Radioactive decay is a first-order process. Radioactive decay kinetics is described by the same mathematics as chemical reaction kinetics. In a sample where the volume does not change, the concentration of a radioactive isotope, R, is proportional to all of these quantities: the radioactivity, A, the number of radioactive particles, N, theamount of radioactive particles, n, and the mass of the radioactive isotope, m. Therefore, the ratio of any of these quantities to its initial value is equal to the ratio of any other quantity to its initial value. That is,This means that the ratio of concentrations it is the same as the ratio of masses and can be used to calculate the mass of a radioisotope after a given time, given the initial mass.Step 1Use the integrated rate law equation for a first order reaction. In this case, [R]; represents the concentration of gold-198 present at any particular time and [R], is the initial concentration.Step 2Calculate the value of the rate constant, k, using the half-life.Step 3Calculate the product of time and the rate constant, kt.Step 4Calculate the ratio of concentrations before and after time has elapsed.Step 5Solve for the mass of gold-198 remaining, Rt.Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days?mg

Radioactive disintegration reactions are first order reactions. Half life of first order reaction is…

Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days? mg

Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days? mg

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter18: Chemical Kinetics

Section: Chapter Questions

Problem 6P

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Similar questions

Explain why half-lives are not normally used to describe reactions other than first order.
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When formic acid is heated, it decomposes to hydrogen and carbon dioxide in a first-order decay: HCOOH(g)CO2(g)+H2(g) The rate of reaction is monitored by measuring the total pressure in the reaction container. Time (s) Pressure (torr) 0 220 50 324 100 379 150 408 200 423 250 431 300 435 Calculate the rate constant and half-life in seconds for the reaction. At the start of the reaction (time = 0), only formic acid is present. (HINT: Find the partial pressure of formic acid using Dalton's law of partial pressure and the reaction stoichiometry to find PHCOOH at each time.)
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