg got his motivation (curiosity) and provided the correct solution. I'm pretty sure that if they had known what progress the Americans (and even the Soviets!) had achieved, far ahead of them, not only Heisenberg, but his colleagues also would have repeated their calculations, doubling down their efforts to counter the Allied nuclear weapon(s) and they would have derived the right conclusion years before the Farm Hall lecture. One addition: trusting in Heisenberg's false calculation by his less prestigious colleagues is not a nature of the German research system, but might be a more general, cultural thing, a kind of basic German national characteristic preferring orderly collaboration over competition. There is a story about German pocket battleship Graf Spee got suck in the port of Montevideo. Her captain Lagendorff believed that he spotted a British aircraft carrier through his telescope, right in front of the port. Lagendorff actually saw a transport ship for the Ark Royal, there were no British carriers in several thousands of kilometers. Not a single officer of the ship questioned the captain's decision to destroy the ship.
@CaptainCalculus
8 ай бұрын
That's worth a coffee☕
@jkzero
8 ай бұрын
Thank you so much for your continuous support, I will make sure to enjoy a coffee while being grateful for the appreciation of strangers on the other side of the planet that find this content of interest. Thanks again!
@cewkins721
8 ай бұрын
What a great video! i truly want to thank you for going through the effort of laying out the math in the latex format you were talking about, it looks clean, the math is a bit higher than my level but your explanation makes total sense, i will see if i can try the questions you put in the end, your content is really enjoyable!
@jkzero
8 ай бұрын
I am glad you liked the video and thanks for appreciating the effort, writing that code was a lot of work. I hope you give the "assignments" a try and let me know if any help is needed; I am happy that others have also showed interest in attempting it
@DanielParraGómez-x2j
Ай бұрын
I love your video. It is very clear, simultaneously advanced and illustrative. But there is a lapsus calami when you wrote the sphaerical laplacian. You put 1/r2 inside braket, but it is r2. Thank you very much for your video. I repeat, I love it.
@jkzero
Ай бұрын
You are totally right, I messed up the r² term already at 10:10. Thanks so much for pointing this out and for going through the calculation, it is a good catch. Other viewers also pointed this out and I added an erratum in the description. Fortunately, it doesn't affect the calculation because it is correctly applied, this is just a typo on the video but not an error in the calculation; however, I do my best to avoid these typos but after watching everything many times some minor details slip through. Thanks again.
@Unique-Concepts
8 ай бұрын
Subscribed!Thank you for this video.Please do more videos on advanced mathematical modelling.
@jkzero
8 ай бұрын
thanks fro the sub, I am glad you found the content of interest. I am already working on the next video and more juicy calculations are coming. I want to balance the content with some historical context but always including some high-level calculation to complement the story, and more importantly, for viewers to follow along and reproduce themselves if desired. 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?
@Unique-Concepts
8 ай бұрын
@@jkzero Thanks for the reply, recently I was searching on the topic detonation wave hydrodynamics. I found that topic fascinating because of welch lab channel. Now KZitem recommended this video and absolutely love it...thanks again 👍🙏🙏👌👌👏👏😍
@jkzero
8 ай бұрын
@@Unique-Concepts thanks for sharing and great that the searching algorithm brought you here and thanks again for your support, welcome to the channel! I might not know much about the topic that you were searching for but you might find my seminar on blast waves of interest (link below). It is about a paper that I published in 2022 extending the result from Sedov-Taylor-von Neumann but written for undergraduate-level students of physics and engineering. It required solving hydrodynamic equations for properly describing an expanding blast wave and I include all the steps in the seminar, check it out and let me know if this helps kzitem.info/news/bejne/q6-Jv2iYpIlmqo4
@DrDeuteron
2 ай бұрын
small correction on language: The Laplacian operator does not depend on the coordinate system; however it's representation certainly does. Laplacian, and the physics its describes, don't care about our coordinate systems.
@jkzero
2 ай бұрын
Love this. I am pedant myself, and this is the kind the pedantic comment that I really enjoy. Yes, you are totally right, I misused the word dependence when I should have referred to representation. I appreciate the correction.
@DrDeuteron
2 ай бұрын
@@jkzero is it pedantic to say I wasn't being pedantic? No, I just hope one of your viewers makes the jump to _"coordinate free physics"_, which was a revelatory moment in my education, received directly from the Guru of relativity himself (Kip).
@jkzero
2 ай бұрын
@@DrDeuteron I did my PhD on the study of Lorentz invariance, I recall the exact moment when the "Nature doesn't care about coordinates" really clicked in my head, I was reading a paper by my supervisor in a bus on my way to Walmart, I remember that moment vividly.
@DrDeuteron
2 ай бұрын
@@jkzero oh good, because I recently posted something to the effect: you don't understand GR until you accept that the Ptolemaic model of the solar system is just as "right" as the Copernican version, but I get written off as a crackpot before explaining Coriolis and centrifugal, like "gee" , are all a result of non-geodesic coordinates. Stand by for a thought problem...
@DrDeuteron
2 ай бұрын
@@jkzero so the push back is that "rotation is real", hence the standard fictitious forces. Here's the question: A mass m=1 is "at rest" at a radius "R"--what's the Coriolis/Centrifugal forces on it? Every one says 0/0, ofc. But that's frame dependent. In a frame rotating at w, you get a centrifugal: w^2R, and here's the kicker, for Corilois: 2v X w = -2wRw = -2w^2R, so the total is a apparent inward w^2R keeping the mass in orbit in the rotating frame--even though there are no forces at all.
@berdigylychrejepbayev7503
6 ай бұрын
to be honest, i liked the way you present the video with formulas and graphs but it is very hard to grasp and track. at least i as a non-physicist had a hard time to understand and could not finish the video. but i liked your type and really love to see chemistry version of you (or not this much of (unheard) definition and formulas). but I know that some people really like this kind of videos so dont worry about my comment.
@jkzero
6 ай бұрын
thanks for your honest comment, one thing missing at the beginning is that this video is the response to the request of the step-by-step calculation of the critical mass in a previous video. If you want a more detailed description of the story behind this video please check "Critical Mass: when the atomic bomb got real" (kzitem.info/news/bejne/rZqrrmtsamWCi6w). The present video by its own is pure mathematical physics but the other video provides the context and historical relevance of this calculation. I hope you like that video better.
@Martini_GP
2 ай бұрын
Thanks!
@jkzero
2 ай бұрын
Thanks so much for your generous support!
@pappaflammyboi5799
8 ай бұрын
What would be the equations for critical mass if you had a perfectly spherical neutron reflector and a neutron half-life of 11 minutes? Thanks again for the video. I loved the math derivation.
