Question

\({ }_{6} \mathrm{C}^{12}\) absorbs an energetic neutron and emits a \(\beta\) Particle. The resulting nucleus is (A) \({ }_{7} \mathrm{~N}^{13}\) (B) \({ }_{7} \mathrm{~N}^{14}\) (C) \({ }_{6} \mathrm{C}^{13}\) (D) \({ }_{6} \mathrm{C}^{12}\)

Short answer

The resulting nucleus after the absorption of a neutron and emission of a beta particle is \({ }_{7} \mathrm{N}^{13}\). The correct answer is option (A).

Step-by-step solution

Identify the initial nucleus

The initial nucleus given in the problem is Carbon-12, which can be written as \({ }_{6} \mathrm{C}^{12}\). This means that it has 6 protons and 6 neutrons (12-6=6).

Absorption of a neutron

When the Carbon-12 nucleus absorbs a neutron, its neutron count increases by 1. So, the new nucleus will have 6 protons and 7 neutrons, making it Carbon-13 (\({ }_{6} \mathrm{C}^{13}\)).

Emission of a beta particle

A beta particle is an electron that is emitted during a beta decay process, in which a neutron changes into a proton. In this reaction, one of the 7 neutrons will change into a proton, so the resulting nucleus will have 7 protons and 6 neutrons (7+6=13).

Identify the final nucleus

The final nucleus will have 7 protons and 6 neutrons, which corresponds to Nitrogen-13. Hence, the resulting nucleus after the absorption of a neutron and emission of a beta particle is \({ }_{7} \mathrm{N}^{13}\). So, the correct answer is option (A) \({ }_{7} \mathrm{~N}^{13}\).

Key concepts

Beta Decay

Beta decay is a fascinating process in nuclear physics where a neutron in a nucleus is transformed into a proton. This transformation comes with the emission of a beta particle, which is essentially an electron.

• This process increases the atomic number by one but keeps the mass number the same, altering the element's identity.
• The beta particle is quickly ejected from the nucleus, carrying away energy and leaving the new nucleus more stable than before.

During beta decay, a neutron is converted into a proton through the weak nuclear force. This involves changing a down quark to an up quark within the neutron, facilitating the release of energy in the form of the beta particle. Understanding beta decay is crucial to studying nuclear transmutation, as it can change one element into another.

Isotopes

Isotopes are various forms of a given element that contain the same number of protons but differ in the number of neutrons. This difference in neutron number leads to different mass numbers, although the chemical properties remain largely unchanged.

• For example, Carbon has isotopes like Carbon-12 and Carbon-13, each with 6 protons but differing in their neutron counts.
• Isotopes play a vital role in nuclear reactions as their stability can dictate whether a reaction will occur naturally, or need human intervention.
• The existence of isotopes is essential for understanding nuclear processes such as decay and absorption.

The average atomic mass listed on the periodic table takes into account the natural abundance of these different isotopes, providing insight into which isotopes are more prevalent in nature.

Neutron Absorption

Neutron absorption is a process where a nucleus captures a free neutron, altering its composition. This process usually results in the nucleus having more energy and possibly becoming unstable.

• Nuclei tend to absorb neutrons when they collide with them, often leading to a change in the neutron-to-proton ratio.
• This can lead to increased instability, and in many cases, it may lead to subsequent nuclear reactions, including decay processes.

In the case of our original exercise, the Carbon-12 nucleus absorbs a neutron to become Carbon-13. This changes its neutron count from 6 to 7, but its atomic number remains the same (still a carbon isotope). When this unstable nucleus undergoes further reactions like beta decay, the element itself can transform, demonstrating how neutron absorption is a precursor to many nuclear transformations.

Nuclear Transmutation

Nuclear transmutation is the conversion of one chemical element or isotope into another, driven by nuclear reactions. This transformation happens naturally and artificially and is a fundamental concept in nuclear chemistry.

• In nature, transmutation occurs over long periods due to radioactive decay, such as Uranium eventually becoming Lead.
• Artificially, transmutation can be induced in nuclear reactors or particle accelerators by forcing nuclei to undergo reactions.
• Each type of transmutation involves changing the number of protons within a nucleus, thereby altering the identity of the element.

In the beta decay of Carbon-13 to Nitrogen-13 discussed in the exercise, transmutation is an essential concept. Through neutron absorption followed by beta decay, the number of protons increases, shifting the element from carbon to nitrogen. Understanding nuclear transmutation provides the foundation for comprehending how elements can transform under different physical processes.