Which of the following are correct nuclear reactions?

Options

A. `""_(27)Co^(60) to ""_(28)Ni^(60) + ""_(-1)e^(0) + barv`
B. `""_(3)Li^(7) + ""_(1)H^(1) to ""_(2)Be^(8) to 2, ""_(2)He^(4) + ""_(-1)e^(0)`
C. `""_(1)H^(2) + gamma to ""_(1)H^(1) + ""_(0)n^(1)`
D. `""_(1)H^(1) + ""_(1)H^(1) to ""_(1)H^(2) + ""_(-1)e^(0)+ ""_(0)n^(1) + 2.5` MeV

Explanation

To determine which of the given nuclear reactions are correct, we need to ensure that both the atomic numbers and mass numbers are conserved in each reaction. Let's analyze each option step by step.

### Step 1: Analyze Option A
**Reaction:** \( ^{60}_{27}Al \rightarrow ^{60}_{28}Rh + \bar{\nu} \)

1. **Check Atomic Numbers:**
- Reactant Side: \( 27 \) (Aluminum)
- Product Side: \( 28 \) (Rhodium) + \( 0 \) (anti-neutrino)
- Total Atomic Number: \( 28 + 0 = 28 \)
- **Balance:** \( 27 \) (reactants) vs \( 28 \) (products) → Not balanced.

2. **Check Mass Numbers:**
- Reactant Side: \( 60 \)
- Product Side: \( 60 \) (Rhodium) + \( 0 \) (anti-neutrino)
- Total Mass Number: \( 60 + 0 = 60 \)
- **Balance:** \( 60 \) (reactants) vs \( 60 \) (products) → Balanced.

**Conclusion for Option A:** Not a correct nuclear reaction due to atomic number imbalance.

### Step 2: Analyze Option B
**Reaction:** \( ^{4}_{2}He + ^{3}_{1}H \rightarrow ^{4}_{2}He + ^{1}_{0}n \)

1. **Check Atomic Numbers:**
- Reactant Side: \( 2 + 1 = 3 \)
- Product Side: \( 2 + 0 = 2 \)
- **Balance:** \( 3 \) (reactants) vs \( 2 \) (products) → Not balanced.

2. **Check Mass Numbers:**
- Reactant Side: \( 4 + 3 = 7 \)
- Product Side: \( 4 + 1 = 5 \)
- **Balance:** \( 7 \) (reactants) vs \( 5 \) (products) → Not balanced.

**Conclusion for Option B:** Not a correct nuclear reaction due to both atomic number and mass number imbalance.

### Step 3: Analyze Option C
**Reaction:** \( ^{2}_{1}H + ^{1}_{1}H \rightarrow ^{2}_{1}H + ^{1}_{0}n \)

1. **Check Atomic Numbers:**
- Reactant Side: \( 1 + 1 = 2 \)
- Product Side: \( 1 + 0 = 1 \)
- **Balance:** \( 2 \) (reactants) vs \( 1 \) (products) → Not balanced.

2. **Check Mass Numbers:**
- Reactant Side: \( 2 + 1 = 3 \)
- Product Side: \( 2 + 1 = 3 \)
- **Balance:** \( 3 \) (reactants) vs \( 3 \) (products) → Balanced.

**Conclusion for Option C:** Not a correct nuclear reaction due to atomic number imbalance.

### Step 4: Analyze Option D
**Reaction:** \( ^{1}_{1}H + ^{1}_{1}H \rightarrow ^{2}_{1}H + ^{0}_{-1}e \)

1. **Check Atomic Numbers:**
- Reactant Side: \( 1 + 1 = 2 \)
- Product Side: \( 1 + (-1) = 0 \)
- **Balance:** \( 2 \) (reactants) vs \( 0 \) (products) → Not balanced.

2. **Check Mass Numbers:**
- Reactant Side: \( 1 + 1 = 2 \)
- Product Side: \( 2 + 0 = 2 \)
- **Balance:** \( 2 \) (reactants) vs \( 2 \) (products) → Balanced.

**Conclusion for Option D:** Not a correct nuclear reaction due to atomic number imbalance.

### Final Conclusion:
After analyzing all options, none of the reactions are correct nuclear reactions as they do not satisfy the conservation of atomic numbers.