To determine which of the following pairs are not isotones, we need to understand the definition of isotones. Isotones are nuclides that have the same number of neutrons (N) but different numbers of protons (Z).
Let's analyze the given pairs step by step:
### Step 1: Identify the pairs
The pairs given in the question are:
1. \( ^{6}_{C} \,^{13} \) and \( ^{7}_{N} \,^{14} \)
2. \( ^{7}_{N} \,^{14} \) and \( ^{9}_{F} \,^{19} \)
3. \( ^{33}_{As} \,^{77} \) and \( ^{34}_{Se} \,^{78} \)
### Step 2: Calculate the number of neutrons for each nuclide
For each nuclide, we can calculate the number of neutrons (N) using the formula:
\[ N = A - Z \]
where \( A \) is the mass number and \( Z \) is the atomic number.
#### Pair 1: \( ^{6}_{C} \,^{13} \) and \( ^{7}_{N} \,^{14} \)
- For \( ^{6}_{C} \,^{13} \):
- \( N = 13 - 6 = 7 \)
- For \( ^{7}_{N} \,^{14} \):
- \( N = 14 - 7 = 7 \)
**Conclusion**: Both have 7 neutrons, so they are isotones.
#### Pair 2: \( ^{7}_{N} \,^{14} \) and \( ^{9}_{F} \,^{19} \)
- For \( ^{7}_{N} \,^{14} \):
- \( N = 14 - 7 = 7 \)
- For \( ^{9}_{F} \,^{19} \):
- \( N = 19 - 9 = 10 \)
**Conclusion**: The first has 7 neutrons and the second has 10 neutrons, so they are not isotones.
#### Pair 3: \( ^{33}_{As} \,^{77} \) and \( ^{34}_{Se} \,^{78} \)
- For \( ^{33}_{As} \,^{77} \):
- \( N = 77 - 33 = 44 \)
- For \( ^{34}_{Se} \,^{78} \):
- \( N = 78 - 34 = 44 \)
**Conclusion**: Both have 44 neutrons, so they are isotones.
### Step 3: Identify the pair that is not isotones
From our calculations:
- Pair 1: Isotones
- Pair 2: Not isotones
- Pair 3: Isotones
Thus, the pair that is not isotones is \( ^{7}_{N} \,^{14} \) and \( ^{9}_{F} \,^{19} \).
### Final Answer
The pair that is not isotones is: **\( ^{7}_{N} \,^{14} \) and \( ^{9}_{F} \,^{19} \)**.
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