(a)
Interpretation:
Half-life of the radionuclide has to be determined if after 5.4 days, 1/16 fraction of undecayed nuclide is present.
Concept Introduction:
Radioactive nuclides undergo disintegration by emission of radiation. All the radioactive nuclide do not undergo the decay at a same rate. Some decay rapidly and others decay very slowly. The nuclear stability can be quantitatively expressed by using the half-life.
The time required for half quantity of the radioactive substance to undergo decay is known as half-life. It is represented as
The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,
(a)
Answer to Problem 11.27EP
Half-life of the radionuclide is 1.4 days.
Explanation of Solution
Number of half-lives can be determined as shown below,
As the bases are equal, the power can be equated. This gives the number of half-lives that have elapsed as 4 half-lives.
In the problem statement it is given that the time is 5.4 days. From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,
Therefore, the half-life of the given sample is determined as 1.4 days.
Half-life of the given sample is determined.
(b)
Interpretation:
Half-life of the radionuclide has to be determined if after 5.4 days, 1/64 fraction of undecayed nuclide is present.
Concept Introduction:
Radioactive nuclides undergo disintegration by emission of radiation. All the radioactive nuclide do not undergo the decay at a same rate. Some decay rapidly and others decay very slowly. The nuclear stability can be quantitatively expressed by using the half-life.
The time required for half quantity of the radioactive substance to undergo decay is known as half-life. It is represented as
The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,
(b)
Answer to Problem 11.27EP
Half-life of the radionuclide is 0.90 day.
Explanation of Solution
Number of half-lives can be determined as shown below,
As the bases are equal, the power can be equated. This gives the number of half-lives that have elapsed as 6 half-lives.
In the problem statement it is given that the time is 5.4 days. From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,
Therefore, the half-life of the given sample is determined as 0.90 day.
Half-life of the given sample is determined.
(c)
Interpretation:
Half-life of the radionuclide has to be determined if after 5.4 days, 1/256 fraction of undecayed nuclide is present.
Concept Introduction:
Radioactive nuclides undergo disintegration by emission of radiation. All the radioactive nuclide do not undergo the decay at a same rate. Some decay rapidly and others decay very slowly. The nuclear stability can be quantitatively expressed by using the half-life.
The time required for half quantity of the radioactive substance to undergo decay is known as half-life. It is represented as
The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,
(c)
Answer to Problem 11.27EP
Half-life of the radionuclide is 0.68 day.
Explanation of Solution
Number of half-lives can be determined as shown below,
As the bases are equal, the power can be equated. This gives the number of half-lives that have elapsed as 8 half-lives.
In the problem statement it is given that the time is 5.4 days. From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,
Therefore, the half-life of the given sample is determined as 0.68 day.
Half-life of the given sample is determined.
(d)
Interpretation:
Half-life of the radionuclide has to be determined if after 5.4 days, 1/1024 fraction of undecayed nuclide is present.
Concept Introduction:
Radioactive nuclides undergo disintegration by emission of radiation. All the radioactive nuclide do not undergo the decay at a same rate. Some decay rapidly and others decay very slowly. The nuclear stability can be quantitatively expressed by using the half-life.
The time required for half quantity of the radioactive substance to undergo decay is known as half-life. It is represented as
The equation that relates amount of decayed radioactive material, amount of undecayed radioactive material and the time elapsed can be given as,
(d)
Answer to Problem 11.27EP
Half-life of the radionuclide is 0.54 day.
Explanation of Solution
Number of half-lives can be determined as shown below,
As the bases are equal, the power can be equated. This gives the number of half-lives that have elapsed as 10 half-lives.
In the problem statement it is given that the time is 5.4 days. From the number of half-lives elapsed and the total time given, the length of one half-life can be calculated as shown below,
Therefore, the half-life of the given sample is determined as 0.54 day.
Half-life of the given sample is determined.
Want to see more full solutions like this?
Chapter 11 Solutions
Study Guide with Selected Solutions for Stoker's General, Organic, and Biological Chemistry, 7th
- General, Organic, and Biological ChemistryChemistryISBN:9781285853918Author:H. Stephen StokerPublisher:Cengage LearningWorld of Chemistry, 3rd editionChemistryISBN:9781133109655Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCostePublisher:Brooks / Cole / Cengage LearningChemistry for Today: General, Organic, and Bioche...ChemistryISBN:9781305960060Author:Spencer L. Seager, Michael R. Slabaugh, Maren S. HansenPublisher:Cengage Learning
- Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage LearningChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage Learning