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If a substance is radioactive, this means that the nucleus is unstable and will therefore decay by any number of processes (alpha decay, beta decay, etc.). The decay of radioactive elements follows first-order kinetics. Therefore, the rate of decay can be described by the same integrated rate equations and half-life equations that are used to describe the rate of first-order chemical reactions: =-kt and In A₁ Ao 0.693 k t1/2 = where Ao is the initial amount or activity, A, is the amount or activity at time t, and k is the rate constant. By manipulation of these equations (substituting 0.693/t1/2 for k in the integrated rate equation), we can arrive at the following formula: fraction remaining = = (0.5) A₁ Ao where n is the number of half-lives. The equation relating the number of half-lives to time t is t 11/2 where t1/2 is the length of one half-life. n= ▾ Part A You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 74.5 minutes, what is the half-life of this substance? Express your answer with the appropriate units. ▸ View Available Hint(s) t1/2 = Value Submit Part B μÀ Ao = Submit HA 3 An unknown radioactive substance has a half-life of 3.20 hours. If 48.9 g of the substance is currently present, what mass Ao was present 8.00 hours ago? Express your answer with the appropriate units. ▸ View Available Hint(s) Value → Units P) ? Units www. ?

If a substance is radioactive, this means that the nucleus is unstable and will therefore decay by any number of processes (alpha decay, beta decay, etc.). The decay of radioactive elements follows first-order kinetics. Therefore, the rate of decay can be described by the same integrated rate equations and half-life equations that are used to describe the rate of first-order chemical reactions: =-kt and In A₁ Ao 0.693 k t1/2 = where Ao is the initial amount or activity, A, is the amount or activity at time t, and k is the rate constant. By manipulation of these equations (substituting 0.693/t1/2 for k in the integrated rate equation), we can arrive at the following formula: fraction remaining = = (0.5) A₁ Ao where n is the number of half-lives. The equation relating the number of half-lives to time t is t 11/2 where t1/2 is the length of one half-life. n= ▾ Part A You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 74.5 minutes, what is the half-life of this substance? Express your answer with the appropriate units. ▸ View Available Hint(s) t1/2 = Value Submit Part B μÀ Ao = Submit HA 3 An unknown radioactive substance has a half-life of 3.20 hours. If 48.9 g of the substance is currently present, what mass Ao was present 8.00 hours ago? Express your answer with the appropriate units. ▸ View Available Hint(s) Value → Units P) ? Units www. ?

Chemistry & Chemical Reactivity
Chemistry & Chemical Reactivity
10th Edition
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Chapter25: Nuclear Chemistry
Section: Chapter Questions
Problem 78SCQ
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If a substance is radioactive, this means that the nucleus is unstable and will therefore decay by any number of processes (alpha decay, beta decay, etc.). The decay of radioactive elements follows first-order kinetics. Therefore, the rate of decay can be described by the same integrated rate equations and half-life equations that are used to describe the rate of first-order chemical reactions: and A₁ In = -kt Ao t1/2 = 0.693 k where Ao is the initial amount or activity, A, is the amount or activity at time t, and k is the rate constant. By manipulation of these equations (substituting 0.693/t1/2 for k in the integrated rate equation), we can arrive at the following formula: fraction remaining : = A₁ A₂ n = = (0.5) where n is the number of half-lives. The equation relating the number of half-lives to time t is t 11/2 where t1/2 is the length of one half-life. ▾ Part A You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 74.5 minutes, what is the half-life of this substance? Express your answer with the appropriate units. ► View Available Hint(s) Submit t1/2 = Value Part B O Ao = HÅ Submit An unknown radioactive substance has a half-life of 3.20 hours. If 48.9 g of the substance is currently present, what mass Ao was present 8.00 hours ago? Express your answer with the appropriate units. ▸ View Available Hint(s) μA Value Units 4 Units ? ?
Transcribed Image Text:If a substance is radioactive, this means that the nucleus is unstable and will therefore decay by any number of processes (alpha decay, beta decay, etc.). The decay of radioactive elements follows first-order kinetics. Therefore, the rate of decay can be described by the same integrated rate equations and half-life equations that are used to describe the rate of first-order chemical reactions: and A₁ In = -kt Ao t1/2 = 0.693 k where Ao is the initial amount or activity, A, is the amount or activity at time t, and k is the rate constant. By manipulation of these equations (substituting 0.693/t1/2 for k in the integrated rate equation), we can arrive at the following formula: fraction remaining : = A₁ A₂ n = = (0.5) where n is the number of half-lives. The equation relating the number of half-lives to time t is t 11/2 where t1/2 is the length of one half-life. ▾ Part A You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 74.5 minutes, what is the half-life of this substance? Express your answer with the appropriate units. ► View Available Hint(s) Submit t1/2 = Value Part B O Ao = HÅ Submit An unknown radioactive substance has a half-life of 3.20 hours. If 48.9 g of the substance is currently present, what mass Ao was present 8.00 hours ago? Express your answer with the appropriate units. ▸ View Available Hint(s) μA Value Units 4 Units ? ?
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