What is X in the following nuclear reaction? `N_7^14 + H_1^1 to O_8^15 +X`

Options

A. `e_(+1)^@`
B. `n_0^1`
C. `gamma`
D. `e_(-1)^@`

Answer

To solve the nuclear reaction \( N_7^{14} + H_1^{1} \to O_8^{15} + X \) and find the unknown particle \( X \), we will follow these steps:

### Step 1: Identify the components of the reaction
- The reactants are \( N_7^{14} \) (Nitrogen-14) and \( H_1^{1} \) (Hydrogen-1).
- The products are \( O_8^{15} \) (Oxygen-15) and \( X \).

### Step 2: Write down the atomic and mass numbers
- For \( N_7^{14} \):
- Atomic number (Z) = 7
- Mass number (A) = 14

- For \( H_1^{1} \):
- Atomic number (Z) = 1
- Mass number (A) = 1

- For \( O_8^{15} \):
- Atomic number (Z) = 8
- Mass number (A) = 15

### Step 3: Calculate the total atomic and mass numbers on the left side
- Total atomic number on the left:
\[ Z_{left} = 7 + 1 = 8 \]
- Total mass number on the left:
\[ A_{left} = 14 + 1 = 15 \]

### Step 4: Set up equations for the right side
Let \( X \) have:
- Atomic number = \( Z \)
- Mass number = \( A \)

From the products, we have:
- Total atomic number on the right:
\[ Z_{right} = 8 + Z \]
- Total mass number on the right:
\[ A_{right} = 15 + A \]

### Step 5: Equate the atomic and mass numbers
1. For atomic numbers:
\[ 8 + Z = 8 \implies Z = 0 \]
2. For mass numbers:
\[ 15 + A = 15 \implies A = 0 \]

### Step 6: Identify the particle \( X \)
- Since both the atomic number and mass number of \( X \) are 0, \( X \) must be a gamma particle, which is represented as \( \gamma \) or \( 0^0\gamma \).

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

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