Complete the following fusion reactions :
(a) ` ""_(2)^(3) He +_(1)^(2) H to_2 He + _1 H + en ergy`
(b) ` ""_(1)^(2) He +_(1)^(2) H to_2 He + ^1 n + en ergy`

Answer

To complete the given fusion reactions, we will follow the steps of balancing the atomic numbers and mass numbers. Let's break down each reaction step by step.

### (a) Reaction: `""_(2)^(3) He + _(1)^(2) H to_2 He + _1 H + energy`

1. **Identify the Reactants**:
- Helium-3 (He) with atomic number 2 and mass number 3.
- Deuterium (H) with atomic number 1 and mass number 2.

2. **Determine the Products**:
- The products are given as Helium (He) and Hydrogen (H) plus energy.
- We need to find the correct mass and atomic numbers for the products.

3. **Calculate Total Atomic and Mass Numbers for Reactants**:
- Total atomic number = 2 (from He) + 1 (from H) = 3.
- Total mass number = 3 (from He) + 2 (from H) = 5.

4. **Assign Products**:
- We know that Helium (He) is produced, and we need to find the other product.
- Let's assume the products are Helium-4 (He) and Hydrogen-1 (H).

5. **Check Atomic and Mass Numbers for Products**:
- Helium-4 has atomic number 2 and mass number 4.
- Hydrogen-1 has atomic number 1 and mass number 1.
- Total atomic number for products = 2 (from He) + 1 (from H) = 3.
- Total mass number for products = 4 (from He) + 1 (from H) = 5.

6. **Conclusion**:
- The completed reaction is:
\[ _{2}^{3}He + _{1}^{2}H \rightarrow _{2}^{4}He + _{1}^{1}H + \text{energy} \]

### (b) Reaction: `""_(1)^(2) He + _(1)^(2) H to_2 He + ^1 n + energy`

1. **Identify the Reactants**:
- Helium-2 (He) with atomic number 1 and mass number 2.
- Deuterium (H) with atomic number 1 and mass number 2.

2. **Determine the Products**:
- The products are given as Helium and a neutron (n) plus energy.
- We need to find the correct mass and atomic numbers for the products.

3. **Calculate Total Atomic and Mass Numbers for Reactants**:
- Total atomic number = 1 (from He) + 1 (from H) = 2.
- Total mass number = 2 (from He) + 2 (from H) = 4.

4. **Assign Products**:
- We know that Helium is produced, and we need to find the other product.
- The neutron has atomic number 0 and mass number 1.

5. **Check Atomic and Mass Numbers for Products**:
- Let’s assume the product is Helium-3 (He) and a neutron (n).
- Helium-3 has atomic number 2 and mass number 3.
- Neutron has atomic number 0 and mass number 1.
- Total atomic number for products = 2 (from He) + 0 (from n) = 2.
- Total mass number for products = 3 (from He) + 1 (from n) = 4.

6. **Conclusion**:
- The completed reaction is:
\[ _{1}^{2}He + _{1}^{2}H \rightarrow _{2}^{3}He + _{0}^{1}n + \text{energy} \]

### Final Completed Reactions:
(a) \(_{2}^{3}He + _{1}^{2}H \rightarrow _{2}^{4}He + _{1}^{1}H + \text{energy}\)

(b) \(_{1}^{2}He + _{1}^{2}H \rightarrow _{2}^{3}He + _{0}^{1}n + \text{energy}\)