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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![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, the
amount 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 1
Use 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 2
Calculate the value of the rate constant, k, using the half-life.
Step 3
Calculate the product of time and the rate constant, kt.
Step 4
Calculate the ratio of concentrations before and after time has elapsed.
Step 5
Solve 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bee9e1f-bba9-49ec-9af9-1f33a22fb871%2F330abad6-f5c2-439e-b95b-7dc5eba61c08%2F75rb3xj_processed.png&w=3840&q=75)
Transcribed Image Text: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, the
amount 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 1
Use 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 2
Calculate the value of the rate constant, k, using the half-life.
Step 3
Calculate the product of time and the rate constant, kt.
Step 4
Calculate the ratio of concentrations before and after time has elapsed.
Step 5
Solve 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
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