176
5 Miscellaneous Calculations
For a 6.3-kg Trinity/Fat Man core, the alpha-decay rate corresponds to a power
output of 12.0 Watts. If spherical, this mass would have a radius of 4.58 cm and a
surface area of 2.64 × 10
–2 m
2 . If we adopt h = 15 W/(m
2 K), then (T – T amb ) ~
30 K, that is, the surface of the core will be some 30 K warmer than the surrounding
air. The claim of warmth is certainly credible.
This calculation is more than a hypothetical exercise. An experimental technique
known as nuclear calorimetry is a non-destructive means to quantify masses of
radioactive material by measuring such temperature differences. This technique has
applications in areas such as fissile material accounting and safeguards enforcement;
see, for example, Bracken and Rudy (2007).
5.2 Brightness of the Trinity Explosion
Much of the analysis presented in this section is adopted from Reed (2006).
Nuclear weapons release fantastic amounts of energy, only some fraction of which
is in the form of visible light. However, they rapidly ionize and heat the surrounding
air to incandescence, creating extremely bright fireballs. Rhodes (1986, p. 672)
remarks of the July 16, 1945, Trinity test that “Had astronomers been watching they
could have seen it reflected from the moon, literal moonshine,” an allusion to Ernest
Rutherford’s famous dismissal of the prospects for atomic energy. Investigating this
impressive claim makes for an informative exercise in the physics of astronomical
magnitudes, and prompts other questions: What fraction of the bomb’s yield was
in the form of visible light? How bright would the explosion have appeared to an
observer on the moon? What about an observer on Mars or otherwise located in the
solar system?
These questions can be addressed with the help of information published in a report
on the Trinity test prepared by the test’s director, Kenneth Bainbridge. His report,
titled Trinity, was prepared soon after the test as Los Alamos report LA-1012. In 1976,
a public version of this report was released as Los Alamos report LA-6300-H, and is
freely available from the Federation of American Scientists (FAS) website at http://
www.fas.org/sgp/othergov/doe/lanl/docs1/00317133.pdf. On page 52 of this report
appears a graph of the illumination created by the Trinity test in “Suns” equivalent
as a function of time at a detector located 10,000 yards from the explosion; this is
reproduced in Fig. 5.1. At t = 10
–4 s the illumination was approximately 80 Suns; it
dropped to about 0.1 Suns at t ~ 0.04 s, rose back to about 2 Suns at t = 0.4 s, and then
declined to about 0.4 Suns at t ~ 10 s. This “double maximum” in the time-evolution
of visible radiation is uniquely characteristic of a nuclear explosion; the reason for
this is described later in this section.
In working the following analysis, it must be remembered that many Trinity diagnostic experiments were overwhelmed by the explosion, and so yielded only approximate results; the following calculations should be regarded as estimates at best. I
interpret “Suns” of illumination to mean multiples of the so-called solar constant,
the measured value of the flux of solar energy at the Earth, about 1400 W/m
2 .
5 Miscellaneous Calculations
For a 6.3-kg Trinity/Fat Man core, the alpha-decay rate corresponds to a power
output of 12.0 Watts. If spherical, this mass would have a radius of 4.58 cm and a
surface area of 2.64 × 10
–2 m
2 . If we adopt h = 15 W/(m
2 K), then (T – T amb ) ~
30 K, that is, the surface of the core will be some 30 K warmer than the surrounding
air. The claim of warmth is certainly credible.
This calculation is more than a hypothetical exercise. An experimental technique
known as nuclear calorimetry is a non-destructive means to quantify masses of
radioactive material by measuring such temperature differences. This technique has
applications in areas such as fissile material accounting and safeguards enforcement;
see, for example, Bracken and Rudy (2007).
5.2 Brightness of the Trinity Explosion
Much of the analysis presented in this section is adopted from Reed (2006).
Nuclear weapons release fantastic amounts of energy, only some fraction of which
is in the form of visible light. However, they rapidly ionize and heat the surrounding
air to incandescence, creating extremely bright fireballs. Rhodes (1986, p. 672)
remarks of the July 16, 1945, Trinity test that “Had astronomers been watching they
could have seen it reflected from the moon, literal moonshine,” an allusion to Ernest
Rutherford’s famous dismissal of the prospects for atomic energy. Investigating this
impressive claim makes for an informative exercise in the physics of astronomical
magnitudes, and prompts other questions: What fraction of the bomb’s yield was
in the form of visible light? How bright would the explosion have appeared to an
observer on the moon? What about an observer on Mars or otherwise located in the
solar system?
These questions can be addressed with the help of information published in a report
on the Trinity test prepared by the test’s director, Kenneth Bainbridge. His report,
titled Trinity, was prepared soon after the test as Los Alamos report LA-1012. In 1976,
a public version of this report was released as Los Alamos report LA-6300-H, and is
freely available from the Federation of American Scientists (FAS) website at http://
www.fas.org/sgp/othergov/doe/lanl/docs1/00317133.pdf. On page 52 of this report
appears a graph of the illumination created by the Trinity test in “Suns” equivalent
as a function of time at a detector located 10,000 yards from the explosion; this is
reproduced in Fig. 5.1. At t = 10
–4 s the illumination was approximately 80 Suns; it
dropped to about 0.1 Suns at t ~ 0.04 s, rose back to about 2 Suns at t = 0.4 s, and then
declined to about 0.4 Suns at t ~ 10 s. This “double maximum” in the time-evolution
of visible radiation is uniquely characteristic of a nuclear explosion; the reason for
this is described later in this section.
In working the following analysis, it must be remembered that many Trinity diagnostic experiments were overwhelmed by the explosion, and so yielded only approximate results; the following calculations should be regarded as estimates at best. I
interpret “Suns” of illumination to mean multiples of the so-called solar constant,
the measured value of the flux of solar energy at the Earth, about 1400 W/m
2 .