The triad of nuclei that is isotonic is:

Options

A. a-`._(6)^(14)C, ._(7)^(15)N, ._(9)^(17)F`
B. b-`._(6)^(14)N, ._(9)^(19)F`
C. c-`._(6)^(14)C, ._(7)^(14)N, ._(9)^(17)F`
D. d-`._(6)^(14)C, ._(7)^(14)N, ._(9)^(19)F`

Explanation

To solve the question regarding the triad of nuclei that is isotonic, we need to understand the concept of isotones. Isotones are nuclei that have the same number of neutrons but different numbers of protons.

### Step-by-Step Solution:

1. **Understanding Isotones**:
- Isotones are defined as nuclei that have the same number of neutrons (N) but different numbers of protons (Z). The relationship between protons, neutrons, and atomic mass (A) can be expressed as:
\[ A = Z + N \]
- Here, \( A \) is the atomic mass, \( Z \) is the atomic number (number of protons), and \( N \) is the number of neutrons.

2. **Analyzing the Options**:
- We will check each option to find the nuclei that have the same number of neutrons.

3. **Option A**:
- **Carbon (C)**: Atomic number = 6, Atomic mass = 14
- Neutrons = 14 - 6 = 8
- **Nitrogen (N)**: Atomic number = 7, Atomic mass = 15
- Neutrons = 15 - 7 = 8
- **Fluorine (F)**: Atomic number = 9, Atomic mass = 17
- Neutrons = 17 - 9 = 8
- All three have 8 neutrons. Therefore, option A is isotonic.

4. **Option B**:
- **Nitrogen (N)**: Atomic number = 7, Atomic mass = 15
- Neutrons = 15 - 7 = 8
- **Carbon (C)**: Atomic number = 6, Atomic mass = 14
- Neutrons = 14 - 6 = 8
- **Not applicable** as it does not provide a third nucleus.

5. **Option C**:
- **Carbon (C)**: Atomic number = 6, Atomic mass = 14
- Neutrons = 14 - 6 = 8
- **Nitrogen (N)**: Atomic number = 7, Atomic mass = 15
- Neutrons = 15 - 7 = 8
- **Oxygen (O)**: Atomic number = 8, Atomic mass = 16
- Neutrons = 16 - 8 = 8
- All three have 8 neutrons, so this option is also isotonic.

6. **Option D**:
- **Carbon (C)**: Atomic number = 6, Atomic mass = 14
- Neutrons = 14 - 6 = 8
- **Nitrogen (N)**: Atomic number = 7, Atomic mass = 15
- Neutrons = 15 - 7 = 8
- **Fluorine (F)**: Atomic number = 9, Atomic mass = 19
- Neutrons = 19 - 9 = 10
- Here, Fluorine has 10 neutrons, which is different from the other two. So, option D is not isotonic.

### Conclusion:
The correct option for the triad of nuclei that is isotonic is **Option A** (C, N, F) as they all have the same number of neutrons.