Atomic and Nuclear PhysicsDOE-HDBK-1019/1-93RADIOACTIVITYRev. 0Page 31NP-01The activity(A) of a sample is the rate of decay of that sample. This rate of decay is usuallymeasured in the number of disintegrations that occur per second. For a sample containingmillions of atoms, the activity is the product of the decay constant and the number of atomspresent in the sample.The relationship between the activity, number of atoms, and decay constant is shown inEquation (1-3).A =N(1-3)where:A =Activity of the nuclide (disintegrations/second)=decay constant of the nuclide (second )-1N =Number of atoms of the nuclide in the sampleSince is a constant, the activity and the number of atoms are always proportional.UnitsofMeasurementforRadioactivityTwo common units to measure the activity of a substance are the curie (Ci) and becquerel (Bq).A curie is a unit of measure of the rate of radioactive decay equal to 3.7 x 10 disintegrations10per second. This is approximately equivalent to the number of disintegrations that one gram ofradium-226 will undergo in one second. A becquerel is a more fundamental unit of measure ofradioactive decay that is equal to 1 disintegration per second. Currently, the curie is morewidely used in the United States, but usage of the becquerel can be expected to broaden as themetric system slowly comes into wider use. The conversion between curies and becquerels isshown below.1 curie = 3.7 x 10 becquerels10VariationofRadioactivityOverTimeThe rate at which a given radionuclide sample decays is stated in Equation (1-3) as being equalto the product of the number of atoms and the decay constant. From this basic relationship itis possible to use calculus to derive an expression which can be used to calculate how thenumber of atoms present will change over time. The derivation is beyond the scope of this text,but Equation (1-4) is the useful result.(1-4)where:N=number of atoms present at time tN=number of atoms initially presento=decay constant (time )-1t=time