NUCLEAR-DEBRIS FORMATION 21 AS a, becomes zero I, becomes n,;ayR, and I,C, equals n;R/2a,.Further evaluation reveals the first-order term (which is the term that becomes important at long times) to be n;. The solution can therefore be written in terms of the fractional departure from equilibrium: n(r,t)—n,; 2R a Bp = Sin a,r 2 exp (—Dajt) sin a,R n=2 This has the extreme radial values n(0,t)0,—t) _ ;20 » exp (~Dait) cos a,R ne n=2 and n(R,t)—nmr 2 2 a 3 Y) ex ( Da;t) n=2 Figure 9 shows how the fractional departure from equilibrium varies with the reduced radius (9 = r/R) for various reduced times (@= Dt/R’). The calculation was carried out to n = 6. Since heat transfer in the particle will be fast in comparison with diffusion, the effect of changing temperature can be accounted for by replacing the exponent @ with —azDy [* exp (-Q/RT)at where Q is the activation energy for diffusion and T is the temperature as a function of time. . Rare-gas Behavior It is worth digressing briefly to consider the behavior of krypton and xenon, the rare-gas precursors prominent in the 89, 90, and 91 and the 137, 140, and 141 chains, respectively. These are not expected to be taken up significantly by fallout particles, but it is of interest to know by how much and by what processes, Gas solubility is conveniently and customarily expressed by a distribution coefficient called the Ostwald coefficient of solubility,8, which is insensitive to << pressure at a given temperature: B= Here. v is the volume of gas dissolved in a volume V of solvent. The value of § for helium has recently been determined for glass melts by