Talk:Frisch–Peierls memorandum

message: Folks, please sanity-check me. The equation given for energy of the bomb, big E, looks wrong - power of tau/time dimension - the whole thing has the dimensions of power not energy, surely? (Apologies if I'm going mad.) Either it means 'power' which isn't useful, or the tau-to-the-minus-3 should read minus-2 perhaps? Or who knows what.
Could someone take a look for me?
CecilWard (talk) 12:23, 1 December 2017 (UTC)
replies: text: In this case, it doesn't matter at all what is right, but what he wrote years ago.  There are many approximations that go into the calculation, and that aren't included. The energy released is growing exponentially, so a tiny increase in the containment time is a huge increase in energy released. The time depends on the inertia of the sphere itself. The term with the square root determines how much the radius can increase before fission stops. I suspect that the 0.2 has units that aren't mentioned. Note that there is no term for the amount of energy per fission, which is important. The energy/fusion divided by m*c**2 for a Uranium atom is about 0.1%, but there are no terms of that order. Gah4 (talk) 16:32, 1 December 2017 (UTC)
replies: text: OK, from which has a transcription of the memorandum, it should be tau**2.  There is a footnote in the transcription about confusion between diameter and radius, though. If you are really interested, read the book, which has annotation (from later) about the original primer. Even so, there is a lot of approximation that isn't described in the memorandum. Gah4 (talk) 17:17, 1 December 2017 (UTC)
replies: text: Thank you. I have corrected the formula. It was a transcription error on my part. (Note that Serber also transcribed it wrongly.) It appears without derivation in the memorandum. If you have a source that explains how Peierls arrived at it, I can include it in the article.  Hawkeye7 (discuss) 19:50, 1 December 2017 (UTC)

text: The archives version says "diameter". The reason why they calculated larger bomb sizes was so they could ignore the surface effects.  Hawkeye7 (discuss) 21:47, 1 March 2018 (UTC)
replies: text: I am assured by an academic with access to a photo-facsimile of the UK National Archives typewritten original of the F & P memo, that it says "radius", not "diameter". Even so: it also shows the (handwritten!) square root sign extending only over the ratio of sphere radius to critical mass radius, not including the "-1". Dr Reed of Alma College has also covered this in a private communication, and Bernstein's 2010 paper, "A memorandum that changed the world", discusses this in detail on page 444 of Am. J. Phys., Vol. 79, No. 5, May 2011. He is equally at a loss for some aspects of these calculations. --115.188.58.71 (talk) 01:41, 2 March 2018 (UTC)
replies: text: Yes that's right; Bernstein says that. I don't know how the bit about diameter crept in.  Hawkeye7 (discuss) 02:48, 2 March 2018 (UTC)
replies: text: If you have any idea where the energy formula come s from, let me know.  Hawkeye7 (discuss) 03:02, 2 March 2018 (UTC)
replies: text: Dr Reed has been in touch with an unpublished paper that I am still working through, that recovers the form of F & P's energy formula, to within a multiplicative constant. When I fully understand it myself, I will let you know. It's not yet in a fit state to publish. --115.188.58.71 (talk) 11:17, 2 March 2018 (UTC)
thread_title:  Formula for 'energy' 

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