nuclear.academy

Decay-chain calculator

In preparation. Solves the Bateman equations for a chain of nuclides and plots activity and atom number against time.

For a chain N1N2NnN_1 \to N_2 \to \cdots \to N_n with decay constants λi\lambda_i and only N1(0)0N_1(0) \neq 0:

Nn(t)=N1(0)(i=1n1λi)i=1neλitji(λjλi)N_n(t) = N_1(0) \left(\prod_{i=1}^{n-1} \lambda_i\right) \sum_{i=1}^{n} \frac{e^{-\lambda_i t}}{\prod_{j \neq i} (\lambda_j - \lambda_i)}