In the nuclear reaction `Mg_12^(24) + He_2^4 to n_0^1 + (?)` The product nucleus is

Options

A. `Al_13^27`
B. `Si_14^27`
C. `Al_13^28`
D. `Mg_12^25`

Answer

To solve the nuclear reaction \( \text{Mg}_{12}^{24} + \text{He}_{2}^{4} \to \text{n}_{0}^{1} + (?) \), we need to determine the product nucleus by balancing both the atomic numbers and mass numbers on both sides of the equation.

### Step-by-Step Solution:

1. **Identify the Reactants:**
- The reactants are \( \text{Mg}_{12}^{24} \) (Magnesium with atomic number 12 and mass number 24) and \( \text{He}_{2}^{4} \) (Helium with atomic number 2 and mass number 4).

2. **Calculate Total Atomic Number on the Left Side:**
- The total atomic number on the left side is:
\[ 12 \, (\text{from Mg}) + 2 \, (\text{from He}) = 14 \]

3. **Calculate Total Mass Number on the Left Side:**
- The total mass number on the left side is:
\[ 24 \, (\text{from Mg}) + 4 \, (\text{from He}) = 28 \]

4. **Identify the Products:**
- One of the products is a neutron \( \text{n}_{0}^{1} \) which has an atomic number of 0 and a mass number of 1.
- Let’s denote the unknown product nucleus as \( \text{X}_{Z}^{A} \), where \( Z \) is the atomic number and \( A \) is the mass number.

5. **Balance the Atomic Numbers:**
- The total atomic number on the right side must equal the total atomic number on the left side:
\[ 0 \, (\text{from neutron}) + Z = 14 \]
- Therefore, \( Z = 14 \).

6. **Balance the Mass Numbers:**
- The total mass number on the right side must equal the total mass number on the left side:
\[ 1 \, (\text{from neutron}) + A = 28 \]
- Therefore, \( A = 28 - 1 = 27 \).

7. **Identify the Product Nucleus:**
- We have determined that the product nucleus is \( \text{X}_{14}^{27} \).
- The atomic number 14 corresponds to Silicon (Si), and the mass number is 27.

### Conclusion:
The product nucleus is \( \text{Si}_{14}^{27} \) (Silicon-27).