Observe the following statements regarding isotones `:`
`a.` `.^(39)K` and `.^(40)Ca` are isotones.
`b.` Nucleides having different atomic number `(Z)` and mass numbers `(a)` but same number of neutrons `(n)` are called isotones.
`c.` `.^(19)F` and `.^(23)Na` are isotones.
The correct answer is `-`

Options

A. `a,b,` and `c` are correct
B. Only `a` and `b` are correct
C. Only `a` and `c` are correct
D. Only `b` and `c` are correct.

Answer

To determine the correctness of the statements regarding isotones, we will analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** \(^{39}K\) and \(^{40}Ca\) are isotones.

1. **Identify the atomic numbers:**
- Potassium (K) has an atomic number \(Z = 19\).
- Calcium (Ca) has an atomic number \(Z = 20\).

2. **Calculate the number of neutrons:**
- For \(^{39}K\):
- Mass number (A) = 39
- Number of protons = 19 (atomic number)
- Number of neutrons = Mass number - Number of protons = \(39 - 19 = 20\).

- For \(^{40}Ca\):
- Mass number (A) = 40
- Number of protons = 20 (atomic number)
- Number of neutrons = Mass number - Number of protons = \(40 - 20 = 20\).

3. **Conclusion for Statement A:**
- Both \(^{39}K\) and \(^{40}Ca\) have the same number of neutrons (20), hence they are isotones.
- **Statement A is correct.**

### Step 2: Analyze Statement B
**Statement B:** Nucleides having different atomic numbers (Z) and mass numbers (A) but the same number of neutrons (n) are called isotones.

1. **Definition Check:**
- By definition, isotones are indeed nucleides that have different atomic numbers and mass numbers but the same number of neutrons.

2. **Conclusion for Statement B:**
- This statement correctly describes isotones.
- **Statement B is correct.**

### Step 3: Analyze Statement C
**Statement C:** \(^{19}F\) and \(^{23}Na\) are isotones.

1. **Identify the atomic numbers:**
- Fluorine (F) has an atomic number \(Z = 9\).
- Sodium (Na) has an atomic number \(Z = 11\).

2. **Calculate the number of neutrons:**
- For \(^{19}F\):
- Mass number (A) = 19
- Number of protons = 9 (atomic number)
- Number of neutrons = Mass number - Number of protons = \(19 - 9 = 10\).

- For \(^{23}Na\):
- Mass number (A) = 23
- Number of protons = 11 (atomic number)
- Number of neutrons = Mass number - Number of protons = \(23 - 11 = 12\).

3. **Conclusion for Statement C:**
- \(^{19}F\) has 10 neutrons, while \(^{23}Na\) has 12 neutrons. Since the number of neutrons is different, they are not isotones.
- **Statement C is incorrect.**

### Final Conclusion
- **Correct Statements:** A and B.
- **Incorrect Statement:** C.