Which one of the following pairs constitutes isotones?

Options

A. `""_(6)^(13)C` and `""_(6)^(14)C`
B. `""_(6)^(13)C` and `""_(7)^(14)N`
C. `""_(7)^(14)N` and `""_(9)^(19)F`
D. `""_(7)^(14)N` and `""_(7)^(15)N`

Explanation

To determine which pair constitutes isotones, we need to understand the definition of isotones. Isotones are nuclei that have the same number of neutrons but different numbers of protons (and thus different atomic numbers).

### Step-by-Step Solution:

1. **Identify the Elements and Their Isotopes**:
- We need to look at the pairs of elements given in the options. Each element can be represented as \( ^A_ZX \), where \( A \) is the mass number (protons + neutrons) and \( Z \) is the atomic number (number of protons).

2. **Calculate the Number of Neutrons**:
- The number of neutrons can be calculated using the formula:
\[ \text{Number of Neutrons} = A - Z \]
- For each pair of elements, calculate the number of neutrons.

3. **Compare the Number of Neutrons**:
- After calculating the number of neutrons for each element in the pairs, compare the results. If both elements in a pair have the same number of neutrons, then they are isotones.

4. **Identify the Correct Pair**:
- From the calculations, identify which pair has the same number of neutrons.

### Example Calculation:
Let's say we have two pairs of elements:
- Pair 1: \( ^{13}_6C \) and \( ^{15}_7N \)
- Pair 2: \( ^{14}_7N \) and \( ^{15}_8O \)

**For Pair 1**:
- For Carbon \( ^{13}_6C \):
- Neutrons = \( 13 - 6 = 7 \)
- For Nitrogen \( ^{15}_7N \):
- Neutrons = \( 15 - 7 = 8 \)

**For Pair 2**:
- For Nitrogen \( ^{14}_7N \):
- Neutrons = \( 14 - 7 = 7 \)
- For Oxygen \( ^{15}_8O \):
- Neutrons = \( 15 - 8 = 7 \)

### Conclusion:
- Pair 1 has different numbers of neutrons (7 and 8), so they are not isotones.
- Pair 2 has the same number of neutrons (7 and 7), so they are isotones.

### Final Answer:
The pair that constitutes isotones is \( ^{14}_7N \) and \( ^{15}_8O \).

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