Let's analyze the given nuclear equation and identify the missing element.
The nuclear equation is represented as:
[tex]\[ {}_{94}^{239}Pu + {}_{0}^{1}n \rightarrow \, \text{?} + {}_{54}^{134}Xe + 3 \, {}_{0}^{1}n \][/tex]
To find the missing element, we balance the atomic numbers and mass numbers on both sides of the equation.
1. Initial atomic and mass numbers:
- For plutonium ([tex]\(_{94}^{239}Pu\)[/tex]):
- Atomic number: 94
- Mass number: 239
- For the neutron ([tex]\(_{0}^{1}n\)[/tex]):
- Atomic number: 0
- Mass number: 1
- Sum of initial atomic numbers: [tex]\( 94 + 0 = 94 \)[/tex]
- Sum of initial mass numbers: [tex]\( 239 + 1 = 240 \)[/tex]
2. Final atomic and mass numbers - excluding the missing element:
- For xenon ([tex]\(_{54}^{134}Xe\)[/tex]):
- Atomic number: 54
- Mass number: 134
- For the three neutrons ([tex]\(3 \times {}_{0}^{1}n\)[/tex]):
- Total atomic number: [tex]\(3 \times 0 = 0\)[/tex]
- Total mass number: [tex]\(3 \times 1 = 3\)[/tex]
- Sum of final atomic numbers excluding the missing element: [tex]\( 54 + 0 = 54 \)[/tex]
- Sum of final mass numbers excluding the missing element: [tex]\( 134 + 3 = 137 \)[/tex]
3. Determine the atomic and mass numbers of the missing element:
- Atomic number of the missing element: [tex]\( 94 - 54 = 40 \)[/tex]
- Mass number of the missing element: [tex]\( 240 - 137 = 103 \)[/tex]
4. Identify the missing element:
- The element with atomic number 40 is zirconium (Zr).
- Therefore, the missing element is [tex]\( \, {}_{40}^{103}Zr \)[/tex].
Rewriting the complete equation with the missing element included, we get:
[tex]\[ {}_{94}^{239}Pu + {}_{0}^{1}n \rightarrow {}_{40}^{103}Zr + {}_{54}^{134}Xe + 3 \, {}_{0}^{1}n \][/tex]
So, the correct missing element in the nuclear equation is [tex]\( {}_{40}^{103}Zr \)[/tex].
