Question

Write equations for the following nuclear reactions. (a) bombardment of \(^{7} \mathrm{Li}\) with protons to produce \(^{8} \mathrm{Be}\) and \(\gamma\) rays (b) bombardment of \(^{9} \mathrm{B}\) with \(_{1}^{2} \mathrm{H}\) to produce \(^{10} \mathrm{B}\) (c) bombardment of \(^{14} \mathrm{N}\) with neutrons to produce \(^{14} \mathrm{C}\)

Short answer

The nuclear reactions can be written as follows: (a) \(^{7} \mathrm{Li} + ^{1} \mathrm{H} \rightarrow ^{8} \mathrm{Be} + \gamma\) (b) \(^{9} \mathrm{B} + _{1}^{2} \mathrm{H} \rightarrow ^{10} \mathrm{B}\) (c) \(^{14} \mathrm{N} + _{0}^{1} \mathrm{n} \rightarrow ^{14} \mathrm{C}\)

Step-by-step solution

Write the nuclear reaction for \(^{7} \mathrm{Li}\) and protons

In the first scenario, \(^{7} \mathrm{Li}\) is bombarded with protons (\(^{1} \mathrm{H}\)). The result is an \(^{8} \mathrm{Be}\) atom and \(\gamma\) rays. The equation for this nuclear reaction can be written as follows: \(^{7} \mathrm{Li} + ^{1} \mathrm{H} \rightarrow ^{8} \mathrm{Be} + \gamma\)

Write the nuclear reaction for \(^{9} \mathrm{B}\) and \(_{1}^{2} \mathrm{H}\)

In the second scenario, \(^{9} \mathrm{B}\) is bombarded with \(_{1}^{2} \mathrm{H}\). The result is an \(^{10} \mathrm{B}\) atom. The equation for this nuclear reaction can be written as follows: \(^{9} \mathrm{B} + _{1}^{2} \mathrm{H} \rightarrow ^{10} \mathrm{B}\)

Write the nuclear reaction for \(^{14} \mathrm{N}\) and neutrons

In the third scenario, \(^{14} \mathrm{N}\) is bombarded with neutrons (\(_{0}^{1} \mathrm{n}\)). The result is an \(^{14} \mathrm{C}\) atom. The equation for this nuclear reaction can be written as follows: \(^{14} \mathrm{N} + _{0}^{1} \mathrm{n} \rightarrow ^{14} \mathrm{C}\)

Key concepts

Nuclear Reaction Equations

Nuclear reaction equations are a way of representing the processes occurring in nuclear reactions, where the nuclei of atoms interact to form different elements. These equations follow the principle of conservation of mass and energy, ensuring that the number of protons and neutrons is the same on both sides of the equation.

For example, when writing a nuclear reaction equation, each reactant and product is represented by its atomic symbol, mass number, and atomic number. In the exercise provided, the nuclear reaction equation for the bombardment of lithium-7 with protons is represented as: \[ ^{7}_{3}\text{Li} + ^{1}_{1}\text{H} \rightarrow ^{8}_{4}\text{Be} + \text{ }\text{gamma rays (}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }) \].

This shows that a lithium-7 nucleus and a proton combine to form a beryllium-8 nucleus while emitting gamma rays, fulfilling the criteria for a balanced nuclear equation.

Isotope Bombardment

Isotope bombardment is a technique used in nuclear chemistry to induce a nuclear reaction by firing a particle at an isotope. This can result in a change in the target's atomic nucleus, creating a new isotope or even a new element.

In the exercise examples, various isotopes are bombarded with different particles. Such as protons (\(^{1}_{1}\text{H}\)), deuterons (\(_{1}^{2}\text{H}\)), and neutrons (\(_{0}^{1}\text{n}\)). The result of each bombardment is the production of a new isotope or element, showcasing the fundamental concept of nuclear transmutation. Isotopes are chosen based on their potential to create desired reactions, as well as considerations like stability and decay products.

Nuclear Transmutation

Nuclear transmutation is the process of converting one element or isotope into another through nuclear reaction or radioactive decay. It is an essential process in nuclear chemistry and plays a vital role in various applications, including the generation of energy in nuclear reactors and the creation of new elements.

In the context of the provided exercise, transmutation occurs when an isotope absorbs a particle and changes into another isotope or element, such as nitrogen-14 absorbing a neutron to become carbon-14. This change is represented by the reaction equation: \[ ^{14}_{7}\text{N} + _{0}^{1}\text{n} \rightarrow ^{14}_{6}\text{C} \].

Understanding nuclear transmutation is crucial for managing nuclear waste, synthesizing new materials, and studying elemental formation in the universe. It represents the transformative power of nuclear physics to alter the very identity of elements at the atomic level.