The triad of nuclie that are isotomic is

Options

A. `._(6)^(14)C _(7)^(15)N_(6)^(17)F`
B. `._(6)^(12)C _(7)^(14)N_(9)^(19)F`
C. `._(6)^(14)C _(7)^(14)N_(6)^(17)F`
D. `._(6)^(14)C _(7)^(14)N_(9)^(19)F`

Explanation

To solve the question about the triad of nuclei that are isotonic, we will follow these steps:

### Step 1: Understand the Concept of Isotonic Nuclei
Isotonic nuclei are those that have the same number of neutrons but different numbers of protons.

### Step 2: Calculate the Number of Neutrons
The number of neutrons in an atom can be calculated using the formula:
\[ \text{Number of Neutrons} = A - Z \]
where \( A \) is the mass number and \( Z \) is the atomic number (number of protons).

### Step 3: Analyze Given Nuclei
We will analyze the nuclei mentioned in the question to find their number of neutrons.

1. **For \( ^6C^{14} \)**:
- Mass number \( A = 14 \)
- Atomic number \( Z = 6 \)
- Neutrons = \( 14 - 6 = 8 \)

2. **For \( ^7N^{15} \)**:
- Mass number \( A = 15 \)
- Atomic number \( Z = 7 \)
- Neutrons = \( 15 - 7 = 8 \)

3. **For \( ^9F^{17} \)**:
- Mass number \( A = 17 \)
- Atomic number \( Z = 9 \)
- Neutrons = \( 17 - 9 = 8 \)

### Step 4: Identify the Isotonic Triad
From the calculations, we see that:
- \( ^6C^{14} \) has 8 neutrons.
- \( ^7N^{15} \) has 8 neutrons.
- \( ^9F^{17} \) has 8 neutrons.

Since all three nuclei have the same number of neutrons (8), they form an isotonic triad.

### Conclusion
The triad of nuclei that are isotonic is:
- \( ^6C^{14} \)
- \( ^7N^{15} \)
- \( ^9F^{17} \)