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The Kinetics of Radioactive Decayincludes:Calculations Using the First Order Rate Equation:r = k [N]Since the rate of radioactive decay is first order we cansay:r = k [N]Determination of the Rate Constant, kDetermination of the Activity
What is the rate constant ofradioactive decay, k?Radioactive decay obeys a first-order rate law, meaningthat the rate (A) is directly proportional to the number ofreactant (radionuclide) atoms/molecules at any giventime:A = kNk is called a rate constant or specific activityk = rate of decay / N
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 rate constant for the isotope, andN is the amount of radioisotope at the moment when the rate is measured.The rate of decay is often referred to as the activity of the isotope and is often measured in Curies(Ci),one curie = 3.700 x 1010atoms that decay/second.By knowing the amount of radioisotope and the activity of the sample, the rate constant can bedetermined.
Determination of the Rate ConstantExample:A 1.00 g sample of cobalt-60 (59.92 g/mol) has anactivity of 1.1 x 103Ci.Determine the rate constant.First, we need to convert the 1.00 g of sample into number of atomsof cobalt-60 and to convert the activity into numbers of atoms thatdecay per second.No. of atoms Co = weight divided by At. Mass times Avog. No.= (1.00 g )(1 mol /59.92 g)(6.022 x 1023atoms Co-60/mol)no. of atoms of Co= 1.01 x1022atoms
Cont.Since rate of activity is in Ci, (1.1 xCi)express this toatomsone curie = 3.700 x 1010atoms that decay/secondr = (1.1 x 103Ci)(3.700 x 1010atoms/s/Ci)= 4.1 x 1013atoms that decay/sec

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Rate equation, First Order Rate Equation