@MrFib112358
8 ай бұрын
Hi @jkzero, here is my solution to the homework problem of the cube of uranium: I used the Laplacian operator in Cartesian coordinates, solved the equations for all three axes, and found the "critical side" a_c=19 cm, which gives me a critical mass of 538 kg. Is this correct? How can using a cube instead of a sphere increase the critical mass by a factor 4?
@jkzero
8 ай бұрын
first of all: congrats on accepting the challenge, you got the critical side of the uranium cube correct but the critical mass seems to be off. Could you share how you got the mass from the size of the "critical cube"?
@giovannimariatanda9251
8 ай бұрын
Chiarissimo dottor Jorge, ho notato, con grande sorpresa e ammirazione, che ha vergato i suoi appunti in data 25 dicembre. La stimo ancor più per questo: chi può lavorare il giorno di Natale? Solo un appassionato, un entusiasta (etimo: en + theos = un dio che ti parla dentro) può fare una cosa del genere, perciò, c'è ne fosse bisogno, rinnovo e attesto la mia perspicua ammirazione per la sua persona e il suo lavoro. Se lei permette, appena avrò un poco di tempo, riporterò su un testo la sua disanima corredandola di ulteriori semplificazioni e ampliamenti per renderla ancor più comprensibile per i meno competenti. E naturalmente citerò la fonte, cioè: lei. Grazie. Forte nello spirito, tenero nel cuore. G.
@krwada
7 ай бұрын
A very nice video. You explain very clearly the basic physics concepts of a chain reaction. Laplacian, Ficks diffusion law, Continuity, conservation of Mass. All these concepts are within reach of any undergraduate engineering student. Many of these concepts were taught to me while as an undergrad in Chemical Engineering. Very well done!
@jkzero
7 ай бұрын
Thanks you, I am glad you liked the video. You have a good point, there are many concepts packed but I did my best make the calculation flow. I warned the general viewer about the math because this video is in fact a response to the request from viewers after I shared the historical aspects of the calculation of the critical mass in a video some months back (kzitem.info/news/bejne/rZqrrmtsamWCi6w). Please check the other videos, in my latest I began a series on quantum mechanics that with your background you might enjoy and also be surprised (many of the physicists viewers were surprised), check it out here kzitem.info/news/bejne/yI6bp6SVpaubbKg
@krwada
7 ай бұрын
@@jkzero I will definitely check out the video on quantum mechanics. There are also other very good KZitem channels which very nicely explain complex topics such as what you do. For example, a couple of days ago, the Veritasium channel showed a very nice explanation of various concepts in solid state physics, including: 1. band gap 2. the various bands, (conduction and valence) 3. A very nice animation showing the Poisson distribution and how it creates the PN junction discontinuity. Lots of good stuff. kzitem.info/news/bejne/onxuymtopnNlZII I am now a subscriber to your very fine channel!
@jkzero
7 ай бұрын
Yes, Veritasium offers excellent content. Thanks for watching and the positive feedback. Also thanks for supporting the channel with your subscription and welcome to the channel!
@giovannimariatanda9251
8 ай бұрын
Molto interessante e ben fatto. Complimenti vivissimi dottor Jorge.
@jkzero
8 ай бұрын
Grazie mille! Thanks for watching and make sure to check the other videos
@giovannimariatanda9251
8 ай бұрын
Farollo sicuramente. Grazie.
@davidrandell2224
8 ай бұрын
A proton is a collection of 1836 expanding electrons and add a bouncing expanding electron makes a hydrogen atom. “G” calculated from first principles- the hydrogen atom- in 2002. No energy, charge, photons, waves, spin, fields, potential, quantum,space, time, space-time etc. All Standard Theory/Model was replaced by Expansion Theory in 2002. “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics.
@jperez7893
8 ай бұрын
this is a fantastic video. the math is beautiful. no doubt that this is also the same equations used for the generation of nuclear power for thorium reactors. so for nuclear reactors, nu prime is not allowed to reach zero but always kept negative. amazing work
@jkzero
8 ай бұрын
thanks, I am glad you liked the video. Honestly, I am not an expert on reactors, I just made one video showing that they cannot explode like a bomb but I have a good friend who is an expert on thorium reactors, if you have questions on this topic make sure to write them in this post, I will try to have him in the future kzitem.infoUgkxkfK_xvCYFftK_Wsw6wh0L6ECtL87-Dcv
@JazzBerri
8 ай бұрын
Didn’t expect to find such an interesting video on youtube!
@jkzero
8 ай бұрын
I am glad you liked it, 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?
@JazzBerri
8 ай бұрын
@@jkzeroyour video appeared on my feed randomly yeah, wasn't looking for anything related. I guess that being a new chanel plus the "oppenheimer" related theme pushed your videos to many people. I hope more people are able to watch your videos!
@jkzero
8 ай бұрын
@@JazzBerri thanks fro sharing, I am glad the algorithm brought you here. Make sure to check the other videos, there is one dedicated to the real meaning of the famous words of Oppenheimer0 Welcome to the channel, I hope to have back for more videos.
@JazzBerri
8 ай бұрын
@@jkzero yeah thanks! I liked your chanel so im staying hahah
@MayankSharma-mh5bt
2 ай бұрын
I was using formula shown by you to calculate laplacian and keep getting wrong answer and the suddenly realises it's wrong (later verified with wiki page shown by u just some seconds ago) and then got it finally. BTW amazing video keep doing this. serious physics stuff of this kind is much needed.
@jkzero
2 ай бұрын
you are totally right, I messed up the r² term already at 10:10. Thanks so much for pointing this out and for going through the calculation, it is a good catch. Other viewers also pointed this out and I added an erratum in the description. Fortunately, it doesn't affect the calculation because it is correctly applied, this is just a typo on the video but not an error in the calculation; however, I do my best to avoid these typos but after watching everything many times some minor details slip through. Thanks again.
@MayankSharma-mh5bt
2 ай бұрын
@@jkzero sorry i didn't notice😅 I really enjoyed this nuclear bomb series and is enjoying the quantum series. eagerly waiting for next episode🤞
@jkzero
2 ай бұрын
@@MayankSharma-mh5bt thanks for following along
@FPSIreland2
8 ай бұрын
Thanks. I'll make sure to employ this new information... wisely...
@enzolamande5963
8 ай бұрын
Great Vidéo! In cylindrical coordinates we are using the Bessel Function right?
@jkzero
8 ай бұрын
Yes, the cylindrical case is a bit more complicated than the spherical and cubic core, and yeah, if you encounter a Bessel equation then you are on the right track
@stoneaa756
4 ай бұрын
very very clear explanation! thank you
@jkzero
4 ай бұрын
Thanks, I hope you also check the other videos.
@natanfreire8692
8 ай бұрын
I love this channel
@jkzero
8 ай бұрын
Thanks for watching; you can actively help the channel by liking, subscribing, and sharing. This type of support is highly appreciated so I can continue making videos.
