Which of the following nuclear change is incorrect?

Options

A. `._(20)Ca^(40) + ._(0)n^(1) rarr ._(19)K^(40) + ._(1)H^(1)`
B. `._(12)Mg^(24) + alpha rarr ._(14)Si^(27) + ._(0)n^(1)`
C. `._(48)Cd^(113) + ._(0)n^(1) rarr ._(48)Cd^(112) + ._(-1)e^(0)`
D. `._(20)Co^(43) + alpha rarr ._(21)Si^(46) + ._(1)H^(1)`

Explanation

To determine which of the given nuclear changes is incorrect, we need to analyze each option based on the conservation of atomic mass and atomic number. The conservation laws state that in a nuclear reaction, the total mass number and the total atomic number must remain constant before and after the reaction.

### Step-by-Step Solution:

1. **Analyze Option A:**
- **Reactants:**
- Mass number = 40 + 1 = 41
- Atomic number = 20 + 0 = 20
- **Products:**
- Mass number = 40 + 1 = 41
- Atomic number = 90 + 1 = 20
- **Conclusion:** Both mass number and atomic number are conserved. Option A is correct.

2. **Analyze Option B:**
- **Reactants:**
- Mass number = 24 + 4 (from alpha particle) = 28
- Atomic number = 12 + 2 (from alpha particle) = 14
- **Products:**
- Mass number = 27 + 1 = 28
- Atomic number = 14 + 0 = 14
- **Conclusion:** Both mass number and atomic number are conserved. Option B is correct.

3. **Analyze Option C:**
- **Reactants:**
- Mass number = 113 + 1 = 114
- Atomic number = 48 + 0 = 48
- **Products:**
- Mass number = 112 + 0 = 112
- Atomic number = 48 - 1 = 47
- **Conclusion:** Mass number is not conserved (114 ≠ 112) and atomic number is also not conserved (48 ≠ 47). Option C is incorrect.

4. **Analyze Option D:**
- **Reactants:**
- Mass number = 43 + 4 = 47
- Atomic number = 20 + 2 = 22
- **Products:**
- Mass number = 46 + 1 = 47
- Atomic number = 21 + 1 = 22
- **Conclusion:** Both mass number and atomic number are conserved. Option D is correct.

### Final Conclusion:
Only option C is the incorrect nuclear change as it violates the conservation of atomic mass and atomic number.

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