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 problem, we need to analyze the given reaction step by step. The reaction is:

\[ _{12}^{24}Mg + _{2}^{4}He \rightarrow _{0}^{1}n + ? \]

### Step 1: Identify the reactants and their properties
- Magnesium (Mg) has an atomic number of 12 and a mass number of 24.
- Helium (He) has an atomic number of 2 and a mass number of 4.

### Step 2: Write down the total mass number and atomic number of the reactants
- Total mass number on the left side = 24 (from Mg) + 4 (from He) = 28
- Total atomic number on the left side = 12 (from Mg) + 2 (from He) = 14

### Step 3: Identify the products
One of the products is a neutron, which has a mass number of 1 and an atomic number of 0. Therefore, we can denote the unknown product as \(X\) with an unknown mass number \(A\) and atomic number \(Z\).

### Step 4: Set up the equations for mass number and atomic number
From the reaction, we can set up the following equations based on the conservation of mass number and atomic number:

1. Mass number:
\[ 28 = 1 + A \quad \text{(where A is the mass number of the unknown product)} \]

2. Atomic number:
\[ 14 = 0 + Z \quad \text{(where Z is the atomic number of the unknown product)} \]

### Step 5: Solve for A and Z
From the mass number equation:
\[ A = 28 - 1 = 27 \]

From the atomic number equation:
\[ Z = 14 \]

### Step 6: Identify the element corresponding to the atomic number 14
The element with atomic number 14 is silicon (Si).

### Final Reaction
Putting it all together, the complete nuclear reaction is:
\[ _{12}^{24}Mg + _{2}^{4}He \rightarrow _{0}^{1}n + _{14}^{27}Si \]

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

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