section_path: Mathematics/Universal law/Alternative modes
section_name: Alternative modes
paragraph_text: Alternative modes
  
  In all of the above examples, the initial nuclide decays into just one product. Consider the case of one initial nuclide that can decay into either of two products, that is A → B and A → C in parallel. For example, in a sample of potassium-40, 89.3% of the nuclei decay to calcium-40 and 10.7% to argon-40. We have for all time t:
  
  which is constant, since the total number of nuclides remains constant. Differentiating with respect to time:
  
  defining the total decay constant λ in terms of the sum of partial decay constants λ and λ:
  
  Solving this equation for N:
  
  where N is the initial number of nuclide A. When measuring the production of one nuclide, one can only observe the total decay constant λ. The decay constants λ and λ determine the probability for the decay to result in products B or C as follows:
  
  because the fraction λ / λ of nuclei decay into B while the fraction λ / λ of nuclei decay into C.