Write The Isotope Needed, By Identifying $A, Z$, And $X$, To Balance The Following Nuclear Fusion Reaction:$\[ {}_1^2 \text{H} + {}_1^2 \text{H} \rightarrow {}_1^1 \text{H} + {}_Z^A \text{X} \\]Express Your Answer As An

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Introduction

Nuclear fusion reactions involve the combination of two or more atomic nuclei to form a single, heavier nucleus. These reactions are the opposite of nuclear fission, where a heavy nucleus splits into two or more lighter nuclei. Balancing nuclear fusion reactions is crucial in understanding the underlying physics and chemistry of these processes. In this article, we will focus on balancing the given nuclear fusion reaction and identifying the isotope needed to achieve equilibrium.

Understanding the Reaction

The given nuclear fusion reaction is:

{ {}_1^2 \text{H} + {}_1^2 \text{H} \rightarrow {}_1^1 \text{H} + {}_Z^A \text{X} \}

In this reaction, two deuterium nuclei ({}{1}^{2}H) combine to form a single nucleus of hydrogen ({}{1}^{1}H) and an unknown nucleus {}{Z}^{A}X. To balance this reaction, we need to identify the isotope {}{Z}^{A}X.

Balancing the Reaction

To balance the reaction, we need to ensure that the number of protons (atomic number, Z) and the number of nucleons (mass number, A) are conserved on both sides of the reaction. Let's start by analyzing the reaction:

  • On the left side, we have two deuterium nuclei, each with 1 proton and 2 nucleons. Therefore, the total number of protons is 2, and the total number of nucleons is 4.
  • On the right side, we have a single hydrogen nucleus with 1 proton and 1 nucleon, and an unknown nucleus {}_{Z}^{A}X.

To balance the reaction, we need to ensure that the number of protons and nucleons are conserved. Let's start by analyzing the number of protons:

  • The total number of protons on the left side is 2.
  • The total number of protons on the right side is 1 (from the hydrogen nucleus) + Z (from the unknown nucleus).

To balance the reaction, we need to set up the following equation:

2 = 1 + Z

Solving for Z, we get:

Z = 1

Therefore, the unknown nucleus {}_{Z}^{A}X has an atomic number of 1.

Next, let's analyze the number of nucleons:

  • The total number of nucleons on the left side is 4.
  • The total number of nucleons on the right side is 1 (from the hydrogen nucleus) + A (from the unknown nucleus).

To balance the reaction, we need to set up the following equation:

4 = 1 + A

Solving for A, we get:

A = 3

Therefore, the unknown nucleus {}_{Z}^{A}X has a mass number of 3.

Conclusion

In conclusion, to balance the given nuclear fusion reaction, we need to identify the isotope {}{Z}^{A}X. By analyzing the reaction and setting up equations to conserve the number of protons and nucleons, we found that the unknown nucleus has an atomic number of 1 and a mass number of 3. Therefore, the isotope needed to balance the reaction is {}{1}^{3}H, also known as tritium.

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Additional Resources

Introduction

In our previous article, we discussed balancing nuclear fusion reactions and identified the isotope needed to achieve equilibrium. In this article, we will address some common questions and concerns related to balancing nuclear fusion reactions.

Q: What is the difference between nuclear fusion and nuclear fission?

A: Nuclear fusion is the process of combining two or more atomic nuclei to form a single, heavier nucleus. This process releases a large amount of energy and is the opposite of nuclear fission, where a heavy nucleus splits into two or more lighter nuclei.

Q: Why is balancing nuclear fusion reactions important?

A: Balancing nuclear fusion reactions is crucial in understanding the underlying physics and chemistry of these processes. It helps us to identify the isotope needed to achieve equilibrium and to predict the outcome of nuclear fusion reactions.

Q: How do I balance a nuclear fusion reaction?

A: To balance a nuclear fusion reaction, you need to ensure that the number of protons (atomic number, Z) and the number of nucleons (mass number, A) are conserved on both sides of the reaction. You can do this by analyzing the reaction and setting up equations to conserve the number of protons and nucleons.

Q: What is the atomic number and mass number of a nucleus?

A: The atomic number (Z) of a nucleus is the number of protons it contains, while the mass number (A) is the total number of nucleons (protons and neutrons) it contains.

Q: How do I determine the isotope needed to balance a nuclear fusion reaction?

A: To determine the isotope needed to balance a nuclear fusion reaction, you need to analyze the reaction and set up equations to conserve the number of protons and nucleons. You can then solve these equations to find the atomic number and mass number of the unknown nucleus.

Q: What is the significance of the isotope {}_{1}^{3}H in nuclear fusion reactions?

A: The isotope {}_{1}^{3}H, also known as tritium, is a key component in nuclear fusion reactions. It is formed when two deuterium nuclei combine and is a necessary step in achieving nuclear fusion.

Q: Can you provide an example of a nuclear fusion reaction?

A: Yes, here is an example of a nuclear fusion reaction:

{ {}_1^2 \text{H} + {}_1^2 \text{H} \rightarrow {}_1^1 \text{H} + {}_1^3 \text{H} \}

In this reaction, two deuterium nuclei combine to form a single nucleus of hydrogen and a nucleus of tritium.

Conclusion

In conclusion, balancing nuclear fusion reactions is a crucial step in understanding the underlying physics and chemistry of these processes. By analyzing the reaction and setting up equations to conserve the number of protons and nucleons, we can determine the isotope needed to achieve equilibrium. We hope this Q&A article has provided you with a better understanding of balancing nuclear fusion reactions.

References

Additional Resources