文档介绍：Chapter 5
Uranium-series Disequilibrium Modeling
The previous four chapters deal with the fractionation of stable trace
elements during partial melting. In this chapter, we study the behaviors
of radioactive uranium decay series during partial melting. Since
quantitative models for uranium-series disequilibria need to include
additional parameters in decay constants and are thus plicated,
for simplicity, we assume that the partition coefficients remain constant
during partial melting. Thus, we only present modal dynamic melting.
238Udecays to stable *%Pb, and *?J decays to stable *"Pb via two
different chains of short-lived intermediate nuclides with a wide range of
half-lives. Among these intermediate nuclides, 23?h and 226Rafrom 238U
and 23'Pa from 23sUare of particular importance to earth sciences. The
half-lives of *'Vh, 226Raand *"Pa are 75,200 y, 1600 y, and 32,800 y,
respectively, and bracket the time scales of geological processes.
Before we work on the uranium decay series, we start with single-
stage radioisotope decay.
. Single-stage Radioisotope Decay
For the decay of N number of radioactive atoms, the rate of decay,
dN ldr , is proportional to the number of atoms N ,
dN
-=-AN,
dr
where A, the decay constant, is essentially the probability of decay per
unit time.
The solution to Eq. () with initial condition N(0)=No is
14
Uranium-series Disequilibrium Modeling 75
N = Nee-*. ()
The number of radiogenic daughter atoms formed, G*, equals the
number of parent atoms consumed:
G* = No - N . ()
Equation () can be re-expressed as
*
No=Ne . ()
Combination of Eq. () and Eq. () yields
G* = N(e* -1).
A useful way of referring to the rate of decay of a radionuclide is the
half-life, t,12,which is the time required for half of the parent atoms to
decay. And according to Eq. (), when N = N0/2, we obtain
In2 -
=--- ()
il il
If the nu