Tritium Assay Analysis by PVT Mass Spectrometer cont'd

DOE-HDBK-1129-99

Substituting Equation {1} into Equation {2}, we have

n(TotCAnlDa) = n(TotCSmplDa) - n(T2CSmplDa) + n(T2CSmplDa) x (2 - e((t x ln(0.5))/4500.88))

Rearranging the equation, it becomes

n(TotCAnlDa) = n(TotCSmplDa) + n(T2CSmplDa) x (1 - e((t x ln(0.5))/4500.88))

{4}

Substituting Equation {3} into Equation {4}, we have

((t x ln(0.5))/4500.88)

((t xln(0.5))/4500.88)

100 (n(T2CSmplDa) e

)/ m%(T2MAnlDa)= n(TotCSmplDa) + n(T2CSmplDa) (1- e

)

Multiplying through by m%(T2MAnlDa), it becomes

((t x ln(0.5))/4500.88)

((t x

100 (n(T2CSmplDa) e

)= m%(T2MAnlDa) n(TotCSmplDa) + m%(T2MAnlDa) n(T2CSmplDa) (1- e

ln(0.5))/4500.88)

)

Rearranging and factoring, we have

(n(TotCSmplDa) x m%(T2MAnlDa))/((e((t x ln(0.5))/4500.88) x (100 + m%(T2MAnlDa))) -

n(T2CSmplDa) =

m%(T2MAnlDa))

The quantity of tritium in grams is then the number of moles of tritium on the Sampling Date,

n(T2CSmplDa),,multiplied by the gram molecular weight of tritium (6.03210 g) or

Grams T2 On Sampling Date = 6.0321 x

(PV/zRT) x

(m%(T2MAnlDa))

((t x ln(0.5))/4500.88)

x (100 + m%(T2MAnlDa))] - m%(T2MAnlDa)

If a container has pure tritium mixed with other non-decaying and non-chemically reacting gases

on the Book Value Date, sampled on the Sample Date and analyzed on the Analysis Date, then

the gram of tritium in the container on the Sample Date can be calculated using the derived

formula, the PV/zRT data and the m%(T2MAnlDa) data measured on the Analysis Date.

Figure C-2 is a graph of the changes in the moles of material taking place in a container of pure

T2 versus time over a period of six tritium half-lifes. The graph shows the moles of tritium

decreasing from 1.0 and approaching 0.0, the 3He increasing from 0.0 and approaching 2.0, and

the total moles increasing from 1.0 and approaching 2.0.

C-9