From the following equation pick out the possible nuclear fusion reactions

Options

A. `6^(C^(13))+1^(H^1)rarr6^(C^(14))+4.3 MeV`
B. `6^(C^(12))+1^(H^1)rarr7^(N^(13))+2 MeV`
C. `7^(C^(14))+1^(H^1)rarr8^(O^(15))+7.3 MeV`
D. `92^(U^(235))+0^(n^(1))rarr54^(Xe^(140))+36Sr^(94)+0^(n^(1))+0^(n^(1))+y+200 MeV`

Answer

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

Let's analyze each option step by step:

1. **Option 1: \( ^{6}_{C}{}^{13} + ^{1}_{H}{}^{1} \rightarrow ^{6}_{C}{}^{14} + \text{energy} \)**
- Here, carbon-13 (\( ^{6}_{C}{}^{13} \)) is combining with a hydrogen nucleus (\( ^{1}_{H}{}^{1} \)) to form carbon-14 (\( ^{6}_{C}{}^{14} \)).
- However, carbon-13 is not abundantly available in nature, which makes this reaction impractical. Therefore, this option is ruled out.

2. **Option 2: \( ^{6}_{C}{}^{12} + ^{1}_{H}{}^{1} \rightarrow ^{7}_{N}{}^{13} + \text{energy} \)**
- In this reaction, carbon-12 (\( ^{6}_{C}{}^{12} \)) combines with a hydrogen nucleus (\( ^{1}_{H}{}^{1} \)) to produce nitrogen-13 (\( ^{7}_{N}{}^{13} \)).
- Both carbon-12 and hydrogen-1 are stable and abundant in nature, making this a valid nuclear fusion reaction. This option is possible.

3. **Option 3: \( ^{7}_{C}{}^{14} + ^{1}_{H}{}^{1} \rightarrow ^{8}_{O}{}^{15} + \text{energy} \)**
- Here, carbon-14 (\( ^{7}_{C}{}^{14} \)) is combining with hydrogen-1 (\( ^{1}_{H}{}^{1} \)) to form oxygen-15 (\( ^{8}_{O}{}^{15} \)).
- However, carbon-14 is not a stable isotope and does not exist abundantly in nature, thus this reaction is also ruled out.

4. **Option 4: \( ^{92}_{U}{}^{235} + ^{0}_{N}{}^{1} \rightarrow ^{54}_{X}{}^{140} + ^{36}_{Z}{}^{94} + \text{neutron} + \text{energy} \)**
- In this case, uranium-235 (\( ^{92}_{U}{}^{235} \)) is interacting with a neutron (\( ^{0}_{N}{}^{1} \)) to produce two smaller nuclei and additional neutrons.
- This is a fission reaction, not fusion, because it involves the splitting of a heavy nucleus into lighter nuclei. Therefore, this option is also ruled out.

**Conclusion:**
The only valid nuclear fusion reaction from the given options is **Option 2**: \( ^{6}_{C}{}^{12} + ^{1}_{H}{}^{1} \rightarrow ^{7}_{N}{}^{13} + \text{energy} \).