Let's solve the nuclear fission equation step-by-step to identify the missing element:
1. Start with the given nuclear equation:
[tex]\[ _{94}^{239} \text{Pu} + _{0}^{1} \text{n} \longrightarrow \text{X} + _{54}^{134} \text{Xe} + 3 \, _{0}^{1} \text{n} \][/tex]
2. Balance the atomic numbers (protons):
On the left side, the total atomic number is:
[tex]\[ 94 (\text{from Pu}) + 0 (\text{from neutron}) = 94 \][/tex]
On the right side, the atomic number should also sum to 94. We have:
[tex]\[ 54 (\text{from Xe}) + \text{atomic number of X} = 94 \][/tex]
Therefore, the atomic number of X is:
[tex]\[ 94 - 54 = 40 \][/tex]
3. Balance the mass numbers (nucleons):
On the left side, the total mass number is:
[tex]\[ 239 (\text{from Pu}) + 1 (\text{from neutron}) = 240 \][/tex]
On the right side, the mass number should also sum to 240. We have:
[tex]\[ 134 (\text{from Xe}) + 3 \times 1 (\text{from three neutrons}) + \text{mass number of X} = 240 \][/tex]
Simplifying this, we get:
[tex]\[ 134 + 3 + \text{mass number of X} = 240 \][/tex]
Therefore, the mass number of X is:
[tex]\[ 240 - 134 - 3 = 103 \][/tex]
4. Put it all together:
The missing element X has an atomic number of 40 and a mass number of 103. The element with an atomic number of 40 is Zirconium (Zr).
Thus, the missing element in the nuclear equation is:
[tex]\[ _{40}^{103} \text{Zr} \][/tex]
Finally, let's see it in the context of the provided choices:
The correct symbol to complete the equation is:
[tex]\[ _{94}^{239} \text{Pu} + _{0}^{1} \text{n} \longrightarrow _{40}^{103} \text{Zr} + _{54}^{134} \text{Xe} + 3 \, _{0}^{1} \text{n} \][/tex]
