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
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1205cd08-0e41-4ad8-bd1c-6b97372ee2c1%2F5e3d2069-92b4-40c3-82c9-3e36778abc9e%2Fn253eb_processed.jpeg&w=3840&q=75)
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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