which of these nuclear reaction is possible?

Options

A. `""_(11)^(23)Na+""_(1)^(1)Hto""_(19)^(20)Ne+""_(2)^(4)He`
B. `""_(5)^(10)B+""_(2)^(4)Heto""_(7)^(13)N+""_(1)^(1)H`
C. `""_(5)^(10)B+""_(0)^(1)nto""_(5)^(11)B+beta^(-1)+barv`
D. `""_(7)^(11)N+""_(1)^(1)Hto""_(6)^(12)C+beta^(-)+barv`

Answer

To determine which of the given nuclear reactions is possible, we need to apply the conservation laws of nuclear reactions, specifically the conservation of nucleon number (mass number) and the conservation of charge (atomic number).

### Step-by-Step Solution:

1. **Identify the Reactions**:
We need to analyze each nuclear reaction provided in the question. Let's denote them as Reaction 1, Reaction 2, Reaction 3, and Reaction 4.

2. **Check Reaction 1**:
- Reaction: \( ^{23}_{11}Na + ^{1}_{0}n \rightarrow ^{24}_{12}Mg + ^{4}_{2}He \)
- Mass Number: Left side = \( 23 + 1 = 24 \); Right side = \( 24 + 4 = 28 \) (not equal)
- Charge: Left side = \( 11 + 0 = 11 \); Right side = \( 12 + 2 = 14 \) (not equal)
- **Conclusion**: This reaction is **not possible**.

3. **Check Reaction 2**:
- Reaction: \( ^{10}_{5}B + ^{4}_{2}He \rightarrow ^{14}_{7}N + ^{1}_{1}H \)
- Mass Number: Left side = \( 10 + 4 = 14 \); Right side = \( 14 + 1 = 15 \) (not equal)
- Charge: Left side = \( 5 + 2 = 7 \); Right side = \( 7 + 1 = 8 \) (not equal)
- **Conclusion**: This reaction is **not possible**.

4. **Check Reaction 3**:
- Reaction: \( ^{10}_{5}B + ^{1}_{0}n \rightarrow ^{11}_{6}C + ^{1}_{-1}e \)
- Mass Number: Left side = \( 10 + 1 = 11 \); Right side = \( 11 + 1 = 12 \) (not equal)
- Charge: Left side = \( 5 + 0 = 5 \); Right side = \( 6 - 1 = 5 \) (equal)
- **Conclusion**: This reaction is **not possible** due to mass number.

5. **Check Reaction 4**:
- Reaction: \( ^{11}_{6}C + ^{1}_{0}n \rightarrow ^{12}_{6}C + ^{1}_{1}H \)
- Mass Number: Left side = \( 11 + 1 = 12 \); Right side = \( 12 + 1 = 13 \) (not equal)
- Charge: Left side = \( 6 + 0 = 6 \); Right side = \( 6 + 1 = 7 \) (not equal)
- **Conclusion**: This reaction is **not possible**.

6. **Final Conclusion**:
After analyzing all the reactions, none of the reactions provided are possible based on the conservation laws of mass number and charge.