To balance the given nuclear fission equation of californium undergoing fission, we need to ensure that both the atomic numbers (protons) and the mass numbers (nucleons) are conserved on both sides of the equation.
The initial unbalanced nuclear equation is given as:
[tex]\[ _{98}^{252} \text{Cf} + \, _{0}^{1} \text{n} \rightarrow \, _{52}^{136} \text{Te} + \, 3 \, _{0}^{1} \text{n} + \, ??? \][/tex]
Let's fill in the missing parts.
1. Conservation of atomic number (protons):
- On the left side:
[tex]\[ 98 \, (\text{Cf}) + 0 \, (\text{n}) = 98 \][/tex]
- On the right side:
[tex]\[ 52 \, (\text{Te}) + 3 \cdot 0 \, (\text{n}) + ??? \][/tex]
To balance, the missing atomic number should be:
[tex]\[ 98 - 52 = 46 \][/tex]
The element with atomic number 46 is palladium (Pd).
2. Conservation of mass number (nucleons):
- On the left side:
[tex]\[ 252 \, (\text{Cf}) + 1 \, (\text{n}) = 253 \][/tex]
- On the right side:
[tex]\[ 136 \, (\text{Te}) + 3 \cdot 1 \, (\text{n}) + ??? \][/tex]
To balance, the missing mass number should be:
[tex]\[ 253 - 139 = 114 \][/tex]
Thus, the missing part is:
[tex]\[ _{46}^{114} \text{Pd} \][/tex]
The balanced nuclear equation is:
[tex]\[ _{98}^{252} \text{Cf} + \, _{0}^{1} \text{n} \rightarrow \, _{52}^{136} \text{Te} + \, 3 \, _{0}^{1} \text{n} + \, _{46}^{114} \text{Pd} \][/tex]
So, the correct arrangement is:
[tex]\[ _{98}^{252} \text{Cf} + \, _{0}^{1} \text{n} \longrightarrow \, _{52}^{136} \text{Te} + 3 \, _{0}^{1} \text{n} + \, _{46}^{114} \text{Pd} \][/tex]
