Chapter 5
Miscellaneous Calculations
In this final chapter, we take up some miscellaneous issues associated with fission
weapons. One often reads that a bomb core is warm to the touch; this is investigated
in Sect. 5.1. Section 5.2 quantifies just how bright the Trinity explosion appeared
to the naked eye. Section 5.3 develops a numerical simulation for estimating the
production of trace isotopes such as
240 Pu in a reactor. Finally, Sect. 5.4 investigates
a claim that one sometimes reads: that the energy liberated in an individual fission
event is sufficient to make a grain of sand visibly jump.
5.1 How Warm Is It?
Would a plutonium bomb core feel warm to the touch?
239 Pu is an alpha emitter
with a half-life of 24,100 years. As seen in the preceding chapter, this corresponds
to some 2.3 × 10
12 alpha-decays per second per kilogram of material. With alphas
of energy 5.2 MeV, the power generated by alpha-decay from a 1-kg mass of
239 Pu
amounts to P ~ 1.9 Watts.
We can make a rough estimate of how much hotter such a mass would be than the
surrounding air by assuming that this power is dissipated in accordance with a semiempirical expression known as Newton’s Law of Cooling. This expression states that
the rate of heat energy loss P (that is, the power emitted) due to convection by a body
of surface temperature T to a surrounding environment at ambient temperature T amb
is given by
P = Ah(T − T amb ),
(5.1)
where A is the surface area of the body and h is an empirical parameter known as the
heat transfer coefficient. The value of h depends on the geometry of the object and
the properties of the surrounding environment, which is usually a “fluid” such as air
or water. For free convection in steady air, h ~ 5–25 W/(m
2 K).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
B. C. Reed, The Physics of the Manhattan Project,
https://doi.org/10.1007/978-3-030-61373-0_5
175
Miscellaneous Calculations
In this final chapter, we take up some miscellaneous issues associated with fission
weapons. One often reads that a bomb core is warm to the touch; this is investigated
in Sect. 5.1. Section 5.2 quantifies just how bright the Trinity explosion appeared
to the naked eye. Section 5.3 develops a numerical simulation for estimating the
production of trace isotopes such as
240 Pu in a reactor. Finally, Sect. 5.4 investigates
a claim that one sometimes reads: that the energy liberated in an individual fission
event is sufficient to make a grain of sand visibly jump.
5.1 How Warm Is It?
Would a plutonium bomb core feel warm to the touch?
239 Pu is an alpha emitter
with a half-life of 24,100 years. As seen in the preceding chapter, this corresponds
to some 2.3 × 10
12 alpha-decays per second per kilogram of material. With alphas
of energy 5.2 MeV, the power generated by alpha-decay from a 1-kg mass of
239 Pu
amounts to P ~ 1.9 Watts.
We can make a rough estimate of how much hotter such a mass would be than the
surrounding air by assuming that this power is dissipated in accordance with a semiempirical expression known as Newton’s Law of Cooling. This expression states that
the rate of heat energy loss P (that is, the power emitted) due to convection by a body
of surface temperature T to a surrounding environment at ambient temperature T amb
is given by
P = Ah(T − T amb ),
(5.1)
where A is the surface area of the body and h is an empirical parameter known as the
heat transfer coefficient. The value of h depends on the geometry of the object and
the properties of the surrounding environment, which is usually a “fluid” such as air
or water. For free convection in steady air, h ~ 5–25 W/(m
2 K).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
B. C. Reed, The Physics of the Manhattan Project,
https://doi.org/10.1007/978-3-030-61373-0_5
175