Question

Write balanced nuclear equations for the following reactions, and identify \(\mathrm{X}:(\mathrm{a}){ }_{34}^{80} \mathrm{Se}(\mathrm{d}, \mathrm{p}) \mathrm{X},\) (b) \(\mathrm{X}(\mathrm{d}, 2 \mathrm{p})_{3}^{9} \mathrm{Li},(\mathrm{c}){ }^{10} \mathrm{~B}(\mathrm{n}, \alpha) \mathrm{X}.\)

Short answer

(a) \(^{81}_{35}\text{Br}\); (b) \(^{12}_{6}\text{C}\); (c) \(^{7}_{3}\text{Li}\).

Step-by-step solution

Balance the equation for part (a)

The reaction given is \(^{80}_{34} \text{Se}(d, p) \text{X}\). Here, \(d\) is a deuteron \(^{2}_{1}\text{H}\), and \(p\) is a proton \(^{1}_{1}\text{H}\). The equation becomes: \\[^{80}_{34}\text{Se} + ^{2}_{1}\text{H} \rightarrow ^{81}_{35}\text{X} + ^{1}_{1}\text{H}\]. \Using the conservation of mass and atomic numbers, we find that \(X\) has an atomic number of 35 and a mass number of 81, making it \(^{81}_{35}\text{Br}\).

Balance the equation for part (b)

The reaction is \(\text{X}(d, 2p)^{9}_{3}\text{Li}\). First, understand that \(d\) is \(^{2}_{1}\text{H}\) and 2p results in two protons each \(^{1}_{1}\text{H}\). The balanced equation is: \\[^{12}_{6}\text{C} + ^{2}_{1}\text{H} \rightarrow \text{X} + 2 imes ^{1}_{1}\text{H}\]. \Rearrange to get \(X\): \\[^{12}_{6}\text{C} = \text{X} + ^{9}_{3}\text{Li} + 2 \times ^{1}_{1}\text{H}\]. \(X\) is \(^{12}_{6}\text{C}\).

Balance the equation for part (c)

For the equation \(^{10}_{5}\text{B}(n, \alpha)\text{X}\), where \(n\) is a neutron \(^{1}_{0}\text{n}\) and \(\alpha\) is an alpha particle \(^{4}_{2}\text{He}\), the balanced equation is: \\[^{10}_{5}\text{B} + ^{1}_{0}\text{n} \rightarrow \text{X} + ^{4}_{2}\text{He}\]. \By balancing the atomic numbers and mass numbers, \(X\) is determined to be \(^{7}_{3}\text{Li}\).

Key concepts

Balanced Nuclear Reactions

A balanced nuclear reaction is an equation where atomic and mass numbers of reactants and products are equal. This balance ensures that the total number of atoms along with their identifiers remains the same on both sides of the equation. To effectively balance a nuclear reaction, here are some steps:

• Identify all particles involved, including protons, neutrons, and any other nucleus.
• Ensure the sum of mass numbers (top numbers) on the reactant side equals that on the product side.
• Ensure atomic numbers (bottom numbers) also match from one side to the other.

Balancing nuclear equations allows us to predict what type of nucleus or particle results from nuclear reactions in a controlled manner.

Conservation of Mass and Atomic Numbers

In nuclear reactions, the law of conservation of mass and atomic numbers is fundamental. This principle dictates that the sum of mass numbers (the number of protons and neutrons, represented by the top number in a nuclear symbol) remains constant through the reaction. Similarly, the atomic numbers (the number of protons, represented by the bottom number) also must sum to the same value before and after the reaction:

• Mass numbers: Add up the mass numbers on the reactant side. They must equal the total mass numbers on the product side.
• Atomic numbers: This is analogous for atomic numbers. The sum on the left must equal that on the right to conserve the number of protons.

Applying this principle allows us to identify any unknown element or particle in a nuclear equation by calculation.

Alpha Particles

Alpha particles are a type of nuclear radiation consisting of two protons and two neutrons—a configuration identical to a helium nucleus, denoted as \(^{4}_{2} ext{He}\).In nuclear equations, alpha decay plays a role in reducing the mass and atomic numbers of the original reactant. When an alpha particle is emitted:

• The mass number of the resulting nucleus decreases by four.
• The atomic number is reduced by two.

Alpha emission is common in heavier nuclei as a natural way for atomic nuclei to move towards a more stable state by shedding some of their mass in the form of helium nuclei.

Proton Interactions

Proton interactions are a vital part of nuclear reactions and largely influence the balance and behaviour of nuclear equations.

• Protons carry a positive charge, noted as \(^{1}_{1} ext{H}\), representing a single proton found within every atomic nucleus.
• Adding or emitting protons from a nucleus changes its atomic identity—effectively transforming it into a different element.

In nuclear equations, such as those involving deuterons (nuclei of deuterium, or \(^{2}_{1} ext{H}\)), interactions between protons, and other subatomic particles, lead to the transformation and production of energy, making understanding proton interactions crucial in studying nuclear reactions.