Identify the unknown particle $X$ in the following equation for fission. (Enter your answer in the form ${ }_z^A X$.)
${ }_{92}^{236} U \rightarrow X+{ }_{42}^{103} Mo+2{ }_0^1 n$
Answer (1)
Conserve the mass number: 236 = A + 103 + 2 , which gives A = 131 .
Conserve the atomic number: 92 = z + 42 , which gives z = 50 .
Identify the element with atomic number 50 as Tin (Sn).
The unknown particle is therefore 50 131 S n , so the answer is 50 131 S n .
Explanation
Understanding the Problem We are given a nuclear fission reaction and asked to identify the unknown particle X :
92 236 U \t \t → X + 42 103 M o + 2 0 1 n In nuclear reactions, both the total mass number (superscript) and the total atomic number (subscript) must be conserved. This means the sum of the mass numbers on the left side must equal the sum of the mass numbers on the right side, and the same for the atomic numbers.
Setting up the Equations Let's denote the unknown particle X as z A X , where A is the mass number and z is the atomic number. We need to find the values of A and z to identify the particle.
Conserving Mass Number First, we'll conserve the mass number: 236 = A + 103 + 2 ( 1 ) 236 = A + 103 + 2 Now, we solve for A :
A = 236 − 103 − 2 = 131
Conserving Atomic Number Next, we'll conserve the atomic number: 92 = z + 42 + 2 ( 0 ) 92 = z + 42 Now, we solve for z :
z = 92 − 42 = 50
Identifying the Element Now that we have A = 131 and z = 50 , we can identify the element with atomic number 50. Looking at the periodic table, the element with atomic number 50 is Tin (Sn). Therefore, the unknown particle X is 50 131 S n .
Final Answer The unknown particle X in the nuclear reaction is 50 131 S n .
Examples
Nuclear fission reactions, like the one in this problem, are used in nuclear power plants to generate electricity. By understanding the products of fission, scientists can better control the reaction and harness the energy released. For example, the fission of uranium can produce lighter elements and neutrons, which then trigger further fission events, creating a chain reaction. The identification of these elements is crucial for managing nuclear waste and ensuring the safe operation of reactors. Also, this type of calculation is used in medical applications such as targeted alpha therapy, where specific isotopes are used to target and destroy cancer cells.
