Textbook Question
Predict a likely mode of decay for each unstable nuclide. b. Ru-90 c. P-27 d. Sn-100
Ch.20 - Radioactivity and Nuclear Chemistry
Chapter 20, Problem 43
Which nuclide in each pair would you expect to have the longer half-life? a. Cs-113 or Cs-125 b. Fe-62 or Fe-70
Verified step by step guidance1
Step 1: Understand the concept of half-life. The half-life of a nuclide is the time required for half of the radioactive atoms in a sample to decay. Generally, nuclides with a higher neutron-to-proton ratio or those that are closer to stability tend to have longer half-lives.
Step 2: Analyze the stability of the nuclides. For each pair, compare the neutron-to-proton ratio and how close each nuclide is to the line of stability on the chart of nuclides. Nuclides closer to the line of stability typically have longer half-lives.
Step 3: Compare Cs-113 and Cs-125. Determine the neutron-to-proton ratio for each nuclide. Cs-125 has more neutrons than Cs-113, which might make it more stable and potentially give it a longer half-life.
Step 4: Compare Fe-62 and Fe-70. Again, calculate the neutron-to-proton ratio for each nuclide. Fe-70 has more neutrons than Fe-62, which could make it more stable and possibly result in a longer half-life.
Step 5: Consider the general trend that heavier isotopes (those with more neutrons) often have longer half-lives due to increased stability, but also take into account specific nuclear properties that might affect stability.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Half-Life
Half-life is the time required for half of the nuclei in a sample of a radioactive substance to decay. It is a key concept in nuclear chemistry and helps in understanding the stability of nuclides. A longer half-life indicates a more stable nuclide, while a shorter half-life suggests a more unstable one that decays rapidly.
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Zero-Order Half-life
Nuclear Stability
Nuclear stability refers to the tendency of a nucleus to remain intact without undergoing radioactive decay. Factors influencing stability include the ratio of neutrons to protons and the overall binding energy of the nucleus. Generally, nuclides with a balanced neutron-to-proton ratio are more stable and exhibit longer half-lives.
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Isotopes
Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons. This difference in neutron count can affect the stability and half-life of the isotopes. For example, isotopes of cesium (Cs-113 and Cs-125) and iron (Fe-62 and Fe-70) can exhibit varying half-lives due to their distinct nuclear compositions.
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Related Practice
Textbook Question
Predict a likely mode of decay for each unstable nuclide. a. Sb-132 b. Te-139 d. Ba-123
Textbook Question
Predict a likely mode of decay for each unstable nuclide. c. Fr-202
Textbook Question
Which nuclide in each pair would you expect to have the longer half-life? a. Cs-149 or Cs-139 b. Fe-45 or Fe-52
Textbook Question
One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will it take for the amount of U-235 to reach 10.0% of its initial amount?