Question

A nuclear reaction of the kind \({ }_{2}^{3} \mathrm{He}+{ }_{6}^{12} \mathrm{C} \rightarrow \mathrm{X}+\alpha\) is called a pick- \(u p\) reaction. a) Why does it have this name, that is, what is picked up, what picked it up, and where did it come from? 40.16 A nuclear reaction of the kind \({ }_{2}^{3} \mathrm{He}+{ }_{6}^{12} \mathrm{C} \rightarrow \mathrm{X}+\alpha\) is called a pick- \(u p\) reaction. a) Why does it have this name, that is, what is picked up, what picked it up, and where did it come from?

Short answer

Question: Explain why the given nuclear reaction is called a pick-up reaction and identify the particles involved. Answer: The given nuclear reaction is called a pick-up reaction because the helium-3 nucleus "picks up" a neutron from the carbon-12 nucleus, forming a carbon-11 nucleus and an alpha particle. In this reaction, a neutron is transferred from one nucleus to another, hence the term "pick-up." The particles involved are helium-3, carbon-12, carbon-11, and an alpha particle.

Step-by-step solution

Identify the conservation rules in nuclear reactions

In any nuclear reaction, certain properties are conserved, such as mass numbers, atomic numbers, and energy. In the given reaction, we have: \({ }_{2}^{3} \mathrm{He}+{ }_{6}^{12}\mathrm{C} \rightarrow \mathrm{X}+\alpha\) Where, α represents an alpha particle which is \({ }_{2}^{4}\mathrm{He}\)

Apply conservation rules to the given equation

Applying conservation of mass numbers: A(He) + A(C) = A(X) + A(α) 3 + 12 = A(X) + 4 Applying conservation of atomic numbers: Z(He) + Z(C) = Z(X) + Z(α) 2 + 6 = Z(X) + 2

Calculate A(X) and Z(X) for the unknown nucleus X

Solve for A(X): 3 + 12 = A(X) + 4 A(X) = 11 Solve for Z(X): 2 + 6 = Z(X) + 2 Z(X) = 6

Identify the nucleus and explain the pick-up reaction

Based on the atomic and mass numbers calculated for the unknown nucleus X, we can identify it as: \({ }_{6}^{11} \mathrm{C}\) Now it's time to explain the pick-up reaction term. In the given reaction, a \({ }_{2}^{3} \mathrm{He}\) nucleus (also known as a helium-3 nucleus) combines with a \({ }_{6}^{12}\mathrm{C}\) nucleus (carbon-12 nucleus). The helium-3 nucleus picks up a neutron from the carbon-12 nucleus and transforms into an alpha particle (\({ }_{2}^{4} \mathrm{He}\) or helium-4 nucleus). This leaves behind a new nucleus, \({ }_{6}^{11} \mathrm{C}\) (carbon-11). So, the pick-up reaction refers to the helium-3 nucleus "picking up" a neutron from the carbon-12 nucleus. The neutron comes from the carbon-12 nucleus, leading to the formation of a carbon-11 nucleus and an alpha particle.

Key concepts

Conservation Rules in Nuclear Reactions

In nuclear physics, one of the fundamental principles is that certain properties remain unchanged before and after a nuclear reaction. These are known as conservation rules and they serve as the backbone for analyzing and predicting the outcomes of nuclear reactions. The key conservation rules include the conservation of mass number and atomic number.

The mass number, denoted by A, represents the total number of protons and neutrons in a nucleus. During a nuclear reaction, the sum of the mass numbers of the reactants must equal the sum of the mass numbers of the products. This ensures that no nucleons are lost or created in the process.

Conservation of Atomic Number

The atomic number, denoted by Z, indicates the number of protons in a nucleus, and by extension, the element's identity. In a reaction, the total atomic number must be conserved, implying that the number of protons is the same before and after the reaction. This conservation is crucial for maintaining the charge balance, as protons are positively charged.

These conservation laws are not just theoretical constructs; they are essential for practical applications in nuclear chemistry and physics. When solving nuclear reactions, scientists use them to determine the identities of unknown products, much like detective work to find missing pieces of a puzzle.

Understanding the Alpha Particle

An alpha particle might sound exotic, but it is essentially just a helium nucleus stripped of its electrons. It consists of two protons and two neutrons, making its representation \( { }_{2}^{4}\mathrm{He} \) in nuclear notation. It's fascinating because, despite being a product of radioactive decay, it's a component of ordinary helium, the second lightest and second most abundant element in the observable universe.

Characteristics of Alpha Particles

Alpha particles are a form of radiation and carry a +2 charge due to the two protons. They are relatively massive compared to other forms of radiation like beta particles or gamma rays, and this massiveness contributes to their inability to penetrate material deeply. They can be stopped by a sheet of paper or a few centimeters of air, making them less dangerous to humans as long as they are not ingested or inhaled.

Alpha particles are significant in nuclear reactions because they can be emitted or absorbed, changing the mass and atomic numbers of elements in the process. Understanding alpha particles thus helps us explain how certain elements transform in radioactive processes and how energy can be harnessed from these reactions.

Deciphering the Nuclear Reaction Equation

A nuclear reaction equation is a symbolic representation that showcases the reactants and products in a nuclear reaction. Think of it like a recipe that details what goes in and what comes out in a nuclear process.

Writing and balancing nuclear equations involves applying the aforementioned conservation rules. These equations are critical for predicting the results of a reaction, calculating the energy released or absorbed, and understanding the underlying changes in the nucleus.

A Quick Guide to Reading Nuclear Equations

To correctly interpret a nuclear equation, knowledge of the format \( _{Z}^{A}\mathrm{Element} \) is essential, where Z is the atomic number and A is the mass number. The element symbol represents the specific element involved. By following the conservation rules, one can balance both sides of the equation to ensure that mass and atomic numbers remain constant. This leads to a coherent and accurate depiction of the nuclear transformation.

Bringing our focus back to the exercise, we see that the nuclear equation given, \( _{2}^{3}\mathrm{He}+ _{6}^{12}\mathrm{C} \rightarrow \mathrm{X}+\alpha \), follows these principles. By determining the identity of the unknown product X, we not only solve a numerical problem but also visualize the rearrangement of nucleons that occurs during the reaction. Understanding these equations is essential for any student or scientist studying nuclear processes, as it provides a clear and concise framework for analysis.