Consider The Nuclear Equation Below.${ J \longrightarrow X + { } 2^4 \text{He} }$What Is The Nuclide Symbol Of { X $} ? ? ? [ \begin{array}{l} { } {94}^{231} \text{Pu} \ { } {90}^{235} \text{Th} \ { } {94}^{239} \text{Pu} \ {

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Introduction

Nuclear equations are a fundamental concept in chemistry, allowing us to understand and predict the behavior of atomic nuclei. In this article, we will explore a specific nuclear equation and solve for the unknown nuclide symbol. We will break down the process into manageable steps, making it easy to follow and understand.

The Nuclear Equation

The given nuclear equation is:

{ J \longrightarrow X + { }_2^4 \text{He} \}

We are asked to find the nuclide symbol of X. To do this, we need to understand the properties of the elements involved and the process of nuclear decay.

Understanding Nuclear Decay

Nuclear decay occurs when an unstable nucleus loses energy by emitting radiation. In this case, the nucleus J decays into X and a helium nucleus (He). The helium nucleus has a mass number of 4 and an atomic number of 2.

Step 1: Identify the Atomic Number of X

The atomic number of an element is equal to the number of protons in its nucleus. Since the helium nucleus has an atomic number of 2, the atomic number of X must be the atomic number of J minus 2.

Step 2: Identify the Mass Number of X

The mass number of an element is equal to the sum of the number of protons and neutrons in its nucleus. Since the helium nucleus has a mass number of 4, the mass number of X must be the mass number of J minus 4.

Step 3: Determine the Nuclide Symbol of X

Now that we have the atomic number and mass number of X, we can determine its nuclide symbol. The nuclide symbol of an element is written in the format:

{ {}_{Z}^{A} \text{Element} \}

where Z is the atomic number and A is the mass number.

Example Nuclide Symbols

Let's look at some example nuclide symbols to illustrate the format:

  • { {}_{6}^{12} \text{C} \} (carbon-12)
  • { {}_{8}^{16} \text{O} \} (oxygen-16)
  • { {}_{26}^{56} \text{Fe} \} (iron-56)

Solving for X

Now that we have the format for the nuclide symbol, we can solve for X. We are given the following options:

  • { {}_{94}^{231} \text{Pu} \} (plutonium-231)
  • { {}_{90}^{235} \text{Th} \} (thorium-235)
  • { {}_{94}^{239} \text{Pu} \} (plutonium-239)

We need to determine which of these options is the correct nuclide symbol for X.

Step 4: Analyze the Options

Let's analyze each option to determine which one is the correct nuclide symbol for X.

  • Option 1: { {}_{94}^{231} \text{Pu} \} (plutonium-231)
    • Atomic number: 94
    • Mass number: 231
    • Helium nucleus: { {}_{2}^{4} \text{He} \} (helium-4)
    • X: { {}_{94-2}^{231-4} \text{X} \} = { {}_{92}^{227} \text{X} \}
  • Option 2: { {}_{90}^{235} \text{Th} \} (thorium-235)
    • Atomic number: 90
    • Mass number: 235
    • Helium nucleus: { {}_{2}^{4} \text{He} \} (helium-4)
    • X: { {}_{90-2}^{235-4} \text{X} \} = { {}_{88}^{231} \text{X} \}
  • Option 3: { {}_{94}^{239} \text{Pu} \} (plutonium-239)
    • Atomic number: 94
    • Mass number: 239
    • Helium nucleus: { {}_{2}^{4} \text{He} \} (helium-4)
    • X: { {}_{94-2}^{239-4} \text{X} \} = { {}_{92}^{235} \text{X} \}

Conclusion

Based on our analysis, we can conclude that the correct nuclide symbol for X is:

{ {}_{92}^{235} \text{U} \}

This is because the mass number of X is 235, which is the mass number of the given options. The atomic number of X is 92, which is the atomic number of uranium.

Discussion

The solution to this problem involves understanding the properties of nuclear decay and the format for nuclide symbols. By analyzing the options and determining the atomic number and mass number of X, we can conclude that the correct nuclide symbol for X is { {}_{92}^{235} \text{U} \}.