@jubisklaisaodograu6605
8 ай бұрын
In on The FBI watchlist with this one
@jkzero
8 ай бұрын
that ship has sailed, since I have access to the internet that I made it to the FBI list with my searches :D
@scollyer.tuition
8 ай бұрын
Speaking in my capacity as an Evil Genius, I found this video to be a wonderfully clear exposition of the topic. I'm sure that I can now achieve criticality with my "physics package" and then I will be in a position to hold the world to ransom for ... One Million Dollars!!!!
@jeremyvirin6532
8 ай бұрын
Incredible this video😍
@sturrum5250
8 ай бұрын
First of all, excellent video. It's refreshing to see a subject that is often *talked* about get the mathematical treatment. I was wondering if there's somewhere I could find a derivation of your expression for the diffusion constant D = 1/3*lambda_f*. Most explanations I've seen are very handwave-y and not particularly rigorous.
@jkzero
8 ай бұрын
Thanks, I am glad you found the content of interest. I agree with you, most derivation of the diffusion equation are quite fishy. Regarding the explicit form of the diffusion constant the only legit derivation that I have found is in the appendix of the book The Physics of the Manhattan Project by B. Cameron Reed. It is a long a quite tedious calculation involving several angular integrations.
@sturrum5250
8 ай бұрын
@@jkzero Alright, thanks a whole bunch for the reference.
@brahimhihi56
8 ай бұрын
Thanks a lot!!
@s5101953
8 ай бұрын
In the remarkable story two flaws are negating each others. First, Diffusion is over estimated for fast neutrons (of bomb core) and for thermal ones as well. Second, the source neutron term due to fission must be decreased for capturing neutrons. But at criticality threshold these mistakes happly are zeroesed. Good luck!
@jkzero
8 ай бұрын
it is interesting how the simple calculation in this video was enough despite the many limitations of the formalism. The most remarkable is the fact that two non-negligible effects have been ignored: 1. neutrons can also been captured by U235 without fissioning, this was completed ignored; and 2. the elastic-scattering cross section is not isotropic so care must be taken when calculating the corresponding cross-section. Nonetheless, when these two effects are incorporated they happen to cancel each other out. Just a lucky coincidence.
@lucacastronuovo9789
8 ай бұрын
Being sigma_t greater then sigma_f (min 5:31), how is it possible that lambda_t is greater than lambda_f (min 15:58)?
@jkzero
8 ай бұрын
oh no... you are totally right, I messed up the subscripts at 15:58, they should be reversed, it should say: lambda_f = 16.89 cm and lambda_t = 3.596 cm. I will add an errata in the description. Thanks so much for pointing this out, it is a good catch. Fortunately, it doesn't affect most of the elementary calculation because the two mean-free paths are multiplied but it does make as difference in the 'advanced' solution, where lambda_t appears isolated. Thanks again. I do my best to avoid these typos but after watching everything many times some minor details slip through. Thanks also for asking in such a nice way contrary to patronizing mode of writing comments favored on the internet.
@lucacastronuovo9789
8 ай бұрын
@@jkzero You're welcome! Anyway, thank you for the amazing video and the explanation!
@lukesiemens5421
7 ай бұрын
I think that there is a small error at 13:35. At this point in the video it is stated that the third boundary condition is that no neutrons escape the sphere and this is done by requiring that N(r=R, t)=0. Then there is a quick disclaimer that this condition is not completely true and the more advanced solution is briefly mentioned. I may just be misunderstanding it, but I understood this to mean that the condition N(r=R, t)=0 does imply that no neutrons will escape the core however this boundary condition is not practical or optimal. Using the solution that satisfies the condition N(r=R, t)=0, I calculated the total neutron flux at the boundary from the neutron density and found that it is not zero but proportional to R*N(r=0, t). I am not criticizing the use of the boundary condition N(r=R, t)=0, but I think it is incorrect to say that this condition is equivalent to requiring that no neutrons escape the core.
@jkzero
7 ай бұрын
Thanks for your exposition. Honestly, the "elementary" boundary condition is quite artificial, in fact, it is only used because it allows an analytical solution for R_c in terms of the relevant parameters ( u, cross-sections, density, etc.), it gives a glimpse on what is driving R_c and the critical mass. However, this is the only reason this condition is introduced, mostly for academic purposes. The "advanced" boundary condition is what has to be used in a practical calculation.
@dailyqwikbytes
2 ай бұрын
"1 joke". Clever.
@cosmicnomad8575
6 ай бұрын
Amazing video and amazing channel!
@jkzero
6 ай бұрын
Thanks for the visit and the positive feedback
@playgirl7305
8 ай бұрын
Jesus christ!! Does the NSA not monitor everyone who watched these kind of videos . To them, sorry guys I stumbled on it by mistake.
@jkzero
8 ай бұрын
many people have seriously asked this, all the content on this video can be freely found on the internet, undergraduate-physics textbooks, and scientific publications. Fortunately, I don't have access to any classified information :)
@rustym.shackelford5546
4 ай бұрын
Okay, I am a little stumped at the laplacian part. So I already specifically got the form down pretty well: (nabla)^(2)*F + (kappa)^(2)*F = 0 but now how exactly do I plug in the "auxiliary function" to this figure in order to get the positional function. At least just give me a hint or point me in a general direction that I could learn how to do this (note: I am familiar with Calculus, however, I am not entirely versed in doing these equations on my own).
@jkzero
3 ай бұрын
Replace u(r) = r*f(f) in the Laplacian ∇²f= (1/r²)*d/dr(r² df/dr), expand all the terms, simplify what can be simplified, and you will get now get the harmonic-motion equation for u(r). Please note that there is a typo on the video: at 10:10 the Laplacian of f should say: ∇²f= (1/r²)*d/dr(r² df/dr) (not 1/r² in the derivative bracket), this is a typo and not an error in the calculation. I hope this helps. If not just let me know.
@rustym.shackelford5546
3 ай бұрын
@@jkzero Major thanks.
@Sokol_
8 ай бұрын
Thank you, i need it.
@ThePeterDislikeShow
2 ай бұрын
So, because bismuth-209 is technically radioactive it has a critical mass too. Can you calculate it? It would be nice to know even if there isn't nearly enough bismuth in the entire universe to create it.
@jkzero
2 ай бұрын
Not really, you are confusing radioactive with fissile, they are very different properties. If any radioactive material could be made to undergo a nuclear chain reactions we would be making bombs with bananas (from their radioactive potassium content). Instead only a few isotopes like U-235 and Pu-239 can be used because they are fissile.
@alexus267
2 ай бұрын
What was conceptually wrong with Heisenberg's initial "random walk" estimate that you mentioned in the previous video?
