In the following nuclear reaction
`._(13)Al^(27)+._(2)He^(4)rarr._(15)P^(30)+X,X` will be

Options

A. `""_(-1)^(" "0)e`
B. `""_1^1H`
C. `""_2^4He`
D. `""_0^1n`

Answer

To solve the nuclear reaction given in the question, we need to identify the particle X in the reaction:

\[ _{13}^{27}\text{Al} + _{2}^{4}\text{He} \rightarrow _{15}^{30}\text{P} + X \]

### Step 1: Identify the mass numbers
First, we will write down the mass numbers involved in the reaction:

- Aluminium (Al) has a mass number of 27.
- Helium (He) has a mass number of 4.
- Phosphorus (P) has a mass number of 30.

### Step 2: Calculate the total mass number on the left side
Now, we will calculate the total mass number on the left side of the equation:

\[ \text{Total mass number on left} = 27 + 4 = 31 \]

### Step 3: Identify the mass number of X
Next, we will set up the equation for mass numbers:

\[ \text{Total mass number on right} = 30 + \text{mass number of } X \]

Setting the two sides equal gives us:

\[ 31 = 30 + \text{mass number of } X \]

Solving for the mass number of X:

\[ \text{mass number of } X = 31 - 30 = 1 \]

### Step 4: Identify the atomic numbers
Now we will look at the atomic numbers:

- Aluminium (Al) has an atomic number of 13.
- Helium (He) has an atomic number of 2.
- Phosphorus (P) has an atomic number of 15.

### Step 5: Calculate the total atomic number on the left side
The total atomic number on the left side is:

\[ \text{Total atomic number on left} = 13 + 2 = 15 \]

### Step 6: Identify the atomic number of X
Now, we set up the equation for atomic numbers:

\[ \text{Total atomic number on right} = 15 + \text{atomic number of } X \]

Setting the two sides equal gives us:

\[ 15 = 15 + \text{atomic number of } X \]

Solving for the atomic number of X:

\[ \text{atomic number of } X = 15 - 15 = 0 \]

### Step 7: Identify particle X
From the calculations, we have determined that:

- The mass number of X is 1.
- The atomic number of X is 0.

This corresponds to a neutron, which is represented as:

\[ _{0}^{1}\text{n} \]

### Conclusion
Thus, the particle X in the nuclear reaction is a neutron.

### Final Answer
X will be a neutron, represented as \( _{0}^{1}\text{n} \).

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