Which pair is isotonic?

Options

A. `""_(7)N^(13),""_(7)N^(14)`
B. `""_(6)C^(14),""_(6)C^(12)`
C. `""_(6)C^(14),""_(7)C^(14)`
D. `""_(7)N^(13),""_(6)C^(12)`

Explanation

To determine which pair is isotonic, we need to identify pairs of nuclei that have the same number of neutrons. The number of neutrons can be calculated using the formula:

\[ \text{Number of Neutrons} = A - Z \]

where:
- \( A \) is the mass number (total number of protons and neutrons),
- \( Z \) is the atomic number (number of protons).

Let's analyze the given options step by step.

### Step 1: Analyze the first option - Nitrogen \( ^7_13N \) and Nitrogen \( ^7_{14}N \)

- For \( ^7_{13}N \):
- \( A = 13 \), \( Z = 7 \)
- Number of Neutrons = \( 13 - 7 = 6 \)

- For \( ^7_{14}N \):
- \( A = 14 \), \( Z = 7 \)
- Number of Neutrons = \( 14 - 7 = 7 \)

**Conclusion**: This pair does not have the same number of neutrons.

### Step 2: Analyze the second option - Carbon \( ^6_{14}C \) and Carbon \( ^6_{12}C \)

- For \( ^6_{14}C \):
- \( A = 14 \), \( Z = 6 \)
- Number of Neutrons = \( 14 - 6 = 8 \)

- For \( ^6_{12}C \):
- \( A = 12 \), \( Z = 6 \)
- Number of Neutrons = \( 12 - 6 = 6 \)

**Conclusion**: This pair does not have the same number of neutrons.

### Step 3: Analyze the third option - Carbon \( ^6_{14}C \) and Nitrogen \( ^7_{14}N \)

- For \( ^6_{14}C \):
- Number of Neutrons = \( 14 - 6 = 8 \)

- For \( ^7_{14}N \):
- \( A = 14 \), \( Z = 7 \)
- Number of Neutrons = \( 14 - 7 = 7 \)

**Conclusion**: This pair does not have the same number of neutrons.

### Step 4: Analyze the fourth option - Nitrogen \( ^7_{13}N \) and Carbon \( ^6_{12}C \)

- For \( ^7_{13}N \):
- Number of Neutrons = \( 13 - 7 = 6 \)

- For \( ^6_{12}C \):
- Number of Neutrons = \( 12 - 6 = 6 \)

**Conclusion**: This pair has the same number of neutrons (6), so they are isotonic.

### Final Answer:
The isotonic pair is Nitrogen \( ^7_{13}N \) and Carbon \( ^6_{12}C \).

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