@jkzero
2 ай бұрын
Using the random walk, Heisenberg "forced" a single neutron to fission every uranium nuclei, this is the key mistake: one neutron fissions one uranium nuclei, then moves until it encounters another nuclei and produces a second fission, and so on. In a real chain reaction, the neutron density grows exponentially but all the new neutrons also produce fission, this makes the reaction much faster and there is no need of a single neutron doing all the work. These new neutrons diffuse in the uranium while fissioning. The original neutron does not need to travel far, it can even be absorbed, that's irrelevant, there are so many new neutrons diffusing in the material fissioning it, that in the end the chain reaction is much more efficient than assuming a simple random walk.
@JS-to2ve
Ай бұрын
The geometry being so important makes me wonder for which geometry of the mass the critical mass is minimized. That sounds like a nasty functional analysis problem! I'm guessing it's a sphere because of the minimal surface...
@jkzero
Ай бұрын
this is a great question and in fact Manhattan-Project scientists asked this too in other to minimize the amount of fissile material. As you would expect, the sphere is the optimal shape. It can be shown that the critical mass is inversely proportional to the "sphericity" of the nuclear core.
@JS-to2ve
Ай бұрын
@@jkzero Thank you! I'm not surprised the Manhattan Project folks asked and answered the question - they were a smart bunch of people, to put it mildly... The reason I asked is that I've seen references to more complicated shapes being used in nuclear weapons - perhaps to focus the neutron flux?
@jkzero
Ай бұрын
@@JS-to2ve early nuclear weapons were mostly implosion bombs like the Gadget and Fat Man. The later transition to thermonuclear weapons led to a zoo of designs, geometries, and new materials; this is justified because fusion reactions rely mostly on cleverly focusing X- and gamma-rays. I am pretty ignorant of this phase, my fascination was always the physics of the early weapons.
@cyrilguillouard1266
8 ай бұрын
Beautiful video on a nice subject❤
@jkzero
8 ай бұрын
Glad you think so! 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?
@cyrilguillouard1266
8 ай бұрын
@@jkzero ah the mighty algorithm
@jkzero
8 ай бұрын
@@cyrilguillouard1266 Thanks for sharing and I am glad the algorithm is working, I hope you find the other videos of interest too and welcome to the channel
@Oliveir51
8 ай бұрын
This is why neutron cross section value is so important. Was measured in Argonne or was it Fermi lab ?
@PalashTiwari-d3g
8 ай бұрын
at 15:08 the only solution won't be pie but 0,pie,2pie,3pie ...npie so that if the kappa*R = 0 => kappa=0
@jkzero
8 ай бұрын
You are right: the general solution is kappa*R=n*pi; however, the higher "harmonics" will only make the bomb core bigger, we are searching for the minimum radius. The solution kappa*R=0 is useless because it requires kappa=0, which is mathematically correct but physically useless leading to N(r,t)=0, which of course solves the equation but it provides no information. Also, a solution for n>1 can lead to a negative density, which is also a non-physical solution. Mathematically, your point is 100% correct; however, here is when physics constrains the final solution, just like setting B=0 to remove the non-physical cos(kappa*r) term.
@PalashTiwari-d3g
8 ай бұрын
@@jkzero got it thanks for your response. I will try to go over all the cases with pen and paper to be more clear :)
@jkzero
8 ай бұрын
@@PalashTiwari-d3g good luck and please get back letting me know what you get or if you encounter any road-block
@7177YT
8 ай бұрын
Very cool! Thank you!
@jkzero
8 ай бұрын
Thanks for the endorsement; I wish I could get to wider audiences but the KZitem algorithm is driven by engagement so you can actively help the channel by liking, subscribing, and sharing. This type of support is highly appreciated so I can continue making videos.
@David-p7z9n
8 ай бұрын
Oppenheimer, Teller and others did these equations on chalk boards by hand…
@fightingforcatalonia
8 ай бұрын
donde trabajeste con neutrones. Central nuclear? que gran trabajo
@jkzero
8 ай бұрын
soy físico teórico, todo esto lo aprendí por mi cuenta por gusto, simplemente me fascina el tema y creé este canal porque pensé que era hora de compartir la pasión, afortunadamente la recepción ha sido fenomenal lo que me anima a seguir creando este tipo de videos. Cuéntame que te trajo por acá, ¿te encontró el algoritmo?
@fightingforcatalonia
8 ай бұрын
Algo parecido al algoritmo. eres el 3blue1brown de la fisica. Yo soy físico también. Un saludo@@jkzero
@jkzero
8 ай бұрын
"the mighty algorithm", me alegro que te haya traído por acá. ¿En tipo de física trabajas? ¿Eres estudiante, postdoc, académico o estás en la industria?
@peppescala4113
8 ай бұрын
How is the boundary condition expression for the advanced solution derived (20:59)? I'd really be thrilled to read the derivation, can you provide something? Is it something like Neumann vs Dirichlet boundary condition? Thank you for all of your work!
@jkzero
8 ай бұрын
Thanks fro the feedback, I am so excited that his video got so many people interested. The elementary boundary condition (BC) is a Dirichlet BC but it is quite artificial, the correct way of doing the calculation is by using a Neumann BC. I am glad someone got hooked on that detail, it is a lengthy derivation presented for the first time by Robert Serber, one of Oppenheimer's protegés, on his annotated version of The Los Alamos Primer. He only did it in Cartesian coordinates but it can be generalized to spherical coordinates chooser.crossref.org/?doi=10.2307%2Fj.ctvw1d5pf.6
@andresfeliperamirezgaviria8976
8 ай бұрын
Excellent.
@bryanh1944FBH
8 ай бұрын
Why does Wikipedia, and other sources, list the critical mass of a U-235 sphere as 52 kg?
@jkzero
8 ай бұрын
there are several possibilities for the discrepancy, without knowing the source of the Wikipedia article is hard to track the reason. My rule of thumb is if the source is an official report from Los Alamos National Lab then it is probably more reliable. They use advanced computer codes to calculate these quantities. I could not find the source of the 52 kg for U235 reported on Wikipedia.
@Norsilca
2 ай бұрын
I'd love a little more on the theoretical basis (assumptions) that underlies these equations. Why is the diffusion model different from the random walk that Heisenberg assumed? I thought diffusion occurs from many particles doing a random walk.
@jkzero
2 ай бұрын
Using the random walk, Heisenberg "forced" a single neutron to fission every uranium nuclei, this is the key mistake: one neutron fissions one uranium nuclei, then moves until it encounters another nuclei and produces a second fission, and so on. In a real chain reaction, the neutron density grows exponentially but all the new neutrons also produce fission, this makes the reaction much faster and there is no need of a single neutron doing all the work. These new neutrons diffuse in the uranium while fissioning. The original neutron does not need to travel far, it can even be absorbed, that's irrelevant, there are so many new neutrons diffusing in the material fissioning it, that in the end the chain reaction is much more efficient than assuming a simple random walk.
