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Unformatted text preview: positron + silicon-28 + mass number: 28 + 28 atomic number: 15 1 + 14 Since radioactive decay is first order, the integrated rate law for a radioactive decay reaction is given by ln(N/N o ) = -kt where N o is the original number of radioactive nuclides, N is the number that remain at time t, and k is the rate constant for the reaction. The relation between the rate constant and the half-life for a first order reaction is kt 1/2 = ln 2 = 0.693 (1) Calculate the rate constant from the half-life given: half-life = t 1/2 = 27.7 days k = (ln 2 / t 1/2 ) = (0.693 / 27.7 days ) = 2.502E-2 d-1 (2) Calculate the time required for the activity to fall to 8.87 percent of its original value: The activity is directly proportional to the number or radioactive nuclides, N. Let N o be the original number of nuclides. N = 8.87E-2 x N o , where 8.87E-2 = 8.87 / 100 Then N/N o = 8.87E-2 Rearranging ln(N/N o ) = -kt t = -(1/k) x ln(N/N o ) = -(1 / 2.502E-2d-1 ) x ln ( 8.87E-2 ) = 96.8 d...
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