Branching Ratios And Partial Activities — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Branching Ratios and Partial Activities This formula applies to any radioactive nucleus that decays via multiple competing pathways (modes), such as electron capture, alpha decay, or beta decay. The total decay rate (or total activity, A total ) is the sum of the decay rates for all individual modes. The total decay constant is defined as the sum of the partial decay constants: total = i. The branching ratio (b i) is defined as the fraction of total decays that occur through a specific mode i. This ratio is calculated by dividing the partial decay constant by the total decay constant: b i = i / total . The partial activity (A i) is then found by multiplying the total activity by the corresponding branching ratio: A i = b i A total . All decay constants ( i) must be non-negative. The total decay constant ( total ) must be greater than zero for decay to occur. The sum of all branching ratios must equal unity: b i = 1. Confusing the decay constant ( ) with the half-life (T 1/2 ). Assuming that the partial activity (A i) is independent of the total activity (A total ). Treating the branching ratio (b i) as a decay constant itself (it is unitless).