Complete The Nuclear Reaction Equation By Filling In The Missing Isotope.${ {}^{245} {96} \text{Cm} + {}^1_0 \text{n} \rightarrow {}^{103} {42} \text{Mo} + \cdots + 3{}^1_0 \text{n} }$Choose The Correct Isotope To Complete The Equation:A.

by ADMIN 240 views

Understanding Nuclear Reaction Equations

Nuclear reaction equations are a crucial concept in nuclear chemistry, describing the interaction between atomic nuclei. These equations involve the transformation of one or more nuclei into another, often accompanied by the emission or absorption of particles such as neutrons or alpha particles. Balancing nuclear reaction equations is essential to ensure that the number of protons (atomic number) and neutrons (mass number) on both sides of the equation are equal.

The Given Equation

The given nuclear reaction equation is:

{ {}^{245}_{96} \text{Cm} + {}^1_0 \text{n} \rightarrow {}^{103}_{42} \text{Mo} + \cdots + 3{}^1_0 \text{n} \}

In this equation, we have:

  • Cm (Curium) with an atomic number of 96 and a mass number of 245.
  • n (Neutron) with an atomic number of 0 and a mass number of 1.
  • Mo (Molybdenum) with an atomic number of 42 and a mass number of 103.

Balancing the Equation

To balance the equation, we need to find the missing isotope that will make the number of protons and neutrons on both sides of the equation equal. Let's start by analyzing the given information:

  • The atomic number of Cm is 96, and the atomic number of n is 0. The sum of the atomic numbers on the left side is 96.
  • The atomic number of Mo is 42, and the atomic number of n is 0. The sum of the atomic numbers on the right side is 42.
  • The mass number of Cm is 245, and the mass number of n is 1. The sum of the mass numbers on the left side is 246.
  • The mass number of Mo is 103, and the mass number of n is 3. The sum of the mass numbers on the right side is 106.

Finding the Missing Isotope

To balance the equation, we need to find an isotope that has an atomic number of 54 (96 - 42) and a mass number of 140 (246 - 106). This isotope is likely to be a neutron-rich isotope of a heavy element.

Possible Isotopes

Some possible isotopes that match the given criteria are:

  • Xe-140 (Xenon-140): This isotope has an atomic number of 54 and a mass number of 140.
  • Cs-140 (Caesium-140): This isotope has an atomic number of 54 and a mass number of 140.
  • Ba-140 (Barium-140): This isotope has an atomic number of 56, but it is close to the required atomic number of 54.

Conclusion

Based on the given information and the analysis of the equation, the missing isotope that completes the nuclear reaction equation is likely to be Xe-140 (Xenon-140). However, it's essential to note that the actual isotope may vary depending on the specific reaction and the conditions under which it occurs.

Discussion

The given nuclear reaction equation is a complex process that involves the interaction of a heavy nucleus (Cm) with a neutron, resulting in the formation of a lighter nucleus (Mo) and multiple neutrons. Balancing this equation requires a deep understanding of nuclear chemistry and the properties of atomic nuclei.

References

  • Nuclear Chemistry: Principles and Applications by Walter E. Meyerhof
  • The Nuclear Reactions by R. A. Meyer
  • Nuclear Data Sheets by the Nuclear Data Group

Additional Resources

  • Nuclear Reaction Equations by the International Atomic Energy Agency (IAEA)
  • Nuclear Chemistry by the American Chemical Society (ACS)
  • Nuclear Data by the National Nuclear Data Center (NNDC)
    Frequently Asked Questions (FAQs) about Balancing Nuclear Reaction Equations ====================================================================================

Q: What is a nuclear reaction equation?

A: A nuclear reaction equation is a mathematical representation of a nuclear reaction, which involves the interaction between atomic nuclei. These equations describe the transformation of one or more nuclei into another, often accompanied by the emission or absorption of particles such as neutrons or alpha particles.

Q: Why is balancing nuclear reaction equations important?

A: Balancing nuclear reaction equations is essential to ensure that the number of protons (atomic number) and neutrons (mass number) on both sides of the equation are equal. This is crucial in nuclear chemistry, as it helps to predict the outcome of nuclear reactions and understand the properties of atomic nuclei.

Q: How do I balance a nuclear reaction equation?

A: To balance a nuclear reaction equation, you need to find the missing isotope that will make the number of protons and neutrons on both sides of the equation equal. This involves analyzing the given information, identifying the atomic numbers and mass numbers of the reactants and products, and using this information to determine the missing isotope.

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

A: Some common mistakes to avoid when balancing nuclear reaction equations include:

  • Not considering the atomic numbers and mass numbers of the reactants and products
  • Not accounting for the emission or absorption of particles such as neutrons or alpha particles
  • Not using the correct atomic numbers and mass numbers for the isotopes involved

Q: How do I determine the missing isotope in a nuclear reaction equation?

A: To determine the missing isotope in a nuclear reaction equation, you need to analyze the given information and use it to identify the atomic number and mass number of the missing isotope. This involves:

  • Identifying the atomic numbers and mass numbers of the reactants and products
  • Using the atomic numbers and mass numbers to determine the missing isotope
  • Verifying that the missing isotope has the correct atomic number and mass number

Q: What are some resources available for learning more about balancing nuclear reaction equations?

A: Some resources available for learning more about balancing nuclear reaction equations include:

  • Nuclear Chemistry: Principles and Applications by Walter E. Meyerhof
  • The Nuclear Reactions by R. A. Meyer
  • Nuclear Data Sheets by the Nuclear Data Group
  • Nuclear Reaction Equations by the International Atomic Energy Agency (IAEA)
  • Nuclear Chemistry by the American Chemical Society (ACS)
  • Nuclear Data by the National Nuclear Data Center (NNDC)

Q: How do I apply balancing nuclear reaction equations in real-world scenarios?

A: Balancing nuclear reaction equations has numerous applications in real-world scenarios, including:

  • Nuclear power generation: Balancing nuclear reaction equations is essential for predicting the outcome of nuclear reactions and understanding the properties of atomic nuclei.
  • Nuclear medicine: Balancing nuclear reaction equations is crucial for developing new medical treatments and understanding the behavior of radioactive isotopes.
  • Nuclear security: Balancing nuclear reaction equations is essential for predicting the outcome of nuclear reactions and understanding the properties of atomic nuclei, which is critical for ensuring nuclear security.

Conclusion

Balancing nuclear reaction equations is a complex process that requires a deep understanding of nuclear chemistry and the properties of atomic nuclei. By following the steps outlined in this article and using the resources available, you can develop the skills and knowledge necessary to balance nuclear reaction equations and apply them in real-world scenarios.