Completing Nuclear Equations Identifying The Missing Particle

#Understanding Nuclear Equations

In the realm of nuclear chemistry, nuclear equations serve as the language through which we describe transformations within the atom's nucleus. These equations, much like their chemical counterparts, depict the rearrangement of nuclear particles, but instead of electrons, we focus on protons, neutrons, and other subatomic entities. Balancing these equations is not merely an exercise in bookkeeping; it's a fundamental principle rooted in the conservation laws that govern the universe. To solve nuclear equations successfully, it is important to grasp the concept of the conservation of nucleons, which states that the total number of protons and neutrons (nucleons) remains constant during a nuclear reaction. This principle dictates that the sum of mass numbers (the superscript) and the sum of atomic numbers (the subscript) must be the same on both sides of the equation. This concept is pivotal in predicting the products of nuclear reactions and understanding the nature of radioactive decay. To illustrate, let's consider the equation provided:

${ }_1^1 H +{ }_7^{15} N ightarrow ? +{ }_2^4 He$

In this equation, we see a proton (${ }_1^1 H$) colliding with a nitrogen-15 nucleus (${ }_7^{15} N$), resulting in an unknown particle and an alpha particle (${ }_2^4 He$). To identify the unknown particle, we must ensure that the mass numbers and atomic numbers balance on both sides. On the left side, we have a total mass number of 16 (1 + 15) and a total atomic number of 8 (1 + 7). On the right side, the alpha particle contributes a mass number of 4 and an atomic number of 2. Therefore, the unknown particle must have a mass number of 12 (16 - 4) and an atomic number of 6 (8 - 2) to balance the equation. In doing so, we use nuclear equations to describe the reactions occurring within the atomic nucleus. By carefully balancing these equations, we can decipher the identities of unknown particles and better understand the fundamental processes governing nuclear transformations. It's a skill that opens doors to a deeper appreciation of the energetic world residing within the atom's core.

#Analyzing the Given Nuclear Reaction

The initial step in unraveling this nuclear reaction involves a meticulous examination of the provided equation. We are presented with the reaction:

${ }_1^1 H +{ }_7^{15} N ightarrow ? +{ }_2^4 He$

Here, a proton (${ }_1^1 H$) collides with a nitrogen-15 nucleus (${ }_7^{15} N$). The products include an alpha particle (${ }_2^4 He$) and an unknown particle, which is our target for identification. The equation is a symbolic representation of a nuclear transformation, where the identity of the atomic nuclei changes as they interact. To decipher the identity of the unknown particle, we must delve into the fundamental principles governing nuclear reactions – the conservation laws. Two key conservation laws are at play in nuclear equations: conservation of mass number and conservation of atomic number. Conservation of mass number dictates that the total number of nucleons (protons and neutrons) remains constant throughout the reaction. This means that the sum of the mass numbers on the left side of the equation must equal the sum of the mass numbers on the right side. Conservation of atomic number mandates that the total number of protons remains constant. Consequently, the sum of the atomic numbers on the left side must equal the sum of the atomic numbers on the right side. Applying these conservation laws to our equation, we can set up a system of equations to determine the mass number (A) and atomic number (Z) of the unknown particle.

On the left side, the total mass number is 1 (from the proton) + 15 (from nitrogen-15) = 16. The total atomic number is 1 (from the proton) + 7 (from nitrogen-15) = 8. On the right side, the alpha particle (${ }_2^4 He$) contributes a mass number of 4 and an atomic number of 2. Let's denote the unknown particle as ${ }_Z^A X$. Now we can express the conservation laws mathematically:

Mass number conservation: 1 + 15 = A + 4 Atomic number conservation: 1 + 7 = Z + 2

Solving these equations will reveal the identity of our mysterious particle. This step-by-step approach, grounded in the fundamental principles of nuclear chemistry, is crucial for correctly solving nuclear equations and understanding the transformations occurring within atomic nuclei. By carefully applying the conservation laws, we can confidently navigate the complexities of nuclear reactions and predict the products formed.