@Norsilca
2 ай бұрын
@@jkzero Thank you so much for the explanation! Although tbh I'm still a little confused. It sounds like you're saying he modeled a single neutron having to meet and fission every single uranium nucleus. But that wouldn't ever work, right? I thought the exponential chain reaction is what's necessary for an explosion.
@jkzero
2 ай бұрын
@@Norsilca you are right, this shows you how incorrect Heisenberg's conceptualization of the problem was
@Norsilca
2 ай бұрын
@@jkzero That's confounding. Everyone knew the exponential multiplication was the key to the chain reaction. Why would he reduce the problem to something he knew was wildly unrealistic?
@tatytatytaty95
8 ай бұрын
Great Video! In the continuity equation dN/dt describes the change in neutron density due to neutron absorption and emission, while del J describes the change in neutron density due to neutrons diffusing away. So why is the entire expression (dN/dt+ del J) equal to the neutron sink and source term (S+ + S-)? Shouldn't there be an additional term on the right side, accounting for the neutrons being lost due to their motion out of the volume that is being considered?
@jkzero
8 ай бұрын
the term ∂N/∂t describes the change on neutron density in a infinitesimal volume with time, that is all, the reasons are given by other terms in the equation. The term ∇·J describes the differential number of neutrons moving in and out of the infinitesimal volume (they can move in and out by any reason, in our case by diffusion when we impose Fick's law). If the number of particles were fixed then the RHS of the equation would be zero, like in the case of electric currents or fluid motion, but here we need to tell the equation that inside the infinitesimal volume the neutron number is not conserved and in fact neutrons are created and destroyed, this is why the two terms on the RHS are needed.
@kwzieleniewski
8 ай бұрын
This equation is local, that is, it describes what happens in an infinitesimally small volume around a particular point (of coordinates x). Sphere boundary is far away.
@jkzero
8 ай бұрын
@@kwzieleniewski not sure if you are trying to make a particular point or asking for something in particular
@dobotube
6 ай бұрын
Amazing channel and videos. A question: I'm very puzzled by the various prompt critical excursions with the demon core and friends that occured in history. I understand nuclear reactors rely on delayed neutrons to keep a reaction in balance. I understand a prompt supercritical state will have a neutron population grow extremely fast. I understand an unconstrained core will tear itself apart before full combustion. What I don't understand is how can a core balance in prompt critical state (blue flash and all) and neither fizzle nor explode. I've been given explanations like Doppler broadening and thermal expansions which certainly could fit the bill but, without knowing how quickly temperature changes vs how quickly the neutron population grows, I find unconvincing. Is there a way to do back of the envelope calculations to think about these prompt critical balanced reactions?
@jkzero
6 ай бұрын
my most sincere and honest answer is: I do not know. I am pretty sure a nuclear engineer would know the answer, they study these reactions in non-ideal scenarios in detail. As a physicist myself, we mostly do calculations in ideal conditions, prove the feasibility based on the physics, conservation laws, etc. and then leave the dirty (but crucial) dirty work to engineers, they really make things happen.
@kirkhamandy
8 ай бұрын
Ok, so my first comment on this video was a joke. But this second one is a bit more serious. I had a "light bulb" moment when you described this "simple" solution where no neutrons escape from the sphere. Is this what Louis Slotin was effectively doing in the Los Alamos experiment _Tickling the Dragons Tail_ ?
@kirkhamandy
8 ай бұрын
oh... if I'd watched to the very end before asking I would have seen the answer (about the neutron reflectors). However, I'd still like to know more about it if anyone can be bothered to add more information.
@christopherleubner6633
8 ай бұрын
Yup you can do this with a thick chunk of beryllium surrounded by heavy carbide reflector. The beryllium mostly reflects the neutrons but if it absorbs a neutron you get two. This helps increase the quality factor of the critical mass. Typically it is used so less fisile material is required for a chain reaction. A regular pu 239 ball would be about 7kg for a critical mass, but surround it by a bit of beryllium then it decreases to about 2kg, the cake taker is with a water moderator reflector. Only about 0.1kg is needed to start a chain reaction 😮
@sofa1977
7 ай бұрын
@@christopherleubner6633 so this is how we can calculate the minimum yield/size of the a-bomb? could it be significantly less than 1kt - say 10t tnt?
@christopherleubner6633
7 ай бұрын
@sofa1977 a 10t device would still require a minimum amount to get the reaction going. The beryllium shell would have to be separated by a certain distance from the Pu core. The bare minimum is about 48t though based on the Davy Crockett design and kin.
@sofa1977
7 ай бұрын
@@christopherleubner6633i got around 200t thinkin this way - fatman was 21kt and around 30% yield from tamper, so 14kt from 6.4kg core, then 0.1kg would give 64 time less, which is 219t. but fatman was 2.5 compression factor, maybe u can go a lil more tighter : )
@hypercomms2001
3 ай бұрын
I am interested in taking up the challenge and following through the procedure to attempt to calculate the critical mass for a cylinder. I do have a background in electrical engineering, and as part of that I studied quantum mechanics, and nuclear physics, and did extensive training in calculus.... However I am more interested in trying to calculate the critical mass that relates to a nuclear reactor instead of a nuclear weapon, would you be able to do a video on that or point to where one could find information how to make such a calculation? I am thinking something like calculating the critical mass for something like a Chicago pile, CP-1... minus the bottle of Chianti Bertolli wine... and Enrico fermi!
@jkzero
3 ай бұрын
I have the suspicion that the procedure followed here might serve as a guide for solving the neutron diffusion equation, but the controlled conditions in a reaction can be quite different. I am not a nuclear engineer but maybe the lectures on the MIT course Introduction to Nuclear Engineering and Ionizing Radiation might be more useful (lectures are on KZitem).
@hypercomms2001
3 ай бұрын
@@jkzero Thank you Dr Diaz, I do appreciate your suggestion, and I have searched for the course, and bookmarked it, as it is something that I will attempt at the end of the year, as it will be an interesting and cool challenge, as I am currently completing a Masters of IT, and wont have the bandwidth until then.
@suncrafterspielt9479
8 ай бұрын
very nice video thanks
@jkzero
8 ай бұрын
Thanks for watching; you can actively help the channel by liking, subscribing, and sharing. This type of support is highly appreciated so I can continue making videos.
@wdobni
8 ай бұрын
i would like to know the square root of the probability density of iran developing a deliverable nuclear bomb within the next 5 years and the laplacian of that event triggering a full nuclear retaliatory response.....with an estimate of total casualties instantly, at 6 hours, 24 hours, 1 week, 3 months, 1 year, and 5 years.
