Ch.20 - Radioactivity and Nuclear Chemistry

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.20 - Radioactivity and Nuclear Chemistry

Problem 38

Chapter 20, Problem 38

Determine whether or not each nuclide is likely to be stable. State your reasons. a. Ti-48 b. Cr-63 c. Sn-102 d. Y-88

Verified step by step guidance

To determine the stability of a nuclide, consider the neutron-to-proton (N/Z) ratio. A stable nuclide typically has an N/Z ratio close to 1 for lighter elements and slightly higher for heavier elements.

For Ti-48: Titanium (Ti) has an atomic number of 22, meaning it has 22 protons. Ti-48 has 48 - 22 = 26 neutrons. Calculate the N/Z ratio: \( \frac{26}{22} \). Compare this ratio to the typical stable range for elements around titanium.

For Cr-63: Chromium (Cr) has an atomic number of 24, meaning it has 24 protons. Cr-63 has 63 - 24 = 39 neutrons. Calculate the N/Z ratio: \( \frac{39}{24} \). Check if this ratio falls within the stable range for elements around chromium.

For Sn-102: Tin (Sn) has an atomic number of 50, meaning it has 50 protons. Sn-102 has 102 - 50 = 52 neutrons. Calculate the N/Z ratio: \( \frac{52}{50} \). Determine if this ratio is typical for stable isotopes of tin.

For Y-88: Yttrium (Y) has an atomic number of 39, meaning it has 39 protons. Y-88 has 88 - 39 = 49 neutrons. Calculate the N/Z ratio: \( \frac{49}{39} \). Evaluate if this ratio is within the stable range for yttrium isotopes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Stability

Nuclear stability refers to the ability of a nuclide to remain unchanged over time without undergoing radioactive decay. Stable nuclides have a balanced ratio of protons to neutrons, which minimizes the forces that can lead to instability. Understanding the stability of a nuclide is crucial for predicting its behavior and longevity.

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. A higher binding energy indicates a more stable nucleus, as it suggests that the nucleons are held together more tightly. This concept helps in assessing the stability of different isotopes based on their nuclear structure.

Magic Numbers

Magic numbers are specific numbers of nucleons (protons or neutrons) that result in particularly stable configurations within a nucleus. These numbers correspond to complete shells of nucleons, leading to enhanced stability. Recognizing magic numbers can aid in predicting the stability of isotopes, as nuclides with these numbers are often more stable.

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Related Practice

Textbook Question

Fill in the missing particles in each nuclear equation. d. ⁷⁵₃₅Br → ____ + ⁰₊₁e

Textbook Question

Predict a likely mode of decay for each unstable nuclide. b. Ru-90 c. P-27 d. Sn-100

Textbook Question

The first six elements of the first transition series have the following number of stable isotopes:

Element Number of Stable Isotopes

Sc 1

Ti 5

V 1

Cr 3

Mn 1

Fe 4

Explain why Sc, V, and Mn each have only one stable isotope while the other elements have several.

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Textbook Question

Determine whether or not each nuclide is likely to be stable. State your reasons. a. Mg-26 b. Ne-25 c. Co-51

Textbook Question

Predict a likely mode of decay for each unstable nuclide. a. Mo-109

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Textbook Question

Determine whether or not each nuclide is likely to be stable. State your reasons. d. Te-124