Let's address each nuclear fission reaction step by step:
### First Reaction:
[tex]\[ {}_{92}^{255} \text{U} + {}_{0}^{1} \text{n} \rightarrow {}_{36}^{90} \text{Kr} + {}_{56}^{A} \text{Ba} + 3 \cdot {}_{0}^{1} \text{n} \][/tex]
1. Mass Number Conservation:
In a nuclear reaction, the total mass number (sum of protons and neutrons) must be conserved. The equation for the mass numbers is:
[tex]\[ 255 \, (\text{U}) + 1 \, (\text{n}) = 90 \, (\text{Kr}) + A \, (\text{Ba}) + 3 \times 1 \, (\text{neutron}) \][/tex]
Solving for [tex]\( A \)[/tex]:
[tex]\[ 256 = 90 + A + 3 \][/tex]
[tex]\[ 256 = 93 + A \][/tex]
[tex]\[ A = 256 - 93 \][/tex]
[tex]\[ A = 163 \][/tex]
2. Atomic Number Conservation:
The total atomic number (number of protons) must also be conserved. The equation for the atomic numbers is:
[tex]\[ 92 \, (\text{U}) + 0 \, (\text{n}) = 36 \, (\text{Kr}) + 56 \, (\text{Ba}) + 3 \times 0 \, (\text{neutron}) \][/tex]
Solving for the atomic number of barium, we already found it to be:
[tex]\[ 56 \][/tex]
Thus, for the first reaction:
- [tex]\( A = 163 \)[/tex]
- The atomic number of barium is 56.
### Second Reaction:
[tex]\[ {}_{94}^{239} \text{Pu} + {}_{0}^{1} \text{n} \rightarrow {}_{ C }^{ 147 } \text{Ba} + {}_{38}^{90} \text{Sr} + 3 \cdot {}_{0}^{1} \text{n} \][/tex]
1. Mass Number Conservation:
For the mass numbers:
[tex]\[ 239 \, (\text{Pu}) + 1 \, (\text{n}) = 147 \, (\text{Ba}) + 90 \, (\text{Sr}) + 3 \times 1 \, (\text{neutron}) \][/tex]
Solving for [tex]\( B \)[/tex]:
[tex]\[ 240 = 147 + 90 + 3 \][/tex]
[tex]\[ 240 = 240 \][/tex]
Thus, the mass number for barium in the second reaction is indeed 147.
2. Atomic Number Conservation:
For the atomic numbers:
[tex]\[ 94 \, (\text{Pu}) + 0 \, (\text{n}) = C \, (\text{Ba}) + 38 \, (\text{Sr}) + 3 \times 0 \, (\text{neutron}) \][/tex]
Solving for the atomic number [tex]\( C \)[/tex]:
[tex]\[ 94 = C + 38 \][/tex]
[tex]\[ C = 94 - 38 \][/tex]
[tex]\[ C = 56 \][/tex]
So, for the second reaction, we find that:
- The atomic number [tex]\( C \)[/tex] for barium is 56.
Therefore, summarizing the results:
1. First Reaction:
- [tex]\( A = 163 \)[/tex]
- Atomic number of barium: 56
2. Second Reaction:
- [tex]\( B = 147 \)[/tex]
- [tex]\( C = 56 \)[/tex]
So, the final answers are:
- _A:_ 163
- _B:_ 147
- _C:_ 56