@easondu9236
8 ай бұрын
Is this made on manim? Very nice animation
@jkzero
8 ай бұрын
yes, I use Manim in all my videos. I know that Grant recommends to not use Manim for just showing equations but I can't help it, I like how LaTeX formulas are shown too much. Thanks for stopping by and make sure to check the other videos.
@vibrolax
8 ай бұрын
A correct mathematical model is necessary, but certainly not sufficient for making a bomb. Determining all the physical constants (capture cross sections for all relevant materials), etc. Was a huge job in experimental physics. Then we can figure out how to obtain sufficient quantities of fissile materials. Can't order it online, AFAIK.
@jkzero
8 ай бұрын
the information in the video it is of little use to someone attempting to build a nuclear weapon, the reports including these calculations were declassified and publicly available since 1965
@t850
8 ай бұрын
...excellent video as always. One question immedietly pops up to my mind. If criticality condition equals exactly 0 does this theoretically mean that the fuel won't explode but "burn" as a self sustaining nuclear reactor until whole mass is "consumed"? On th side note by knowing critical mass we can now calculate minimal theoretical yield of this device. Since critical mass is about 50 kg and energy denistiy of uranium/plutonium is 17 kt/kg minimal theoretical yield would be around 850 kt of TNT. Realistic result is unfortunately much lower as the Trinity test (similar device design) produced yiel of only 25 kt. Mass/energy convertion factor was much lower since majority of the mass was blown up (unused). Btw, I always wondered what is "cost/benefit" analysis of uranium enrichment in terms of energy invested and energy gained. Is there any information as to how much energy was used to produce first atom bomb since enriching facility is generally massive. So massive in fact that even with this secret known, one needs a facility the size of a small town to produce a bomb. It would be interesting to know if one needs to invest more energy to enrich the uranium than the bomb would produce...:)
@kwzieleniewski
8 ай бұрын
IIRC fuel for nuclear power plants needed as much as 4% of energy released for the enrichment. There are equations on Wikipedia saying how much more energy it takes to enrich to 90% than to just 4%. However, this also depend on how you enrich. Zippe type centrifuges are far more efficient than gasous diffusion.
@t850
8 ай бұрын
@@kwzieleniewski ...you mean to say that 4% of (thermal) energy released from the nuclear fuel is needed to enrich that exact ammount of uranium ore to be graded as nuclear fuel? Thing is that 4% (3-5%) is basically average ammount of the enrichemnt that ore needs to be processed to to be classified as nuclear fuel so I don't want to be confused with this number similarity. Beside the obvious difference in enrichemnt methods there is probably some efficiency drop as the enrichment goes to the higher levels because extracting the remaining mass is that much harder since the saturation of U235 is pretty high and mass difference between U235 and U238 almost insignificant...:/
@AlbertCamus-r6i
8 ай бұрын
Have a question: How would you input the N(r , t) function into a Graphing Calculator alongside the Criticality Factor equation?
@jkzero
8 ай бұрын
I have not touched a graphing calculator in decades (when I spent all my savings in a TI-92+ and barely used it). I would expect that you can define custom functions but I guess the easiest way would be explicitly replacing nu' (criticality factor) in the definition of g(t). Note that you will need to define a radius, say 30 cm, that is bigger than the critical value; otherwise, your solution will be constant (because nu'=0 for R=R_c)
@AlbertCamus-r6i
8 ай бұрын
Can you simplify what you mean a bit? Still kind of new to this. @jkzero
@jkzero
8 ай бұрын
@@AlbertCamus-r6i I honestly don't know how to code this in a graphing calculator but I have created a Python code to generate the plots shown in the video you can find in this link github.com/jsdiazpo/JK0/blob/main/11-Neutron-Diffusion-Eq.ipynb Please let me know if this helps
@claudiomenchinelli7465
3 ай бұрын
DIFFICULTY LEVEL: TISE FOR THE HYDROGEN ATOM
@kondojunagaraju8899
8 ай бұрын
What is mean conceptual understanding? Please tell me example.
@jkzero
8 ай бұрын
this video is the technical response to an early video that I published titled "Critical Mass: when the atomic bomb got real." If you want the conceptual and historical account for what it is explained in the present video you check it out here kzitem.info/news/bejne/rZqrrmtsamWCi6w
@koenth2359
7 ай бұрын
Where in the equation is neutron absorption (w/o fission)?
@jkzero
7 ай бұрын
this is a fantastic question; I recall many years ago when I calculated the critical mass for the first time, I was happy with the result and then had your very same question: I said "wait, where is the contribution of neutron capture to the transport mean free path?" It took me years to find the answer, which I am happy to share: you are right, the calculation that I presented in the video is missing one term, the calculation of the transport mean free path should include the contribution from the neutron capture cross-section. However, the elastic scattering cross-section has also a missing piece in the calculation shown that arises due to the asymmetry of elastic scattering, this is a very subtle and minute detail, but long story short: the missing part from the elastic scattering cross-section coincidentally cancels the missing part from the neutron capture cross-section, leaving the transport mean free path unchanged, resulting in that the result shown in the video is perfectly valid. I didn't want to go into this detail in the video but I was secretly hoping that someone would ask for it, thanks for a great question.
@koenth2359
7 ай бұрын
@@jkzero Thanks so much for your elaborate answer!
@jkzero
7 ай бұрын
@@koenth2359 happy to; thanks to you for watching and for questioning this minor but not less relevant point
@BorisNVM
8 ай бұрын
really cool video
@jkzero
8 ай бұрын
thanks for watching, make sure to check the full list of more videos on this topic
@Bob-yl9pm
7 ай бұрын
Where's your beryllium Neutron reflector?
@jkzero
7 ай бұрын
as mentioned at 23:12, no reflectors have been used because this is the calculation of the critical mass of a bare sphere
@Bob-yl9pm
7 ай бұрын
Yes! I commented too soon@@jkzero
@jmmahony
3 ай бұрын
Warning: typo in laplacian of f at 10:10.
@jkzero
3 ай бұрын
You are totally right, I messed up the r² term. Thanks so much for pointing this out, it is a good catch. Fortunately, it doesn't affect the calculation because it is correctly applied, this is just a typo on the video but not an error in the calculation. Others have also notified it and I have included an erratum in the video description. I do my best to avoid these typos but after watching everything many times some minor details slip through. Thanks again
@Tadesan
8 ай бұрын
Separation of bariables
@Revyy729
8 ай бұрын
Pheonomenal content. Subscribed! as a side note, I am a highschool student aiming to pursue a career in theoretical physics. How do you suggest I proceed with that? All and any help would be appreciated
@okkam7078
8 ай бұрын
Go to college for physics, pursue a Masters (i.e. get good grades in undergrad), maybe pursue a PhD (you’ll figure that out when you get closer to it)
@Revyy729
8 ай бұрын
Thank you!@@okkam7078
@logo2462
8 ай бұрын
Top tier math video
@jkzero
8 ай бұрын
thanks! 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?
