Decay Helium - std301320040063

DOE-STD-3013-2004

V1 = (Vc - m/ρ)

where ρ is the density of the oxide.

B.2.4

Decay Helium

For a radioactive species, the decay rate (and, hence, the helium generation rate, h, for alpha

decay) is

h=λN

[14]

where λ is the decay constant and N is the number of atoms of the decaying material. As a

function of time, N is given by

N = N0e-λt.

[15]

The total amount of helium generated, H, over a period of time τ is therefore

H = ∫ h dt = ∫ λ N0e-λt dt = N0(1 - e-λτ).

[16]

For values of λτ which are small, the term in parentheses can be replaced by its linear

approximation, λτ. This approximation is conservative because λτ ≥ 1 - e-λτ. Also, since the units

of H are the same as the units of N0, it is possible to consider both as moles, rather than as

atoms, and the volume of helium thus produced (in liters at STP) is

H = 22.4(1000 m/271)λτ

[17]

where m is the oxide mass in kg, and 271 is the molecular weight of PuO2.

The pressure due to this volume of helium is

PHe = (14.7)[22.4(1000 m/271)λτ](T1/273)/V1

PHe= 4.4507mλτT1/V1.

[18]

239

Pu with a half-life of 24,110 years, then

If it is assumed that the radioactive species is

Equation [18] becomes

PHe = 1.28x10-4 m τT1/V1.

[19]

Equation [19] is the same as the third term of the equation in DOE-STD-3013-99.

An alternative formulation of this term is possible. The heat generation rate of the contents is

given by

Q = EλN = EλN0e-λt

[20]