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Chapter 1: Problem 6

Specific activity is the radioactivity as expressed in disintegrations/second per mole of a compound or atom. Which of the following has the highest specific activity? a. \({ }^{125} \mathrm{I}\left(\mathrm{t}_{1 / 2}=60\right.\) days) b. \({ }^{35} \mathrm{~S}\left(\mathrm{t}_{1 / 2}=62\right.\) days \()\) c. \({ }^{3} \mathrm{H}\left(\mathrm{t}_{1 / 2}=12\right.\) years \()\) d. \({ }^{14} \mathrm{C}\left(\mathrm{t}_{1 / 2}=5000\right.\) years \()\) e. \(^{131} \mathrm{I}\left(\mathrm{t}_{1 / 2}=8\right.\) days \()\)

Short Answer

Expert verified
{ }^{131} \text{I}

Step by step solution

01

Understand Specific Activity

Specific activity is defined as the radioactivity per mole of a substance. It can be calculated using the half-life of the isotopes. Shorter half-lives indicate higher decay rates and therefore higher specific activities.
02

Half-Life and Radioactivity Relationship

Radioactivity is inversely proportional to the half-life. The shorter the half-life, the higher the disintegration per second (radioactivity).
03

Compare Half-Lives

Review the given half-lives of the isotopes:a. \({}^{125}\mathrm{I} (\mathrm{t}_{1/2} = 60 \text{ days})\) b. \({}^{35}\mathrm{S} (\mathrm{t}_{1/2} = 62 \text{ days})\) c. \({}^{3}\mathrm{H} (\mathrm{t}_{1/2} = 12 \text{ years})\) d. \({}^{14}\mathrm{C} (\mathrm{t}_{1/2} = 5000 \text{ years})\) e. \({}^{131}\mathrm{I} (\mathrm{t}_{1/2} = 8 \text{ days})\)
04

Identify the Shortest Half-Life

From the list, identify that \({}^{131}\mathrm{I}\) has the shortest half-life of 8 days.
05

Conclusion

Since \({}^{131}\mathrm{I}\) has the shortest half-life, it will have the highest specific activity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

What is Radioactivity?
Radioactivity refers to the process by which unstable atomic nuclei lose energy by emitting radiation. This radiation can be in the form of alpha particles, beta particles, or gamma rays. It's a natural process that occurs in various elements, particularly in radioactive isotopes.
  • The atomic nucleus becomes stable by emitting radiation.
  • Radioactivity is a measure of how much radiation a material emits.
Marie Curie and Henri Becquerel were pioneers in studying this phenomenon. By understanding radioactivity, we can grasp how substances and their atoms decay over time.
Understanding Half-Life
The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay. Half-life is a crucial concept in understanding the rate of radioactive decay.
  • A shorter half-life means the substance decays faster.
  • A longer half-life indicates slower decay rates.
For example, if a substance has a half-life of 10 years, after 10 years, only half of the original radioactive atoms will remain. After another 10 years, only a quarter will remain. Using this concept, we can predict the activity of a radioactive sample over time.
What are Isotopes?
Isotopes are different forms of the same element, which have the same number of protons but different numbers of neutrons in their nuclei. This difference in neutron number results in varying atomic masses and sometimes in different nuclear properties. Some isotopes are stable, while others are radioactive.
  • Stable isotopes do not change over time.
  • Radioactive isotopes decay over time, emitting radiation.
For instance, Carbon-12 and Carbon-14 are both isotopes of carbon. Carbon-12 is stable, whereas Carbon-14 is radioactive and is used in radiocarbon dating. This diversity in isotopes allows scientists to utilize them in various fields, including medicine and archaeology.

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