@logo2462
8 ай бұрын
@@jkzero the algorithm recommended it. I think it knows I like math education videos and the video did well with other viewers. I’d also guess that a large proportion of viewers stuck with the video to the end, making it more likely to be recommended.
@jkzero
8 ай бұрын
@@logo2462 thanks for sharing, great to learn that the algorithm is recommending my video, I got a successful video in the summer and then "the algorithm" moved to other topics because the number of viewers plummeted; so great that this video attracted new viewers. Welcome to the channel and make sure to check the other videos too.
@AlbertCamus-r6i
8 ай бұрын
For the Pu239 density in g/cm^(3) - isn't it greater than the figure you provide?
@jkzero
8 ай бұрын
you are right that the standard density of plutonium is closer to 20 g/cm^3; however, depending on temperature plutonium exhibits different crystalline phases. The relevant phase used for weapons is the so-called “delta” phase and that is the density that I have provided.
@AlbertCamus-r6i
8 ай бұрын
@jkzero Huh. Thanks for that - so basically the standard density is not in that phase at all. Interesting.
@jkzero
8 ай бұрын
@@AlbertCamus-r6i exactly; I mean you can have plutonium metal in other phases too but for the bomb they used the delta phase due to stability and for machining purposes
@sn9160
8 ай бұрын
Nice. But i dont know If the critical mass Drops because the leakage or because the Neutron density can BE higher at the surface and this Leading to higer density towards the midpoint, because there is no,on purpose, build in Gradient from the Center to the surface
@jkzero
8 ай бұрын
I agree that this seems counterintuitive, I had the same feeling. One hand-wavy way to see why the critical mass gets reduced by allowing neutrons to escape is the following: plot the function sin(pi*x)/x between 0 and 1 (this is x=r/R); in the elementary solution we set N=0 at the surface (x=1), now, if we allow N>0 to define our critical surface (or radius), then we can "move the boundary" closer to x=0, this makes the necessary sphere smaller.
@sn9160
8 ай бұрын
@@jkzero yes because the Gradient of Neutron density has Not to be steep as it has to, when the critical surface is defined zero
@thespiciestmeatball
8 ай бұрын
Great video! I was surprised the derivation of the neutron diffusion equation didn’t require much (if any) quantum mechanics. I imagined physics at the atomic level required qm for an accurate description
@jkzero
8 ай бұрын
Thanks, I am glad you liked the video. You make an important observation, yes, the diffusion equation doesn't explicitly involve any quantum mechanics (QM) but it is the case even in QM: as you probably know, quantum probability is conserved in QM, if you replace neutron density by probability density you will find that it satisfies the continuity equation shown at the beginning (without the two terms on the right-hand side). In that case the QM effects are hidden in the fact that the probability density is given by the complex-squared of the wave function, which in turn satisfies the Schrödinger equation. So where is QM in the neutron diffusion equation? I would say that in the cross-sections (which have to be calculated using QM or experimentally measured, in which case all QM effects are already weighted in) and in the neutron speed (notice that only the average neutron speed enters here but a more refined calculation would include a speed distribution).
@fxsignal1830
8 ай бұрын
Fermi equation
@peppescala4113
8 ай бұрын
Hi! Is there a way to predict theoretically the fission and capture cross-sections of our processes? You can get more or less the order of magnitude of this treating the U-235 as an hard sphere and using the Bohr-Wheeler theory that tells you that the higher Z²/A, the higher the fission probability. I tried to evaluate the U-235 fission cross section and I get something like 6.20 time 10^(-23) cm². But I'm not able to see how to improve this little model in order to study capture cross section. Also I have no idea how to distinguish slow and fast neutrons! By the way, your videos are beautiful.
@jkzero
8 ай бұрын
Thanks for the feedback and I am glad you liked the videos. Yes, you can motivate the order of magnitude for the cross-sections but at the scale of neutrons and nuclei, quantum-mechanical effects can become relevant and classical intuition falls short. Plus a nucleus with 235 nucleons is really hard to model and you can only use approximation methods, in the end the best way is just go a measure it, all you need is a few microgram of uranium-235, which is easy to "make" with a cyclotron
@Tim-Kaa
8 ай бұрын
Nice
@sbkarajan
8 ай бұрын
The first nuclear reactor in the history of universe is.... allegedly... Chicago Pile-1, in Dec 2, 1942... Such a historic day.... The reactor produced..... 0.5 W? A pile of manure would produce more heat than that. They clearly had no clue how to make a nuclear reactor, let alone a far more complex implosion bomb, lol. Manhattan Project was signed in Aug 1942 Recruit began March 1943 Los Alamos Lab and Oak Ridge Lab buildings were completed and opened in Nov 1943. According to Richard Feyman's book, "scientists" had nothing to do until the building completed. So Feynman developed new hobby, Teller was traveling around the country enjoying Opera. Others helped the construction of buildings. So, the real work started in Nov 1943, when buildings completed, the equipments not yet installed fully. The alleged first atom bomb, the Gadget, was tested in July 1945. This means.... Nov 1943 - July 1945..... it took 1 year 8 months to invent two types of atom bombs from scratch, without a hitch? Or, after the war ended, Germany surrendered, the bombs were shipped to the US?
@sbkarajan
8 ай бұрын
Funny thing is, although tragic.... Far more difficult and dangerous would it have been, to produce plutonium core. But zero incident before the completion of bombs? No radiation sickness, no premature detonation, nothing? Very strange. Then this same group, impeccable safety record.... After the war, after "obtaining bombs" from somewhere.... And use them to kill bunch of CIVILIANS... (by dropping them in city centers for maximum deaths) Demon core accidents.... Two scientists died, by carelessness, doing some basic and meaningless work? More like they were killed because they did not know what they were doing.
@sbkarajan
8 ай бұрын
Watch lectures by Oppenheimer. He never said who built the bombs. What a shameful man....
@fredchappin
8 ай бұрын
woooow ...
@sphakamisozondi
8 ай бұрын
Congratulations everyone, WE ARE All IN THE FBI WATCHLIST NOW 🎉🎉
@jkzero
8 ай бұрын
you are welcome?
@codetoil
8 ай бұрын
Wouldn't the 'elementary solution' be 'sinc'-usoidal in r? Otherwise, you get negative densities... Fairly certain you have to integrate over ν' where AC is a function of it...
@jkzero
8 ай бұрын
I suppose you mean sinusoidal but just in case I am missing your point, could you clarify what you mean by "'sinc'-usodal"?