Key Takeaways

  • Nuclear decay occurs when an unstable nucleus loses energy by emitting radiation.
  • The nuclide symbol of an element is written in the format { {}_{Z}^{A} \text{Element} \}.
  • To solve for X, we need to determine the atomic number and mass number of X.
  • By analyzing the options and determining the atomic number and mass number of X, we can conclude that the correct nuclide symbol for X is { {}_{92}^{235} \text{U} \}.

References

  • Chemistry: The Central Science, 14th edition, by Theodore L. Brown, H. Eugene LeMay, Jr., and Bruce E. Bursten.
  • Nuclear Chemistry, 2nd edition, by James E. Huizenga.

Additional Resources

  • Khan Academy: Nuclear Chemistry
  • Chemistry LibreTexts: Nuclear Chemistry
    Frequently Asked Questions: Nuclear Equations and Nuclide Symbols ====================================================================

Q: What is a nuclear equation?

A: A nuclear equation is a mathematical representation of a nuclear reaction, where an unstable nucleus loses energy by emitting radiation.

Q: What is a nuclide symbol?

A: A nuclide symbol is a notation used to represent an element, consisting of the atomic number (Z) and mass number (A) of the element, followed by the symbol of the element.

Q: How do I write a nuclide symbol?

A: To write a nuclide symbol, you need to follow the format: { {}_{Z}^{A} \text{Element} \}. For example, the nuclide symbol for carbon-12 is { {}_{6}^{12} \text{C} \}.

Q: What is the difference between atomic number and mass number?

A: The atomic number (Z) is the number of protons in the nucleus of an atom, while the mass number (A) is the sum of the number of protons and neutrons in the nucleus.

Q: How do I determine the atomic number and mass number of an element?

A: To determine the atomic number and mass number of an element, you need to look at the periodic table. The atomic number is listed in the top left corner of each element's box, while the mass number is listed below the element's symbol.

Q: What is the significance of the helium nucleus in nuclear equations?

A: The helium nucleus is a stable nucleus that is often emitted during nuclear decay. Its presence in a nuclear equation indicates that the nucleus is losing energy by emitting radiation.

Q: How do I solve for X in a nuclear equation?

A: To solve for X in a nuclear equation, you need to determine the atomic number and mass number of X by analyzing the options and using the format for nuclide symbols.

Q: What is the correct nuclide symbol for X in the given nuclear equation?

A: Based on the analysis, the correct nuclide symbol for X is { {}_{92}^{235} \text{U} \}.

Q: What are some common mistakes to avoid when working with nuclear equations and nuclide symbols?

A: Some common mistakes to avoid include:

  • Confusing atomic number and mass number
  • Not following the format for nuclide symbols
  • Not analyzing the options carefully
  • Not considering the significance of the helium nucleus in nuclear equations

Q: Where can I find more information on nuclear equations and nuclide symbols?

A: You can find more information on nuclear equations and nuclide symbols in chemistry textbooks, online resources, and educational websites.

Q: What are some real-world applications of nuclear equations and nuclide symbols?

A: Nuclear equations and nuclide symbols have many real-world applications, including:

  • Nuclear power generation
  • Medical imaging
  • Radiation therapy
  • Nuclear waste management

Q: How can I practice solving nuclear equations and nuclide symbols?

A: You can practice solving nuclear equations and nuclide symbols by working through example problems, using online resources, and taking practice quizzes.

Q: What are some tips for mastering nuclear equations and nuclide symbols?

A: Some tips for mastering nuclear equations and nuclide symbols include:

  • Practicing regularly
  • Understanding the format for nuclide symbols
  • Analyzing options carefully
  • Considering the significance of the helium nucleus in nuclear equations

Conclusion

Nuclear equations and nuclide symbols are fundamental concepts in chemistry that have many real-world applications. By understanding the format for nuclide symbols, analyzing options carefully, and considering the significance of the helium nucleus in nuclear equations, you can master nuclear equations and nuclide symbols.