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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, At 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 = A= (0.5) where n is the number of half-lives. The equation relating the number of half-lives to time t is n=_t 1/2 where t1/2 is the length of one half-life. ▼ Part C Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years. How long will it take in years for 38.0 % of an Am-241 sample to decay? Express your answer with the appropriate units. ▸ View Available Hint(s) t = Submit ▾ Part D Value t= IMA O A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil? Express your answer with the appropriate units. View Available Hint(s) HA 3 Value Units 1 B) ? Units []? A JV

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, At 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 = A= (0.5) where n is the number of half-lives. The equation relating the number of half-lives to time t is n=_t 1/2 where t1/2 is the length of one half-life. ▼ Part C Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years. How long will it take in years for 38.0 % of an Am-241 sample to decay? Express your answer with the appropriate units. ▸ View Available Hint(s) t = Submit ▾ Part D Value t= IMA O A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil? Express your answer with the appropriate units. View Available Hint(s) HA 3 Value Units 1 B) ? Units []? A JV

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
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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, At 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 = A= (0.5)" where n is the number of half-lives. The equation relating the number of half-lives to time t is n=_t t1/2 where t1/2 is the length of one half-life. ▼ Part C Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years. How long will it take in years for 38.0 % of an Am-241 sample to decay? Express your answer with the appropriate units. ▸ View Available Hint(s) t = Submit ▾ Part D Value t = μA O A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil? Express your answer with the appropriate units. View Available Hint(s) HA 3 Value Units B) ? Units []? A V
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, At 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 = A= (0.5)" where n is the number of half-lives. The equation relating the number of half-lives to time t is n=_t t1/2 where t1/2 is the length of one half-life. ▼ Part C Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years. How long will it take in years for 38.0 % of an Am-241 sample to decay? Express your answer with the appropriate units. ▸ View Available Hint(s) t = Submit ▾ Part D Value t = μA O A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil? Express your answer with the appropriate units. View Available Hint(s) HA 3 Value Units B) ? Units []? A V
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