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Stepbystep guide on how to derive and solve the neutron diffusion equation to determine the critical mass of an atomic bomb, following the steps of Rudolf Peierls and Otto Fritsch. It involves solving a partial differential equation but every step is presented. In the end a general formula for a nuclear critical mass is found.

Relevant links:

• Critical Mass: when the atomic bomb got real    • Critical Mass: when the atomic bomb g...  
• Physics of a Nuclear Explosion    • Physics of a nuclear explosion  
• Nuclear Weapons Q&A #1    • Nuclear Weapons Q&A #1  
• Series on Nuclear Weapons Physics    • Physics of Nuclear Weapons  
• "Critical Assembly Simulator" by Alex Wellerstein https://blog.nuclearsecrecy.com/misc/...
• The Feynman Lectures on Physics https://www.feynmanlectures.caltech.edu/

Errata:
• 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; thanks to @fatassmonkey37 for pointing this out
• at 15:58 the subscripts are reversed, it should say: λ_f = 16.89 cm, λ_t = 3.596 cm; thanks to @lucacastronuovo9789 for pointing this out

Credits:

"Critical Assembly Simulator" courtesy of Alex Wellerstein https://blog.nuclearsecrecy.com/misc/...
Diffusion by JrPol under CC BY 3.0 Deed https://creativecommons.org/licenses/...
Metal cube by JOGOS Public Assets under CC BYSA 4.0 Deed https://creativecommons.org/licenses/...

Chapters:
00:00 Neutron diffusion equation
05:41 Solution
15:24 Critical mass
20:13 Advanced solution