Calculations Using the First Order RateEquation: r = k[N]•Since the rate of radioactive decay is first order we can say:r = k[N]1,where r is a measurement of the rate of decay, k is the first order rateconstant for the isotope, and N is the amount of radioisotope at themoment when the rate is measured.•The rate of decay is often referred to as the activity of the isotope andis often measured in Curies (Ci), one curie = 3.700 x 1010atoms thatdecay/second.By knowing the amount of radioisotope and theactivity of the sample, the rate constant can be determined.
Determination of the Rate ConstantExample:A 1.00 g sample of cobalt-60 (59.92 g/mol) has an activity of1.1 x 103Ci.Determine the rate constant.•First, we need to convert the 1.00 g of sample into number of atoms ofcobalt-60 and to convert the activity into numbers of atoms that decayper second.(1.00 g Co-60)(1 mol Co-60/59.92 g)(6.022 x 1023atoms Co-60/mol) =1.01 x 1022atoms(1.1 x 103Ci)(3.700 x 1010atoms/s/Ci) = 4.1 x 1013atoms that decay/sec
•Second, we can then use the first-order rate equation to find the rateconstant, k4.1 x 1013atoms decaying/sec = k[1.01 x 1022atoms]k = 4.1 x 10-9s-1
Determination of the ActivityExample:Determine the activity (in Curies) of a 2.00 mg sample of Cobalt-60.•First, we need to convert the 2.00 mg sample of cobalt-60 into numbers of atoms.(2.00 mg Co-60)(1 g/1000 mg)(1 mol/59.92 g)(6.022 x 1023atoms/mol) = 2.01 x1019atoms