What is `X` in the nuclear reaction
`._(7)N^(14) + ._(1)H^(1) rarr ._(8)O^(15) + X`

Options

A. `._(1)H^(2)`
B. `._(0)n^(1)`
C. `gamma`
D. `._(-1)e^(0)`

Explanation

To determine what `X` is in the nuclear reaction:

\[ _{7}^{14}N + _{1}^{1}H \rightarrow _{8}^{15}O + X \]

we can follow these steps:

### Step 1: Identify the Reactants and Products
We have:
- Reactants: Nitrogen-14 \((_{7}^{14}N)\) and Hydrogen-1 \((_{1}^{1}H)\)
- Product: Oxygen-15 \((_{8}^{15}O)\) and an unknown particle \(X\)

### Step 2: Write Down the Atomic Numbers and Mass Numbers
- For Nitrogen-14: Atomic number = 7, Mass number = 14
- For Hydrogen-1: Atomic number = 1, Mass number = 1
- For Oxygen-15: Atomic number = 8, Mass number = 15

### Step 3: Calculate Total Atomic and Mass Numbers for Reactants
- Total Atomic Number (Reactants) = \(7 + 1 = 8\)
- Total Mass Number (Reactants) = \(14 + 1 = 15\)

### Step 4: Calculate Total Atomic and Mass Numbers for Products
- Total Atomic Number (Products) = \(8 + \text{Atomic Number of } X\)
- Total Mass Number (Products) = \(15 + \text{Mass Number of } X\)

### Step 5: Set Up Equations for Balancing
Since the reaction must be balanced, we can set up the following equations:
1. For Atomic Numbers:
\[ 8 + \text{Atomic Number of } X = 8 \]
This implies that the Atomic Number of \(X\) must be 0.

2. For Mass Numbers:
\[ 15 + \text{Mass Number of } X = 15 \]
This implies that the Mass Number of \(X\) must also be 0.

### Step 6: Identify the Particle \(X\)
Since both the Atomic Number and Mass Number of \(X\) are 0, \(X\) must be a neutral particle. The only particle that fits this description is a gamma particle (γ), which has no mass and no charge.

### Conclusion
Thus, \(X\) in the nuclear reaction is a gamma particle (γ).

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