116
2 Critical Mass, Efficiency, and Yield
8.0
9.0
10.0
11.0
12.0
120
121
122
123
124
125
126
17
19
21
23
Radius (cm)
Mass (kg)
Length (cm)
Fig. 2.25 Computed 235 U critical mass (solid line, left scale) and radius (dashed line, right scale)
as a function of length for a cylindrical core. Note that these results hold only for the simplified
boundary condition N(edge) = 0
Figure 2.25 shows the critical mass and cylinder radius corresponding to a given
choice of L in (2.171) and (2.173) for our usual parameters for
235 U: (σ f , σ el , ν, ρ) =
(1.235 bn, 4.566 bn, 2.637, 18.71 gr cm
−3 ). The minimum critical mass corresponds
to a length of about 19.2 cm, and a radius of about 10.3 cm: A cylinder almost as
long as it is wide.
References
Bernstein, J.: Hitler’s Uranium Club: The Secret Recordings at Farm Hall. Copernicus Books, New
York (2001)
Bernstein, J.: Heisenberg and the critical mass. Am. J. Phys. 70(9), 911–916 (2002)
Bernstein. J.: A memorandum that changed the world. Am. J. Phys. 79(5), 440–446 (2011)
Glasstone, S., Dolan, P.J.: The Effects of Nuclear Weapons. United States Department of Defense,
Washington, DC (1977)
Koch, L.J., Paxton, H.C.: Fast reactors. Ann. Rev. Nuc. Sci. 9, 437–472 (1959)
Logan, J.: The critical mass. Am. Sci. 84, 263–277 (1996)
Malik, J.: The Yields of the Hiroshima and Nagasaki Nuclear Explosions, Los Alamos National
Laboratory Report LA-8819 (1985). http://atomicarchive.com/Docs/pdfs/00313791.pdf
Peierls, R.: Critical conditions in neutron multiplication. Proc. Cam. Phil. Soc. 35, 610–615 (1939)
Penney, W., Samuels, D.E.J., Scorgie, G.C.: The nuclear explosive yields at Hiroshima and Nagasaki.
Phil. Trans. Roy. Soc. London. A266(1177), 357–424 (1970)
Reed, B.C.: Arthur Compton’s 1941 Report on explosive fission of U-235: a look at the physics.
Am. J. Phys. 75(12), 1065–1072 (2007)
Reed, B.C.: Rudolf Peierls’ 1939 analysis of critical conditions in neutron multiplication. Phys.
Soc. 37(4), 10–11 (2008)
Reed, B.C.: A brief primer on tamped fission-bomb cores. Am. J. Phys. 77(8), 730–733 (2009)
2 Critical Mass, Efficiency, and Yield
8.0
9.0
10.0
11.0
12.0
120
121
122
123
124
125
126
17
19
21
23
Radius (cm)
Mass (kg)
Length (cm)
Fig. 2.25 Computed 235 U critical mass (solid line, left scale) and radius (dashed line, right scale)
as a function of length for a cylindrical core. Note that these results hold only for the simplified
boundary condition N(edge) = 0
Figure 2.25 shows the critical mass and cylinder radius corresponding to a given
choice of L in (2.171) and (2.173) for our usual parameters for
235 U: (σ f , σ el , ν, ρ) =
(1.235 bn, 4.566 bn, 2.637, 18.71 gr cm
−3 ). The minimum critical mass corresponds
to a length of about 19.2 cm, and a radius of about 10.3 cm: A cylinder almost as
long as it is wide.
References
Bernstein, J.: Hitler’s Uranium Club: The Secret Recordings at Farm Hall. Copernicus Books, New
York (2001)
Bernstein, J.: Heisenberg and the critical mass. Am. J. Phys. 70(9), 911–916 (2002)
Bernstein. J.: A memorandum that changed the world. Am. J. Phys. 79(5), 440–446 (2011)
Glasstone, S., Dolan, P.J.: The Effects of Nuclear Weapons. United States Department of Defense,
Washington, DC (1977)
Koch, L.J., Paxton, H.C.: Fast reactors. Ann. Rev. Nuc. Sci. 9, 437–472 (1959)
Logan, J.: The critical mass. Am. Sci. 84, 263–277 (1996)
Malik, J.: The Yields of the Hiroshima and Nagasaki Nuclear Explosions, Los Alamos National
Laboratory Report LA-8819 (1985). http://atomicarchive.com/Docs/pdfs/00313791.pdf
Peierls, R.: Critical conditions in neutron multiplication. Proc. Cam. Phil. Soc. 35, 610–615 (1939)
Penney, W., Samuels, D.E.J., Scorgie, G.C.: The nuclear explosive yields at Hiroshima and Nagasaki.
Phil. Trans. Roy. Soc. London. A266(1177), 357–424 (1970)
Reed, B.C.: Arthur Compton’s 1941 Report on explosive fission of U-235: a look at the physics.
Am. J. Phys. 75(12), 1065–1072 (2007)
Reed, B.C.: Rudolf Peierls’ 1939 analysis of critical conditions in neutron multiplication. Phys.
Soc. 37(4), 10–11 (2008)
Reed, B.C.: A brief primer on tamped fission-bomb cores. Am. J. Phys. 77(8), 730–733 (2009)