To complete the given nuclear reactions, we need to ensure that both the mass numbers (the superscripts) and the atomic numbers (the subscripts) balance on both sides of the reaction equation.
Let's analyze each reaction step by step:
### First Reaction:
Given:
[tex]\[ {}_1^2 H + {}_1^2 H \rightarrow {}_{a}^{d} He + {}_0^1 n \][/tex]
1. Initial Mass and Atomic Numbers:
- [tex]\({}_1^2 H\)[/tex] (Hydrogen isotope): Mass Number = 2, Atomic Number = 1
- [tex]\({}_1^2 H\)[/tex] (Hydrogen isotope): Mass Number = 2, Atomic Number = 1
2. Total Mass Number Before the Reaction:
- [tex]\(2 (from the first \ {}_1^2 H) + 2 (from the second \ {}_1^2 H) = 4\)[/tex]
3. Total Atomic Number Before the Reaction:
- [tex]\(1 (from the first \ {}_1^2 H) + 1 (from the second \ {}_1^2 H) = 2\)[/tex]
Now, we need to balance the mass number and atomic number on the product side:
4. The neutron [tex]\({}_0^1 n\)[/tex]:
- Mass Number = 1
- Atomic Number = 0
5. For Helium [tex]\({}_{a}^{d} He\)[/tex]:
- The remaining mass number from the total should be [tex]\(4 - 1 = 3\)[/tex]
- The remaining atomic number should be [tex]\(2 - 0 = 2 \)[/tex]
Therefore, Helium must have:
- Mass Number = 4
- Atomic Number = 2
So, the completed reaction is:
[tex]\[ {}_1^2 H + {}_1^2 H \rightarrow {}_{2}^{4} He + {}_0^1 n \][/tex]
### Second Reaction:
Given:
[tex]\[ {}_{92}^{238} U \rightarrow {}_{g}^{e} Th + {}_{2}^{4} He \][/tex]
1. Initial Mass and Atomic Numbers:
- [tex]\({}_{92}^{238} U\)[/tex] (Uranium): Mass Number = 238, Atomic Number = 92
- [tex]\({}_{2}^{4} He\)[/tex] (Helium or Alpha particle): Mass Number = 4, Atomic Number = 2
2. Products (Th and He):
- Total Mass Number After Reaction = 238
- Total Atomic Number After Reaction = 92
For Thorium [tex]\({}_{g}^{e} Th\)[/tex]:
3. Mass Number :
- [tex]\(238 - 4 = 234\)[/tex]
4. Atomic Number :
- [tex]\(92 - 2 = 90\)[/tex]
So, Thorium [tex]\({}_{g}^{e} Th\)[/tex]: Mass Number = 234, Atomic Number = 90
Thus, the completed reaction is:
[tex]\[ {}_{92}^{238} U \rightarrow {}_{90}^{234} Th + {}_{2}^{4} He \][/tex]
### Summary of Results:
- For the first reaction:
[tex]\[ D : 4, F : 2 \][/tex]
- For the second reaction:
[tex]\[ E : 234, G : 90 \][/tex]
#### Final Answers:
[tex]\[ D: 4 \][/tex]
[tex]\[ F: 2 \][/tex]
[tex]\[ E: 234 \][/tex]
[tex]\[ G: 90 \][/tex]
