Problem 82 - General Chemistry: Principles and Modern Applications

Question

Of the following nuclides, the highest nuclear binding energy per nucleon is found in (a) \(_{1}^{3} \mathrm{H} ;\) (b) \(_{8}^{16} \mathrm{O} ;\) (c) \(_{26}^{56} \mathrm{Fe}\); (d) \(_{92}^{235} \mathrm{U}\).

Step-by-Step Solution

Answer

The nuclide with the highest nuclear binding energy per nucleon is \(_{26}^{56} \mathrm{Fe}\).

Step 1: Understanding the information

The task gives us four nuclides: Tritium \(_{1}^{3} \mathrm{H}\), Oxygen \(_{8}^{16} \mathrm{O}\), Iron \(_{26}^{56} \mathrm{Fe}\), and Uranium \(_{92}^{235} \mathrm{U}\). We need to determine which one of these has the highest nuclear binding energy per nucleon.

Step 2: Refer to the binding energy curve

The binding energy curve charts binding energy per nucleon against atomic number. First, it increases, reaching a maximum at Iron-56 (\(_{26}^{56} \mathrm{Fe}\)), then it decreases for elements with higher atomic numbers.

Step 3: Apply knowledge of the binding energy curve to given nuclides

According to the curve, the binding energy per nucleon is highest for Iron-56 (\(_{26}^{56} \mathrm{Fe}\)), lower for elements lighter than iron like Tritium (\(_{1}^{3} \mathrm{H}\)) and Oxygen (\(_{8}^{16} \mathrm{O}\)), and even lower for heavier elements like Uranium (\(_{92}^{235} \mathrm{U}\)).

Key Concepts

Nuclides

When discussing nuclear physics, the term "nuclides" comes up frequently. A nuclide refers to a specific type of atomic nucleus, defined by its number of protons (atomic number) and neutrons. This means that each nuclide is characterized by a unique combination of these two subatomic particles. Understanding nuclides is crucial because they form the foundation of nuclear chemistry and physics. They help in identifying the stability and energy characteristics of atoms.

Nuclides are often represented using the notation \(_{Z}^{A}X\), where:

• \(Z\) is the atomic number (number of protons)
• \(A\) is the mass number (total number of protons and neutrons)
• \(X\) is the chemical symbol of the element

This notation gives clarity on the composition of the nucleus of each element, making it easier to compare and understand their properties, especially when discussing concepts like nuclear binding energy.

Iron-56

Iron-56 is a special nuclide often referenced in the study of nuclear physics and chemistry. It is denoted as \(_{26}^{56} \, \mathrm{Fe}\), where it consists of 26 protons and 30 neutrons. This particular nuclide is significant because it has one of the highest binding energies per nucleon. Binding energy per nucleon is an indicator of the stability of a nucleus - the higher it is, the more stable the nucleus.

In fact, Iron-56 is considered to be the most stable nuclide in existence, at least in terms of nuclear binding energy. This results from the optimal ratio and distribution of protons and neutrons within its nucleus. Due to its stability, it is prevalent in the universe and commonly discussed in the context of stellar nuclear processes, where many elements form and degrade based on their stability relative to Iron-56.

Binding Energy Curve

The concept of the "Binding Energy Curve" is essential for understanding the stability of different nuclides. This curve represents the binding energy per nucleon plotted against the atomic number of different elements. Initially, as the atomic number increases, so does the binding energy per nucleon. This trend reaches its peak at Iron-56, which holds the maximum value.

• This indicates that Iron-56 is the most stable, with a strong nuclear force holding together its protons and neutrons.
• After Iron-56, the binding energy per nucleon begins to decrease as elements become heavier.

This decrease implies that the nuclei of heavier elements, such as Uranium-235, are less stable due to the excess of protons and higher repulsive forces. Understanding the binding energy curve is crucial for comprehending why certain elements undergo processes like nuclear fission while others, like Iron-56, do not actively engage in such reactions.