section_path: Mathematics/Decay timing: definitions and relations/Time constant and mean-life
section_name: Time constant and mean-life
paragraph_text: Time constant and mean-life
  
  For the one-decay solution A → B:
  
  the equation indicates that the decay constant λ has units of t, and can thus also be represented as 1/ τ, where τ is a characteristic time of the process called the time constant.
  
  In a radioactive decay process, this time constant is also the mean lifetime for decaying atoms. Each atom "lives" for a finite amount of time before it decays, and it may be shown that this mean lifetime is the arithmetic mean of all the atoms' lifetimes, and that it is τ, which again is related to the decay constant as follows:
  
  This form is also true for two-decay processes simultaneously A → B + C, inserting the equivalent values of decay constants (as given above)
  
  into the decay solution leads to: