Lesson 4 ◆ 4.3 Calculating Fission Product Inventories

For hand calculations and exam-style problems, we make two simplifying assumptions:

Assumption (a): The only source of fission product ii is direct production from fission of 235^{235}U (we ignore precursor decay and neutron capture pathways).

Assumption (b): We neglect burn-up of fission product ii (i.e. we ignore neutron absorption by the fission product).

With these assumptions, the general equation reduces to:

dNdt=R−λN\frac{dN}{dt} = R - \lambda N

where:

  • RR = production rate = Fission Rate ×\times Yield Factor = F⋅YF \cdot Y
  • λ\lambda = decay constant of the fission product
  • NN = number of atoms of the fission product

This is a first-order linear ODE that you have seen in radiation science. The solution, starting from N(0)=0N(0) = 0, is:

N(t)=Rλ(1−e−λt)\boxed{N(t) = \frac{R}{\lambda}\left(1 - e^{-\lambda t}\right)}

Converting to activity A=λNA = \lambda N:

A(t)=R(1−e−λt)\boxed{A(t) = R\left(1 - e^{-\lambda t}\right)}

where AA is in becquerels (Bq) if RR is in atoms per second (i.e. disintegrations per second).