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Chapter 16: Problem 28

Of all of the elements and all of their isotopes, which would take the most energy to convert its nucleus into isolated nucleons? Explain why.

Short Answer

Expert verified
The element that would take the most energy to convert its nucleus into isolated nucleons is Iron-56 (\(^{56}\textrm{Fe}\)), as it has the highest binding energy per nucleon. This is due to an optimal balance between the attractive strong nuclear force and the repulsive electrostatic force between the protons, resulting in the most stable nucleus among all elements and their isotopes.

Step by step solution

01

Understanding Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is the measure of the stability of a nucleus. A higher binding energy per nucleon means a more stable nucleus, and therefore, more energy required to break it apart into isolated nucleons.
02

Finding the Isotope with Highest Binding Energy per Nucleon

To find the isotope with the highest binding energy per nucleon, we need to analyze the binding energy per nucleon curve. The curve is a plot of binding energy per nucleon against the mass number of different elements and their isotopes. The peak of the curve represents the isotope with the highest binding energy per nucleon, and hence, the most stable nucleus.
03

Identifying the Isotope with the Highest Binding Energy per Nucleon

When we analyze the binding energy per nucleon curve, we find that the peak occurs at the isotope of iron, specifically Iron-56 (\(^{56}\textrm{Fe}\)). This means that Iron-56 has the highest binding energy per nucleon, and therefore, will require the most energy to break its nucleus into isolated nucleons.
04

Explaining the Result

Iron-56 has the highest binding energy per nucleon because it has an optimal balance between the attractive strong nuclear force and the repulsive electrostatic force between the protons. This balance makes it the most stable nucleus among all the elements and their isotopes. As a result, it takes the most energy to convert its nucleus into isolated nucleons.

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Most popular questions from this chapter

Radioactivity is often called ionizing radiation. Why?

The argon isotope \({ }_{18}^{37} \mathrm{Ar}\) undergoes electron capture. (a) Write a nuclear reaction for this process. (b) Where on the band of stability would you expect to find \({ }_{18}^{37} \mathrm{Ar}\) ? (c) What is the daughter nucleus produced?

Why does nuclear fission often proceed as a chain reaction?

What in Einstein's energy equation ensures that a tiny mass defect results in a tremendous amount of energy? Explain.

Discuss the benefits and problems associated with using nuclear fission to produce electricity.
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