The Nuclear Equation Is Incomplete.$\[ {}_1^1 H + {}_7^{15} N \rightarrow {}_7^{15} O + {}_2^4 He \\]What Particle Completes The Equation?A. \[${}_6^{12} Mg\$\]B. \[${}_5^{11} B\$\]C. \[${}_5^{11} Na\$\]D.

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The Nuclear Equation is Incomplete: Uncovering the Missing Particle

In nuclear reactions, atoms undergo transformations to form new elements, releasing or absorbing energy in the process. These reactions are governed by the laws of nuclear physics, which dictate the conservation of mass, charge, and other fundamental properties. However, in some cases, the nuclear equation appears incomplete, leaving us wondering about the identity of the missing particle. In this article, we will delve into a specific nuclear equation and explore the possible solutions to complete it.

The Incomplete Nuclear Equation

The given nuclear equation is:

11H+715N→715O+24He{ {}_1^1 H + {}_7^{15} N \rightarrow {}_7^{15} O + {}_2^4 He }

This equation represents a nuclear reaction between a proton (hydrogen-1) and a nitrogen-15 nucleus, resulting in the formation of an oxygen-15 nucleus and an alpha particle (helium-4). However, the equation seems incomplete, as it lacks a particle on the reactant side.

Analyzing the Reaction

To complete the equation, we need to identify the missing particle. Let's analyze the reaction:

  • The atomic number (number of protons) on the reactant side is 1 (hydrogen) + 7 (nitrogen) = 8.
  • The atomic number on the product side is 7 (oxygen) + 2 (helium) = 9.
  • The mass number (total number of protons and neutrons) on the reactant side is 1 (hydrogen) + 15 (nitrogen) = 16.
  • The mass number on the product side is 15 (oxygen) + 4 (helium) = 19.

Conservation of Mass and Charge

The law of conservation of mass states that the total mass number of the reactants must equal the total mass number of the products. Similarly, the law of conservation of charge states that the total atomic number of the reactants must equal the total atomic number of the products.

In this case, the mass number on the reactant side (16) does not match the mass number on the product side (19). This discrepancy suggests that a particle with a mass number of 3 is missing from the reactant side.

Possible Solutions

Now, let's examine the possible solutions to complete the equation:

A. {{}_6^{12} Mg$}$

B. {{}_5^{11} B$}$

C. {{}_5^{11} Na$}$

D. {{}_6^{13} C$}$

Solution Analysis

Let's analyze each option:

A. {{}_6^{12} Mg$}$

  • The atomic number of magnesium is 12, which is not equal to the atomic number on the reactant side (8).
  • The mass number of magnesium is 12, which is less than the mass number on the product side (19).

B. {{}_5^{11} B$}$

  • The atomic number of boron is 5, which is not equal to the atomic number on the reactant side (8).
  • The mass number of boron is 11, which is less than the mass number on the product side (19).

C. {{}_5^{11} Na$}$

  • The atomic number of sodium is 11, which is not equal to the atomic number on the reactant side (8).
  • The mass number of sodium is 11, which is less than the mass number on the product side (19).

D. {{}_6^{13} C$}$

  • The atomic number of carbon is 6, which is not equal to the atomic number on the reactant side (8).
  • The mass number of carbon is 13, which is less than the mass number on the product side (19).

Conclusion

After analyzing the possible solutions, we can conclude that none of the options A, B, C, or D complete the nuclear equation. The missing particle must have an atomic number of 8 and a mass number of 3.

The Correct Answer

The correct answer is not among the options provided. The missing particle is actually a tritium nucleus ({{}_1^3 H$}$), which has an atomic number of 1 and a mass number of 3.

Discussion

The nuclear equation is a fundamental concept in nuclear physics, and understanding the conservation of mass and charge is crucial in solving these types of problems. The missing particle in this equation is a tritium nucleus, which is a rare isotope of hydrogen.

References

  • Nuclear Physics: Principles and Applications by Kenneth S. Krane
  • The Elements by Theodore Gray
  • Nuclear Reactions by J. R. Lamarsh

Additional Resources

  • Nuclear Physics by the American Physical Society
  • Nuclear Reactions by the International Atomic Energy Agency
  • The Nuclear Equation by the Nuclear Energy Institute
    The Nuclear Equation is Incomplete: Q&A

In our previous article, we explored a nuclear equation that seemed incomplete, leaving us wondering about the identity of the missing particle. We analyzed the reaction, conserved mass and charge, and examined possible solutions. In this Q&A article, we will delve deeper into the topic and answer some of the most frequently asked questions.

Q: What is a nuclear equation?

A: A nuclear equation is a mathematical representation of a nuclear reaction, where atoms undergo transformations to form new elements, releasing or absorbing energy in the process.

Q: What is the law of conservation of mass?

A: The law of conservation of mass states that the total mass number of the reactants must equal the total mass number of the products in a nuclear reaction.

Q: What is the law of conservation of charge?

A: The law of conservation of charge states that the total atomic number of the reactants must equal the total atomic number of the products in a nuclear reaction.

Q: How do you determine the missing particle in a nuclear equation?

A: To determine the missing particle, you need to analyze the reaction, conserved mass and charge, and examine possible solutions. You can use the laws of conservation of mass and charge to identify the missing particle.

Q: What is the significance of the missing particle in a nuclear equation?

A: The missing particle is crucial in understanding the nuclear reaction and the properties of the elements involved. It can provide valuable information about the reaction mechanism, the energy released or absorbed, and the stability of the resulting nuclei.

Q: Can you provide an example of a nuclear equation with a missing particle?

A: Yes, here is an example:

11H+715N→715O+24He{ {}_1^1 H + {}_7^{15} N \rightarrow {}_7^{15} O + {}_2^4 He }

This equation is incomplete, and we need to identify the missing particle.

Q: How do you solve a nuclear equation with a missing particle?

A: To solve a nuclear equation with a missing particle, you need to:

  1. Analyze the reaction and identify the reactants and products.
  2. Conserved mass and charge by calculating the total mass number and atomic number of the reactants and products.
  3. Examine possible solutions and identify the missing particle.
  4. Verify the solution by checking the laws of conservation of mass and charge.

Q: What are some common mistakes to avoid when solving nuclear equations?

A: Some common mistakes to avoid when solving nuclear equations include:

  • Failing to conserve mass and charge.
  • Ignoring the laws of conservation of mass and charge.
  • Not considering the properties of the elements involved.
  • Not verifying the solution.

Conclusion

In this Q&A article, we explored the concept of nuclear equations, the laws of conservation of mass and charge, and the process of determining the missing particle. We also provided examples and tips for solving nuclear equations. By understanding these concepts, you can better appreciate the complexity and beauty of nuclear reactions.

Additional Resources

  • Nuclear Physics: Principles and Applications by Kenneth S. Krane
  • The Elements by Theodore Gray
  • Nuclear Reactions by J. R. Lamarsh
  • Nuclear Physics by the American Physical Society
  • Nuclear Reactions by the International Atomic Energy Agency
  • The Nuclear Equation by the Nuclear Energy Institute