Identify the unknown particle $X$ in the following nuclear reaction equations. (Enter your answers in the form ${ }_z^A X$.)
(a) ${ }_0^1 n + X \rightarrow{ }_{50}^{131} Sn +{ }_{42}^{103} Mo +2{ }_0^1 n$
Answer (2)
The unknown particle X in the nuclear reaction is identified as 92 235 U (Uranium). We found this by applying conservation laws for mass number and atomic number. The calculations showed that A = 235 and Z = 92 for the unknown particle X .
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Apply conservation of mass number: 1 + A = 131 + 103 + 2 ( 1 ) .
Solve for A : A = 131 + 103 + 2 − 1 = 235 .
Apply conservation of atomic number: 0 + Z = 50 + 42 + 2 ( 0 ) .
Solve for Z : Z = 50 + 42 = 92 . The unknown particle X is 92 235 U . 92 235 U
Explanation
Understanding the Problem We are given a nuclear reaction equation: 0 1 n + X → 50 131 S n + 42 103 M o + 2 0 1 n . Our goal is to identify the unknown particle X . In nuclear reactions, both the total mass number (A) and the total atomic number (Z) must be conserved on both sides of the equation.
Setting up the Equations Let's represent the unknown particle X as Z A X , where A is the mass number and Z is the atomic number. We will use the conservation laws to find A and Z .
Conserving Mass Number First, we apply the conservation of mass number. The total mass number on the left side is 1 + A , and on the right side, it is 131 + 103 + 2 ( 1 ) . Therefore, we have the equation: 1 + A = 131 + 103 + 2 ( 1 ) 1 + A = 131 + 103 + 2
Solving for A Now, we solve for A :
A = 131 + 103 + 2 − 1 A = 235
Conserving Atomic Number Next, we apply the conservation of atomic number. The total atomic number on the left side is 0 + Z , and on the right side, it is 50 + 42 + 2 ( 0 ) . Therefore, we have the equation: 0 + Z = 50 + 42 + 2 ( 0 ) Z = 50 + 42
Solving for Z Now, we solve for Z :
Z = 50 + 42 Z = 92
Identifying the Element We have found that the unknown particle X has a mass number A = 235 and an atomic number Z = 92 . The element with atomic number 92 is Uranium (U). Therefore, the unknown particle X is 92 235 U .
Examples
Nuclear reactions are used in many applications, such as nuclear power generation, medical isotope production, and cancer therapy. Identifying unknown particles in nuclear reactions is crucial for understanding the reaction mechanisms and predicting the products. For example, in nuclear medicine, radioactive isotopes are used for diagnosis and treatment. Knowing the exact composition of these isotopes and the particles emitted during their decay is essential for ensuring the safety and efficacy of the procedures. This problem demonstrates the fundamental principle of conservation laws in nuclear reactions, which is vital for these applications.
