188
5 Miscellaneous Calculations
of ν is 1.801, which rises to 1.807 after 100 days. In Sect. 4.2, the
240 Pu contamination
fraction for the Trinity and Fat Man devices was assumed to be 1.2%, but it must be
remembered that the simulation developed here does not account for all processes
going on within the reactor. If the Fat Man predetonation probability calculation of
that section is repeated for a 6.3 kg core containing 0.34%
240 Pu (0.0211 kg), the
probability that the bomb will function correctly for a 100 µs assembly time is only
45% (zero scatterings); implosion would still be required to achieve a sensibly high
probability of avoiding predetonation.
5.4 Can Fission Make a Grain of Sand Visibly Jump?
The idea of a grain of sand being propelled off your desk by the fission of a single
uranium nucleus is an appealing image, but, alas, the physics does not hold up. I do
not know where this claim originated, but it can be found in, for example, Gerard
DeGroot’s book The Bomb: A Life, where he mistakenly attributes it to having been
calculated by Lise Meitner and Otto Frisch when they were preparing their paper
on the physics of fission [DeGroot (2004)]. I analyzed the physics of this claim in a
paper published in The Physics Teacher [Reed (2018)].
Some numbers: The most common form of sand is silicon dioxide, usually in
the form of quartz, which has a density of 2.65 g cm
–3 . A grain of diameter 1 mm
will have a mass of about 1.4 mg. The energy released in fission averages about 170
million electron-volts (MeV) per event, or about 2.7 × 10
–11 J. If all of this energy is
directed into projecting the grain upwards, then the usual mgh formula for potential
energy shows that we can expect to reach a maximum height of about 0.002 mm,
or a mere 1/250 of the radius of the grain itself. Unless the grain is much smaller
than this or you have super-power eyes, you are unlikely to be able to discern this.
The visual acuity of the eye is about one minute of arc. If we optimistically assume
half a minute, we can use a standard arc-length calculation to estimate the distance
from which we would have to view the jump in order to resolve it. For a jump of
0.002 mm, this gives about 14 mm, or a little over a half-inch. The near point of the
eye (the closest distance at which one can still focus) is about 25 cm, so we are out
of luck.
References
Bracken, D.S., Rudy, C.R.: Principles and applications of calorimetric assay. Los Alamos National
Laboratory report LA-UR-07-5226. http://www.lanl.gov/orgs/n/n1/panda/10.%20Calorimetry.
pdf (2007)
DeGroot, G.: The Bomb: A Life. Harvard University Press, Cambridge, MA (2004). See p. 16
DOE: Historic American Engineering Record: B Reactor (105-B Building), HAER No. WA-164.
http://www.cfo.doe.gov/me70/history/NPSweb/DOE-RL-2001-16.pdf (2001)
5 Miscellaneous Calculations
of ν is 1.801, which rises to 1.807 after 100 days. In Sect. 4.2, the
240 Pu contamination
fraction for the Trinity and Fat Man devices was assumed to be 1.2%, but it must be
remembered that the simulation developed here does not account for all processes
going on within the reactor. If the Fat Man predetonation probability calculation of
that section is repeated for a 6.3 kg core containing 0.34%
240 Pu (0.0211 kg), the
probability that the bomb will function correctly for a 100 µs assembly time is only
45% (zero scatterings); implosion would still be required to achieve a sensibly high
probability of avoiding predetonation.
5.4 Can Fission Make a Grain of Sand Visibly Jump?
The idea of a grain of sand being propelled off your desk by the fission of a single
uranium nucleus is an appealing image, but, alas, the physics does not hold up. I do
not know where this claim originated, but it can be found in, for example, Gerard
DeGroot’s book The Bomb: A Life, where he mistakenly attributes it to having been
calculated by Lise Meitner and Otto Frisch when they were preparing their paper
on the physics of fission [DeGroot (2004)]. I analyzed the physics of this claim in a
paper published in The Physics Teacher [Reed (2018)].
Some numbers: The most common form of sand is silicon dioxide, usually in
the form of quartz, which has a density of 2.65 g cm
–3 . A grain of diameter 1 mm
will have a mass of about 1.4 mg. The energy released in fission averages about 170
million electron-volts (MeV) per event, or about 2.7 × 10
–11 J. If all of this energy is
directed into projecting the grain upwards, then the usual mgh formula for potential
energy shows that we can expect to reach a maximum height of about 0.002 mm,
or a mere 1/250 of the radius of the grain itself. Unless the grain is much smaller
than this or you have super-power eyes, you are unlikely to be able to discern this.
The visual acuity of the eye is about one minute of arc. If we optimistically assume
half a minute, we can use a standard arc-length calculation to estimate the distance
from which we would have to view the jump in order to resolve it. For a jump of
0.002 mm, this gives about 14 mm, or a little over a half-inch. The near point of the
eye (the closest distance at which one can still focus) is about 25 cm, so we are out
of luck.
References
Bracken, D.S., Rudy, C.R.: Principles and applications of calorimetric assay. Los Alamos National
Laboratory report LA-UR-07-5226. http://www.lanl.gov/orgs/n/n1/panda/10.%20Calorimetry.
pdf (2007)
DeGroot, G.: The Bomb: A Life. Harvard University Press, Cambridge, MA (2004). See p. 16
DOE: Historic American Engineering Record: B Reactor (105-B Building), HAER No. WA-164.
http://www.cfo.doe.gov/me70/history/NPSweb/DOE-RL-2001-16.pdf (2001)