AA_{o} etAA_{o} etAA_{o}etlnAA_{o}ttlnAA_{o}t_{1/2}ln12t_{1/2}ln 20.693RADIOACTIVITYDOE-HDBK-1019/1-93 Atomic and Nuclear PhysicsNP-01Page 32Rev. 0Since the activity and the number of atoms are always proportional, they may be usedinterchangeably to describe any given radionuclide population. Therefore, the following is true.(1-5)where:A=activity present at time tA=activity initially presento=decay constant (time )-1t=time RadioactiveHalf-LifeOne of the most useful terms for estimating how quickly a nuclide will decay is the radioactivehalf-life. The radioactive half-life is defined as the amount of time required for the activity todecrease to one-half of its original value. A relationship between the half-life and decay constantcan be developed from Equation (1-5). The half-life can be calculated by solving Equation (1-5)for the time, t, when the current activity, A, equals one-half the initial activity A ._{o}First, solve Equation (1-5) for t.If A is equal to one-half of A , then A/A is equal to one-half. Substituting this in the equationooabove yields an expression for t .1/2(1-6)