Problem 53 - Chemistry and Chemical Reactivity

Question

Deuterium nuclei \(\left(_{1}^{2} \mathrm{H}\right)\) are particularly effective as bombarding particles to carry out nuclear reactions. ng equations: (a) \(^{114}_{48} \mathrm{Cd}+\\_{2}^{1} \mathrm{H} \longrightarrow ?+\\_{1}^{1} \mathrm{H}\) (b) \(_{3}^{6} \mathrm{Li}+\\_{2}^{1} \mathrm{H} \longrightarrow ?+\\_{1}^{0} \mathrm{n}\) (c) \(\\_{40}^{20} \mathrm{Ca}+\\_{2}^{1} \mathrm{H} \longrightarrow_{11}^{38} \mathrm{K}+?\) (d) \(?+\\_{2}^{1} \mathrm{H} \longrightarrow_{30}^{65} \mathrm{Zn}+\gamma\)

Step-by-Step Solution

Answer

(a) \( _{48}^{115} \mathrm{In} \), (b) \( _{4}^{7} \mathrm{Be} \), (c) \( _{2}^{4} \mathrm{He} \), (d) \( _{29}^{63} \mathrm{Cu} \)

Step 1: Understanding the Problem

For each nuclear reaction, we need to determine the unknown nucleus or particle that completes the given nuclear equation. These reactions involve the absorption of a deuterium nucleus by a target nucleus, resulting in the emission of a specific particle.

Step 2: Solving Part (a)

The reaction involves \[ _{48}^{114} \text{Cd} + _{1}^{2} \text{H} \rightarrow ? + _{1}^{1} \text{H} \]To find the missing product, maintain mass and atomic numbers:1. Total mass number on the left = 114 + 2 = 116.2. Total atomic number on the left = 48 + 1 = 49.Thus the missing nucleus has a mass number of 115 and an atomic number of 48. This corresponds to \[ _{48}^{115} \text{In} \] (Indium).

Step 3: Solving Part (b)

The reaction involves \[ _{3}^{6} \text{Li} + _{1}^{2} \text{H} \rightarrow ? + _{0}^{1} \text{n} \]To find the missing product, maintain mass and atomic numbers:1. Total mass number on the left = 6 + 2 = 8.2. Total atomic number on the left = 3 + 1 = 4.Thus the missing nucleus has a mass number of 7 and an atomic number of 4, which corresponds to \[ _{4}^{7} \text{Be} \] (Beryllium).

Step 4: Solving Part (c)

This reaction is \[ _{20}^{40} \text{Ca} + _{1}^{2} \text{H} \rightarrow _{19}^{38} \text{K} + ? \]1. Total mass number on the left = 40 + 2 = 42.2. Total atomic number on the left = 20 + 1 = 21.The missing particle or nucleus will have a mass number of 42 - 38 = 4 and an atomic number of 21 - 19 = 2, which corresponds to \[ _{2}^{4} \text{He} \] (Helium nucleus or alpha particle).

Step 5: Solving Part (d)

For this reaction \[ ? + _{1}^{2} \text{H} \rightarrow _{30}^{65} \text{Zn} + \gamma \]Since gamma (\( \gamma \)) emission doesn't change mass or atomic numbers:1. The resultant nucleus is zinc with mass number 65 and atomic number 30.2. Mass and atomic numbers should be equal on both sides: - Missing nucleus has mass number 65 - 2 = 63. - Missing atomic number has 30 - 1 = 29, which corresponds to \[ _{29}^{63} \text{Cu} \] (Copper).

Key Concepts

Deuterium Nuclei

Deuterium is a form of hydrogen commonly known for its abundance and unique properties. It has one proton and one neutron, making its mass number 2, thus represented as \(_{1}^{2} \text{H}\). Unlike the more common hydrogen isotope, which has no neutron, deuterium is often used in nuclear reactions. This is because the additional neutron provides stability in nuclear processes.

Deuterium nuclei serve as effective bombarding particles. When used in nuclear reactions, they can facilitate the transformation of elements. This happens through the absorption of the deuterium into a target nucleus, often leading to the release or production of other particles. These characteristics make deuterium a valuable participant in nuclear fusion experiments and other advanced technological applications.

Nuclear Equations

Nuclear equations are symbolic representations of nuclear reactions. They are similar to chemical equations in that they represent the reactants and products of a reaction, but they specifically involve atomic nuclei. The key components in a nuclear equation include the initial elements, any particles like deuterium or alpha particles, and the resultant products.

Writing balanced nuclear equations ensures that both the mass numbers and atomic numbers are conserved on both sides of the equation. This conservation principle is crucial because it reflects the fundamental law of conservation of mass and energy in nuclear processes. Properly identifying and balancing these equations help in predicting the products of nuclear reactions and understanding the interaction between different nuclear species.

Atomic Numbers

Atomic numbers are fundamental to understanding elements and nuclear reactions. Each element on the periodic table is defined by its atomic number, which equals the number of protons in its nucleus. For example, hydrogen has an atomic number of 1, meaning it has one proton, so a deuterium nucleus (a form of hydrogen) would also have an atomic number of 1, despite its increased mass number due to the additional neutron.

Understanding atomic numbers is essential when analyzing nuclear reactions, as they allow identification of reactants and products in a nuclear equation. In any given reaction, the atomic numbers of all reactants and products must add up to the same sum. This ensures the preservation of charge and element identity throughout the reaction, which is critical for determining what new elements or isotopes may form.

Mass Numbers

Mass numbers are the total count of protons and neutrons in an atomic nucleus. It's important to note that while the atomic number defines what the element is, the mass number gives information about the specific isotope of that element. For example, deuterium has a mass number of 2 because it includes one proton and one neutron.

In nuclear reactions, balancing mass numbers is as important as balancing atomic numbers. The sum of mass numbers in reactants must equal the sum of the mass numbers in products. This ensures that the reaction adheres to the principle of conservation of mass. Understanding mass numbers allows us to deduce unknown products in nuclear reactions, which is fundamental in applications involving nuclear energy and research.