Certainly! Let's go through the process of completing each nuclear reaction step-by-step.
1. First Reaction:
[tex]\[
{ }_1^2 H +{ }_1^2 H \rightarrow{ }_8^9 He +{ }_0^1 n
\][/tex]
- On the left side, we have two hydrogen nuclei (^2H):
- Sum of atomic numbers (protons): [tex]\(1 (H) + 1 (H) = 2\)[/tex]
- Sum of mass numbers (nucleons): [tex]\(2 (H) + 2 (H) = 4\)[/tex]
- On the right side, we have a helium-3 nucleus (^3He) and a neutron (n):
- Atomic number of helium (He): [tex]\(2\)[/tex]
- Atomic number of neutron (n): [tex]\(0\)[/tex]
[tex]\[
\text{He (atomic number)}: 2 \quad \text{Neutron (atomic number)}: 0
\][/tex]
- Mass number of helium (He): [tex]\(3\)[/tex]
- Mass number of neutron (n): [tex]\(1\)[/tex]
[tex]\[
\text{He (mass number)}: 3 \quad \text{Neutron (mass number)}: 1
\][/tex]
- Balancing the equation:
[tex]\[
{_1^2 H +{ }_1^2 H \rightarrow{ }_2^3 He +{ }_0^1 n}
\][/tex]
- Therefore, [tex]\(D\)[/tex] represents the sum of atomic numbers on the left side, and [tex]\(F\)[/tex] represents the sum of mass numbers on the left side.
[tex]\[
D = 2 \quad F = 4
\][/tex]
2. Second Reaction:
[tex]\[
{ }_{02}^{238} U \rightarrow{ }_{\circ}^{ T } Th +{ }_2^4 He
\][/tex]
- On the left side, we have uranium-238 (^238U):
- Atomic number: [tex]\(92\)[/tex]
- Mass number: [tex]\(238\)[/tex]
- On the right side, we have thorium (^234Th) and a helium nucleus (^4He):
- Sum of atomic numbers: [tex]\(90 (Th) + 2 (He) = 92\)[/tex]
- Sum of mass numbers: [tex]\(234 (Th) + 4 (He) = 238\)[/tex]
- Balancing the equation:
[tex]\[
{ }_{92}^{238} U \rightarrow{ }_{90}^{234} Th +{ }_2^4 He
\][/tex]
- Therefore, [tex]\(E\)[/tex] represents the atomic number of uranium, and [tex]\(G\)[/tex] represents the mass number of uranium.
[tex]\[
E = 92 \quad G = 238
\][/tex]
Finally, summarizing all the values:
[tex]\[
D: 2 \quad F: 4 \quad E: 92 \quad G: 238
\][/tex]
