(a)
Interpretation:
Half-life of the radionuclide has to be determined if after 3.2 days, 1/8 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 11.28EP
Half-life of the radionuclide is 1.1 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 3 half-lives.
In the problem statement it is given that the time is 3.2 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 1.1 days.
Half-life of the given sample is determined.
(b)
Interpretation:
Half-life of the radionuclide has to be determined if after 3.2 days, 1/128 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 11.28EP
Half-life of the radionuclide is 0.46 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 7 half-lives.
In the problem statement it is given that the time is 3.2 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 0.46 day.
Half-life of the given sample is determined.
(c)
Interpretation:
Half-life of the radionuclide has to be determined if after 3.2 days, 1/32 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 11.28EP
Half-life of the radionuclide is 0.64 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 5 half-lives.
In the problem statement it is given that the time is 3.2 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 0.64 day.
Half-life of the given sample is determined.
(d)
Interpretation:
Half-life of the radionuclide has to be determined if after 3.2 days, 1/512 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 11.28EP
Half-life of the radionuclide is 0.36 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 9 half-lives.
In the problem statement it is given that the time is 3.2 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 0.36 day.
Half-life of the given sample is determined.
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Chapter 11 Solutions
Study Guide with Selected Solutions for Stoker's General, Organic, and Biological Chemistry, 7th
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