Which of the following equations, pick out the possible nuclear fusion reactions?

Options

A. `._6^13C +._1^1H to ._6^14C` +4.3 MeV
B. `._6^12C + ._1^1H to ._7^13N` + 2 MeV
C. `._7^14N + ._1^1H to ._8^15O ` + 7.3 MeV
D. `._92^235U + ._0^1N to ._54^140 Xe + ._38^94Sr + ._0^1n + ._0^1n` + 200 MeV

Answer

To determine which of the given equations represent possible nuclear fusion reactions, we first need to understand what a nuclear fusion reaction is. A nuclear fusion reaction occurs when two lighter atomic nuclei combine to form a heavier nucleus, releasing energy in the process.

Now, let's analyze each option step by step:

### Step 1: Analyze the First Option
**Reaction:** An isotope of carbon (C-13) combines with a hydrogen atom (H-1) to produce C-14 and energy.

- **Mass Number Check:**
- Reactants: C-13 (mass number 13) + H-1 (mass number 1) = 14
- Products: C-14 (mass number 14)
- Mass number is conserved.

- **Atomic Number Check:**
- Reactants: C (atomic number 6) + H (atomic number 1) = 7
- Products: C (atomic number 6)
- Atomic number is not conserved (6 + 1 ≠ 6).

**Conclusion:** This reaction is not a valid nuclear fusion reaction due to the violation of atomic number conservation.

### Step 2: Analyze the Second Option
**Reaction:** C-12 combines with H-1 to produce nitrogen (N-13) and energy.

- **Mass Number Check:**
- Reactants: C-12 (mass number 12) + H-1 (mass number 1) = 13
- Products: N-13 (mass number 13)
- Mass number is conserved.

- **Atomic Number Check:**
- Reactants: C (atomic number 6) + H (atomic number 1) = 7
- Products: N (atomic number 7)
- Atomic number is conserved (6 + 1 = 7).

**Conclusion:** This reaction is a valid nuclear fusion reaction.

### Step 3: Analyze the Third Option
**Reaction:** A nitrogen atom (N-14) combines with a hydrogen atom (H-1) to produce an isotope of oxygen (O-15).

- **Mass Number Check:**
- Reactants: N-14 (mass number 14) + H-1 (mass number 1) = 15
- Products: O-15 (mass number 15)
- Mass number is conserved.

- **Atomic Number Check:**
- Reactants: N (atomic number 7) + H (atomic number 1) = 8
- Products: O (atomic number 8)
- Atomic number is conserved (7 + 1 = 8).

**Conclusion:** This reaction is a valid nuclear fusion reaction.

### Step 4: Analyze the Fourth Option
**Reaction:** A uranium atom (U-235) combines with a neutron to produce two lighter atoms.

- **Nature of Reaction:**
- This reaction involves a heavy nucleus splitting into lighter nuclei, which is characteristic of nuclear fission, not fusion.

**Conclusion:** This reaction is not a nuclear fusion reaction.

### Final Conclusion
The possible nuclear fusion reactions from the options provided are:
- **Option 2:** C-12 + H-1 → N-13 + energy
- **Option 3:** N-14 + H-1 → O-15 + energy

### Summary of Valid Options
- **Valid Fusion Reactions:** Option 2 and Option 3
- **Invalid Fusion Reactions:** Option 1 and Option 4