Hi Niels Wolff ,

Mathematically, if your independent parameters are H, r, C=1.5e-15, E, n, B, M=exp(-μd), and their uncertainties are ΔH, Δr, ΔC, ΔE, Δn, ΔB, ΔM, then

• A=(H r^2)/(C E n B M)
• (ΔA/A)^2=(ΔH/H)^2+(2*Δr/r)^2+(ΔC/C)^2+(ΔE/E)^2+(Δn/n)^2+(ΔB/B)^2+(ΔM/M)^2.

To know ΔA, you need input all uncertainties of the parameters used for determining A. If there is little or no uncertainty in a parameter, then the value of the term for that parameter is 0. It is clear from the form of the equation that if the relative uncertainty of one parameter is large, then the relative uncertainty of A is determined almost entirely by the effect of that term.

I see two problems that might prevent you to obtain accurate activity values and that could make impossible the evaluation of the uncertainty.

The first one is the formula itself, which is an approximate formula, very useful for fast routine evaluations, but not suitable for accurate calculations.

The correct formula would be

gamma.A.B.exp(-mu.d)/r^2

where gamma is the doserate constant of the radionuclide.

The second problem is that the accuracy of the build-up factor is often not known, in particular because often the true experimental setup does not coincide exactly with the setup used for the determination of B.

Usually, using of the partial differentiation method to equate the value calculation is most appropriate to obtain the uncertainty value.