Which of the following triads represents isotones?

Options

A. `""_(6)^(12)C, ""_(6)^(13)C, ""_(6)^(14)C`
B. `""_(18)^(40)Ar, ""_(20)^(42)Ca, ""_(21)^(43)Se`
C. `""_(18)^(40)Ar, ""_(20)^(40)Ca, ""_(21)^(41)Sc`
D. `""_(7)^(14)N, ""_(8)^(16)O, ""_(9)^(18)F`

Answer

To determine which of the given triads represents isotones, we need to understand the concept of isotones. Isotones are nuclei that have the same number of neutrons (N) but different numbers of protons (Z) and mass numbers (A).

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Mass Number (A)**: Total number of protons and neutrons in the nucleus.
- **Atomic Number (Z)**: Number of protons in the nucleus.
- **Number of Neutrons (N)**: Can be calculated using the formula:
\[ N = A - Z \]

2. **Calculate Neutrons for Each Triad**:
- For each option, calculate the number of neutrons using the formula \( N = A - Z \).

3. **Evaluate Each Option**:
- **Option 1**:
- \( ^{12}_{6}C \): \( N = 12 - 6 = 6 \)
- \( ^{13}_{6}C \): \( N = 13 - 6 = 7 \)
- \( ^{14}_{6}C \): \( N = 14 - 6 = 8 \)
- **Result**: Not isotones (6, 7, 8 are different).

- **Option 2**:
- \( ^{40}_{18}Ar \): \( N = 40 - 18 = 22 \)
- \( ^{42}_{20}Ca \): \( N = 42 - 20 = 22 \)
- \( ^{43}_{21}Sc \): \( N = 43 - 21 = 22 \)
- **Result**: Isotones (all have 22 neutrons).

- **Option 3**:
- \( ^{40}_{18}Ar \): \( N = 40 - 18 = 22 \)
- \( ^{40}_{20}Ca \): \( N = 40 - 20 = 20 \)
- \( ^{41}_{21}Sc \): \( N = 41 - 21 = 20 \)
- **Result**: Not isotones (22, 20, 20 are different).

- **Option 4**:
- \( ^{14}_{7}N \): \( N = 14 - 7 = 7 \)
- \( ^{16}_{8}O \): \( N = 16 - 8 = 8 \)
- \( ^{18}_{9}F \): \( N = 18 - 9 = 9 \)
- **Result**: Not isotones (7, 8, 9 are different).

4. **Conclusion**:
- The only triad that represents isotones is **Option 2**: \( ^{40}_{18}Ar \), \( ^{42}_{20}Ca \), and \( ^{43}_{21}Sc \) because they all have 22 neutrons.

### Final Answer:
**Option 2** is the correct answer as it represents isotones.