74

WORLDWIDE EFFECTS OF ATOMIC WEAPONS

W’,, = the number of grams of available natural strontium per square mile
of area,

wo, = the numberof gramsof natural strontium fixed in the human skeleton
at maturity,
T = the number of grams ofSr®° fixed in the skeleton that is considered
to be the level of interest (MPC orany other standard),
m = the number of grams of Sr°° produced by the release of 1 MT of
fission energy,
A = the area of the earth in square miles,
then

MT = <- (4) x Wy, XA.
nT

WR

Since there is little chance that m will be changed appreciably by future measurements and A is fixed, this relation can be simplified as follows (taking # = 1000
gmand A = 3 X 10° mi’):
op

Taking T to be 1 pe (the international MPC), o, = 0.7 gm, and W’,, = 1.7
X 107 gm, one finds (as in Chapter 4) MT to be 2.5 10* on an idealized worldwide basis. The validity of the assumption underlying this calculation is discussed
in Chapter1.

APPENDIX II

PARTICLE SIZE OF DEBRIS FROM THE ATOMIC BOMB"
A theoretical consideration that may apply to the condensation process of the
solid material in the fireball of an atomic bomb is presented here. The well-established nucleation theory of Becker and Déring, and others,‘ is used, Only a
treatment of the condensation by self-nucleation of a homogeneous gaseous system
cooled at a uniform rate is treated here. Application to the atomic bomb involves
complications that have not as yet been considered in detail. However, a rough
check on the magnitudes of the physical quantities seems to indicate that the
mechanism is reasonable.

The slow process in the condensation is assumed to be the formation of the solid
oxides from gaseous oxide molecules. The gaseous oxide molecules should form on
a much shorter time scale and at much higher temperatures than those involved in
the condensation.
CONDENSATION MODEL: SIMPLE ANALYTICAL FORM

In a homogeneoussupersaturated gas at constant temperature, nuclei are forming
at a constant rate. Once formed, a nucleus grows by condensing single molecules on
its surface. The growth rate of a particle having radius R is given by

‘ (“") = AnRFry,
3

(1)

where F is the flux of single moleculest and v, is the volume of a single molecule.
This equation simplifies to
dR
a”
= Fry = B,
“
eT

"

erTrett

4

uhm

(2)

.
Ra

“Communicated by John L. Magee, University of Notre Dame.
tAn accommodation coefficient should be used, too, since all molecules that strike the
surface may not remain.
75

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