#Balancing Nuclear Equations and Identifying the Unknown Particle

Having established the foundation of conservation laws, we now proceed to the crucial step of balancing the nuclear equation and identifying the elusive unknown particle. Recall our equation:

${ }_1^1 H +{ }_7^{15} N ightarrow ? +{ }_2^4 He$

We've already determined that we can apply the conservation of mass number and atomic number. Let's revisit the equations we set up:

Mass number conservation: 1 + 15 = A + 4 Atomic number conservation: 1 + 7 = Z + 2

Solving for A (the mass number of the unknown particle):

16 = A + 4 A = 16 - 4 A = 12

Solving for Z (the atomic number of the unknown particle):

8 = Z + 2 Z = 8 - 2 Z = 6

Thus, we've deduced that the unknown particle has a mass number of 12 and an atomic number of 6. The atomic number is the key to unlocking the element's identity. The atomic number uniquely identifies an element because it corresponds to the number of protons in the nucleus. Consulting the periodic table, we find that the element with an atomic number of 6 is carbon (C). Therefore, our unknown particle is a carbon isotope with a mass number of 12. We can now confidently write the complete nuclear equation:

${ }_1^1 H +{ }_7^{15} N ightarrow { }_6^{12} C +{ }_2^4 He$

This balanced equation tells the full story of the nuclear reaction: a proton collides with a nitrogen-15 nucleus, resulting in the formation of a carbon-12 nucleus and an alpha particle. This process, known as nuclear transmutation, exemplifies the power of nuclear reactions to transform one element into another. Our systematic approach, grounded in conservation laws and the periodic table, has allowed us to successfully identify the unknown particle and gain a deeper understanding of this nuclear transformation.

#Evaluating the Answer Choices

With the identity of the unknown particle firmly established as carbon-12 (${ }_6^{12} C$), we can now turn our attention to evaluating the provided answer choices. This step is crucial to ensure we select the correct answer and reinforce our understanding of the concepts involved. The answer choices presented are:

A. ${ }_6^{12} Mg$ B. ${ }_5^{11} B$ C. ${ }_5^{11} Na$ D. ${ }_6^{12} C

Let's examine each option in light of our determined identity of the unknown particle:

A. ${ }_6^{12} Mg$: This option represents magnesium-12. While it shares the same mass number (12) as our unknown particle, it has an atomic number of 6, which corresponds to magnesium. Since we've established that the unknown particle has an atomic number of 6 (carbon), this option is incorrect.

B. ${ }_5^{11} B$: This option represents boron-11. It has a different mass number (11) and a different atomic number (5) compared to our unknown particle (mass number 12, atomic number 6). Therefore, this option is also incorrect.

C. ${ }_5^{11} Na$: This option seems to have a typo and it should represent sodium-11. It has a different mass number (11) and a different atomic number (5) compared to our unknown particle (mass number 12, atomic number 6). Therefore, this option is incorrect.

D. ${ }_6^{12} C$: This option represents carbon-12. It perfectly matches our determined identity of the unknown particle, having a mass number of 12 and an atomic number of 6. Therefore, this is the correct answer.

By systematically evaluating each answer choice against our calculated identity of the unknown particle, we can confidently affirm that option D, ${ }_6^{12} C$, is the correct answer. This process not only leads us to the solution but also reinforces the importance of understanding atomic numbers, mass numbers, and the periodic table in nuclear chemistry. The ability to critically assess answer choices is a valuable skill in problem-solving, ensuring accuracy and a deeper grasp of the subject matter.

#Final Answer

Based on our comprehensive analysis of the nuclear equation, the principles of conservation of mass number and atomic number, and the evaluation of answer choices, we have confidently identified the unknown particle that completes the equation.

The correct answer is:

D. ${ }_6^{12} C$

This final answer represents carbon-12, a stable isotope of carbon. Our journey through this nuclear reaction has highlighted the importance of balancing nuclear equations, applying conservation laws, and utilizing the periodic table to decipher the identities of nuclear particles. Understanding these concepts is crucial for navigating the fascinating world of nuclear chemistry and appreciating the transformations that occur within the atomic nucleus.