In the reaction, identify`X,""_(7)N^(14)+alphato""_(8)X^(17)+""_(1)P^(1)`

Options

A. An oxygen nucleus with mass 17
B. An oxygen nucleus with mass 16
C. An nitrogen nucleus with mass 17
D. A nitrogen nucleus with mass 16

Answer

To identify the element \( X \) in the nuclear reaction given by:

\[ _{7}^{14}N + \alpha \rightarrow _{8}^{17}X + _{1}^{1}P \]

we can follow these steps:

### Step 1: Understand the Reaction
The reaction involves a nitrogen nucleus (\( _{7}^{14}N \)) interacting with an alpha particle (\( \alpha \)), which is equivalent to a helium nucleus (\( _{2}^{4}He \)). The products of the reaction are an unknown nucleus \( X \) and a proton (\( _{1}^{1}P \)).

### Step 2: Write Down the Known Values
- The atomic number of nitrogen (\( N \)) is 7, and its mass number is 14.
- The alpha particle has an atomic number of 2 and a mass number of 4.
- The proton has an atomic number of 1 and a mass number of 1.

### Step 3: Set Up the Conservation Equations
In nuclear reactions, both the atomic number and the mass number must be conserved.

1. **Conservation of Mass Number:**
\[ 14 + 4 = 17 + A_X + 1 \]
where \( A_X \) is the mass number of \( X \).

Simplifying gives:
\[ 18 = 17 + A_X \]
Thus,
\[ A_X = 1 \]

2. **Conservation of Atomic Number:**
\[ 7 + 2 = 8 + Z_X + 1 \]
where \( Z_X \) is the atomic number of \( X \).

Simplifying gives:
\[ 9 = 8 + Z_X \]
Thus,
\[ Z_X = 1 \]

### Step 4: Identify the Element \( X \)
From the values obtained:
- The mass number \( A_X = 17 \)
- The atomic number \( Z_X = 8 \)

The element with atomic number 8 is oxygen (\( O \)). Therefore, the nucleus \( X \) is \( _{8}^{17}O \).

### Final Answer
The element \( X \) is \( _{8}^{17}O \) (Oxygen-17).

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