Consider the nuclear equation below.
${ }_{94}^{239} Pu \longrightarrow X+{ }_2^4 He$
What is $X$ ?
A. ${ }_{96}^{235} Cm$
B. ${ }_{92}^{243} U$
C. ${ }_{92}^{235} U$
D. ${ }_{96}^{243} Cm$
Answer (2)
Conserve mass number: 239 = A + 4 , so A = 235 .
Conserve atomic number: 94 = Z + 2 , so Z = 92 .
Identify the element with Z = 92 as Uranium (U).
Therefore, X is 92 235 U .
Explanation
Understanding the Problem We are given a nuclear equation and asked to identify the unknown element X . In nuclear reactions, both the mass number (superscript) and the atomic number (subscript) must be conserved. This means the sum of the mass numbers on the left side of the equation must equal the sum of the mass numbers on the right side, and the same holds for the atomic numbers.
Setting up Equations The given nuclear equation is: 94 239 P u ⟶ X + 2 4 He Let A be the mass number of X and Z be the atomic number of X . Then, according to the conservation laws, we have the following two equations:
Mass number conservation: 239 = A + 4 Atomic number conservation: 94 = Z + 2
Solving for A and Z Now, we solve for A and Z :
A = 239 − 4 = 235 Z = 94 − 2 = 92
Identifying the Element The element with atomic number 92 is Uranium (U). Therefore, X is Uranium with a mass number of 235, which is represented as 92 235 U .
Examples
Nuclear equations are used in various fields, such as nuclear medicine for diagnostic imaging and cancer treatment, and in nuclear power plants for energy production. Understanding how to balance these equations is crucial for predicting the products of nuclear reactions and ensuring safety in these applications. For example, in nuclear medicine, radioactive isotopes like 92 235 U are used to trace biological processes, and the decay products must be carefully considered to minimize radiation exposure to patients.
In the nuclear equation 94 239 P u ⟶ X + 2 4 He , the unknown element X has a mass number of 235 and an atomic number of 92, which corresponds to Uranium (U). Therefore, X is represented as 92 235 U , making option C the correct choice. Conservation laws in nuclear reactions dictate that both mass and atomic numbers must be conserved in the process.
;
