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(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)
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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)
![Check Mark](/static/check-mark.png)
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)
![Check Mark](/static/check-mark.png)
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)
![Check Mark](/static/check-mark.png)
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.
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