The product nucleus in the nuclear reaction is `""_(12)Mg^(24)+""_2He^4=""0n^1+` ?

Options

A. `""_13Al^27`
B. `""_14Si^27`
C. `""_13Al^28`
D. `""_12Al^25`

Answer

To solve the nuclear reaction given in the question, we need to identify the product nucleus formed when magnesium-24 reacts with helium-4 and produces a neutron.

### Step-by-Step Solution:

1. **Identify the Reactants:**
- Magnesium-24 (Mg) has an atomic number of 12 and a mass number of 24.
- Helium-4 (He) has an atomic number of 2 and a mass number of 4.
- The neutron (n) has an atomic number of 0 and a mass number of 1.

2. **Write the Nuclear Reaction:**
The reaction can be written as:
\[ {}_{12}^{24}\text{Mg} + {}_{2}^{4}\text{He} \rightarrow {}_{0}^{1}\text{n} + {}_{Z}^{A}\text{X} \]
where \(Z\) is the atomic number and \(A\) is the mass number of the product nucleus \(X\).

3. **Conservation of Mass Number:**
The total mass number on the left side must equal the total mass number on the right side:
\[ 24 + 4 = 1 + A \]
Simplifying this gives:
\[ 28 = 1 + A \implies A = 27 \]

4. **Conservation of Atomic Number:**
The total atomic number on the left side must equal the total atomic number on the right side:
\[ 12 + 2 = 0 + Z \]
Simplifying this gives:
\[ 14 = Z \]

5. **Identify the Product Nucleus:**
The product nucleus has an atomic number of 14 and a mass number of 27. Referring to the periodic table, the element with atomic number 14 is silicon (Si).

6. **Final Reaction:**
Therefore, the complete nuclear reaction is:
\[ {}_{12}^{24}\text{Mg} + {}_{2}^{4}\text{He} \rightarrow {}_{0}^{1}\text{n} + {}_{14}^{27}\text{Si} \]

### Conclusion:
The product nucleus in the nuclear reaction is silicon-27 (\( {}_{14}^{27}\text{Si} \)).