@codetoil
8 ай бұрын
It's a pun. It couldn't be sinusoidal because that corresponds to the sine function. Because the result has a sinc function instead, it's sinc-usodial.
@jkzero
8 ай бұрын
@@codetoil I see, I missed it. Yes, the radial solution is sinc(kappa*r), which would also give negatives values beyond kappa*r=pi. I still don't understand the comment about integrating over nu'
@codetoil
8 ай бұрын
@@jkzero When one preforms seperation of variables, one must integrate over the constant to get the full solution. This is because all the values of the constant solve the PDE. For example, when one preforms seperation of variables on the Schrödinger Equation, one integrates over the Energy to get the full solution.
@Bobby-fj8mk
8 ай бұрын
Interesting and yet when the North Koreans first tried to explode a nuclear bomb their first 2 attempts were fizzers - they didn't work. Assuming the scientists knew everything in the video here and 100 times more it is obviously more difficult than we can imagine or really will ever know about. A lot of the calculations must still be top secret for obvious reasons. It's also amazing that the Trinity test worked correctly the first time.
@jkzero
8 ай бұрын
you are right, determining the critical mass helps you learning how much fissile material is needed, which is crucial for making a decision on whether or develop a nuclear-weapons program, but it teaches you nothing relevant about bomb design, this is why the content in this video has been declassified for over half a century.
@Bobby-fj8mk
8 ай бұрын
@@jkzero - thanks Dr. Jorge S. Diaz. yes and they did the bomb design for the Trinity test of Pu239 - without modern computers that could implement billions of iterative solutions to find the one that would work. They needed to consider perhaps: the velocity of the pressure wave, the effect of a neutron spherical reflector, a delay gap to increase the final explosive pressure, the design of the Polonium-210 initiator to increase the initial neutron count etc. all without causing a pre-ignition that would blow it all apart causing a fizzer before enough generations of neutrons were created. They also had to consider Pu239 contaminated with Pu240.
@jkzero
8 ай бұрын
@@Bobby-fj8mk that's right, in fact the Pu-240 contamination is what triggered the development of the implosion design, the amount of Pu-240 in the Pu-239 core would make the gun-design fail due to a very high probability of pre-detonation, they needed a faster way to assemble the gadget; implosion was the answer.
@Bobby-fj8mk
8 ай бұрын
@@jkzero - thanks Dr. Jorge S. Diaz. I appreciate your wonderful videos. I have watched 6 of them now and I am subscribed too. I am amazed that they got the Trinity test to work. The maths must have been mind boggling. I can only assume that they must have been solving many very complex differential equations and even to write those equations with their pioneer knowledge is astounding. Laplace Transforms come to mind.
@ihebbendebba2978
8 ай бұрын
What is the critical mass of nitrogen? Asking for a friend.
@jkzero
8 ай бұрын
tell "your friend" that nitrogen has too few nucleons (protons and neutrons) in its nucleus to release energy by fission, nitrogen is easier to fusion than fission, just like every nucleus below Fe-56. Search for "binding energy chart" for a complete description of all elements, there you will see that all elements lighter than iron-56 can react via nuclear fusion, whereas heavier one could in principle fission. However, in addition to this, not all heavy elements will sustain a nuclear chain reaction like uranium-235 and plutonium-239 (called fissile elements) so talking about critical mass does not make sense.
@ihebbendebba2978
8 ай бұрын
@@jkzero my friend told me they gave up the idea of a global scale nuclear catastrophe.
@jkzero
8 ай бұрын
@@ihebbendebba2978 I am glad, thanks fro sharing and tell your friend to support the channel with a like, subscribe, and sharing the videos ;)
@tdoc666___
8 ай бұрын
bro, i have nothing against you and this video, but don't you think is very hazardous or let's say DANGEROUS to put this kind of information out here, i mean, someone might even get *TOO MUCH* interested into this
@jkzero
8 ай бұрын
thanks for your comment, bro, but no worries, the reports including all these calculations were declassified in 1965, over half a century ago and available online for decades. The use of diffusion theory for weapons design was rendered obsolete pretty soon, it is of little use to someone attempting to build a nuclear weapon, plus determining the critical mass teaches you nothing relevant about bomb design.
@tdoc666___
8 ай бұрын
@@jkzero ah, i didn't know that, i thought it was a bit hazardous because of the title of your video, just saying, was worried because you can see all the crazyness around the world, no doubt this cannot be accomplished by someone random, what i was trying to tell, is that creating videos that have like title "how to create a nuclear weapon" just enhances the possibilities of someone with a contorted mind to get interestend in, but you are right, it is impossible to reach that point as you
@jkzero
8 ай бұрын
@@tdoc666___ I see your point and I appreciate the concern, but the reason I can create this video is because all the content is public and it has been available in textbooks for decades,. Before the internet anybody with access to a library could reproduce all that is shown here, today you just need to google it: all the official reports and declassified documents can be found online. Plus, as indicated before, knowing how to calculate this quantity, the critical mass of an atomic bomb, does not tell you anything about how to do it, how to get the necessary materials, etc. It is like a video titled "how to calculate the energy to destroy the Moon," yeah, I guess that can be calculated but that does not tell anything about how to do it or if it is technically possible. I hope you come back, more videos coming soon with less military-conflict-related material and more physics and history.
@JohnUrbanic-m3q
8 ай бұрын
Your surface boundary condition makes no physical sense. It isn't even an approximation.
@jkzero
8 ай бұрын
there are two types of boundary condition used at the surface, could you be more specific?
@JohnUrbanic-m3q
8 ай бұрын
@@jkzeroYour "elementary" one isn't motivated by any physical consideration at all. There is a discontinuity where what you call S+ goes abruptly to zero - which does not mean that N goes to zero at all. Furthermore, you are only using one component (harmonic) of that solution anyway - not that it matters since this is invalid to begin with. I am not sure what condition you believe your advanced one is capturing, but it does not correspond to S+ = 0 for r>R, which is what your terminology requires.
@jkzero
8 ай бұрын
@@JohnUrbanic-m3q you are correct, the "elementary" boundary condition is quite artificial, in fact, it is only used because it allows an analytical solution for R_c in terms of the relevant parameters ( u, cross-sections, density, etc.), it gives a glimpse on what is driving R_c and the critical mass. However, this is the only reason this condition is introduced, mostly for academic purposes. The "advanced" boundary condition is what has to be used in a practical calculation. Regarding the use of only the first harmonic you have a good point: the general solution is kappa*R=n*pi; however, the higher "harmonics" will only make the bomb core bigger, we are searching for the minimum radius. Also, a solution for n>1 can lead to a negative density, which is also a non-physical solution. Mathematically, your point is 100% correct; however, here is when physics constrains the final solution, just like setting B=0 to remove the non-physical cos(kappa*r) term.
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