Consider The Nuclear Equation Below:$\[ {}_{94}^{239} \text{Pu} \longrightarrow X + {}_2^4 \text{He} \\]What Is \[$X\$\]?A. \[${}_{96}^{235} \text{Cm}\$\] B. \[${}_{92}^{243} \text{U}\$\] C. \[${}_{92}^{235}

by ADMIN 210 views

Understanding Nuclear Reactions

Nuclear reactions involve changes to the nucleus of an atom, resulting in the formation of new elements or isotopes. These reactions can be either nuclear fission, where a heavy nucleus splits into two or more lighter nuclei, or nuclear fusion, where two or more light nuclei combine to form a heavier nucleus. In this article, we will focus on balancing a nuclear equation, specifically the one given below:

94239Pu⟶X+24He{ {}_{94}^{239} \text{Pu} \longrightarrow X + {}_2^4 \text{He} }

Balancing Nuclear Equations

To balance a nuclear equation, we need to ensure that the number of protons (atomic number) and neutrons (mass number) on both sides of the equation are equal. The atomic number is the number of protons in an atom's nucleus, while the mass number is the total number of protons and neutrons.

In the given equation, we have a plutonium-239 nucleus (Pu-239) decaying into an unknown nucleus (X) and a helium-4 nucleus (He-4). To balance the equation, we need to find the unknown nucleus X.

Step 1: Determine the Atomic Number of X

The atomic number of Pu-239 is 94. When it decays into X, the atomic number of X must be the same as that of Pu-239, which is 94. Therefore, the atomic number of X is 94.

Step 2: Determine the Mass Number of X

The mass number of Pu-239 is 239. When it decays into X and He-4, the mass number of X must be the difference between the mass number of Pu-239 and the mass number of He-4. The mass number of He-4 is 4. Therefore, the mass number of X is 239 - 4 = 235.

Step 3: Determine the Element of X

With an atomic number of 94 and a mass number of 235, we can determine the element of X. The element with atomic number 94 is plutonium (Pu). However, since the mass number of X is 235, which is different from the mass number of Pu-239, X must be a different isotope of plutonium.

Step 4: Determine the Isotope of X

The isotope with atomic number 94 and mass number 235 is plutonium-235 (Pu-235). Therefore, the unknown nucleus X is Pu-235.

Conclusion

In conclusion, the unknown nucleus X in the given nuclear equation is Pu-235. This is because the atomic number of X must be the same as that of Pu-239, which is 94, and the mass number of X must be the difference between the mass number of Pu-239 and the mass number of He-4, which is 235.

Answer

The correct answer is:

94235Pu{ {}_{94}^{235} \text{Pu} }

Discussion

This problem requires a good understanding of nuclear reactions and the properties of elements. The student must be able to analyze the given equation and determine the unknown nucleus X by balancing the atomic and mass numbers on both sides of the equation.

Common Mistakes

  • Failing to balance the atomic and mass numbers on both sides of the equation.
  • Not considering the properties of elements and their isotopes.
  • Not using the correct atomic and mass numbers for the elements involved.

Tips and Tricks

  • Always start by determining the atomic number of the unknown nucleus X.
  • Use the mass number of the unknown nucleus X to determine its isotope.
  • Make sure to balance the atomic and mass numbers on both sides of the equation.
  • Use the properties of elements and their isotopes to determine the correct answer.

Practice Problems

  1. Balance the nuclear equation:

92238U⟶X+24He{ {}_{92}^{238} \text{U} \longrightarrow X + {}_2^4 \text{He} }

  1. Balance the nuclear equation:

98244Cf⟶X+24He{ {}_{98}^{244} \text{Cf} \longrightarrow X + {}_2^4 \text{He} }

  1. Balance the nuclear equation:

96242Cm⟶X+24He{ {}_{96}^{242} \text{Cm} \longrightarrow X + {}_2^4 \text{He} }

Solutions

  1. The correct answer is:

90234Th{ {}_{90}^{234} \text{Th} }

  1. The correct answer is:

96240Cm{ {}_{96}^{240} \text{Cm} }

  1. The correct answer is:

94238Pu{ {}_{94}^{238} \text{Pu} }

Conclusion

Frequently Asked Questions

Q: What is a nuclear reaction?

A: A nuclear reaction is a process in which the nucleus of an atom is changed, resulting in the formation of new elements or isotopes.

Q: What are the two main types of nuclear reactions?

A: The two main types of nuclear reactions are nuclear fission and nuclear fusion. Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei, while nuclear fusion is the process in which two or more light nuclei combine to form a heavier nucleus.

Q: How do you balance a nuclear equation?

A: To balance a nuclear equation, you need to ensure that the number of protons (atomic number) and neutrons (mass number) on both sides of the equation are equal. This involves determining the atomic and mass numbers of the elements involved and using them to balance the equation.

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

A: The atomic number is the number of protons in an atom's nucleus, while the mass number is the total number of protons and neutrons.

Q: How do you determine the atomic number of an element?

A: The atomic number of an element is equal to the number of protons in its nucleus.

Q: How do you determine the mass number of an element?

A: The mass number of an element is equal to the total number of protons and neutrons in its nucleus.

Q: What is the significance of balancing a nuclear equation?

A: Balancing a nuclear equation is important because it allows us to determine the unknown nucleus in a given nuclear reaction.

Q: How do you determine the unknown nucleus in a nuclear reaction?

A: To determine the unknown nucleus in a nuclear reaction, you need to balance the atomic and mass numbers on both sides of the equation.

Q: What are some common mistakes to avoid when balancing a nuclear equation?

A: Some common mistakes to avoid when balancing a nuclear equation include failing to balance the atomic and mass numbers on both sides of the equation, not considering the properties of elements and their isotopes, and not using the correct atomic and mass numbers for the elements involved.

Q: What are some tips and tricks for balancing a nuclear equation?

A: Some tips and tricks for balancing a nuclear equation include always starting by determining the atomic number of the unknown nucleus, using the mass number of the unknown nucleus to determine its isotope, making sure to balance the atomic and mass numbers on both sides of the equation, and using the properties of elements and their isotopes to determine the correct answer.

Q: What are some practice problems for balancing a nuclear equation?

A: Some practice problems for balancing a nuclear equation include:

  1. Balance the nuclear equation:

92238U⟶X+24He{ {}_{92}^{238} \text{U} \longrightarrow X + {}_2^4 \text{He} }

  1. Balance the nuclear equation:

98244Cf⟶X+24He{ {}_{98}^{244} \text{Cf} \longrightarrow X + {}_2^4 \text{He} }

  1. Balance the nuclear equation:

96242Cm⟶X+24He{ {}_{96}^{242} \text{Cm} \longrightarrow X + {}_2^4 \text{He} }

Solutions

  1. The correct answer is:

90234Th{ {}_{90}^{234} \text{Th} }

  1. The correct answer is:

96240Cm{ {}_{96}^{240} \text{Cm} }

  1. The correct answer is:

94238Pu{ {}_{94}^{238} \text{Pu} }

Conclusion

In conclusion, balancing a nuclear equation requires a good understanding of nuclear reactions and the properties of elements. By following the steps outlined in this article and practicing with the provided practice problems, students can become proficient in balancing nuclear equations.