Which of these are a pair of Isotones and Isobars?

Options

A. `""_(20)^(40)Ca & ""_(19)^(39)K`
B. `""_(6)^(12)C & ""_(8)^(16)O`
C. `""_(20)^(40)Ca & ""_(18)^(40)Ar`
D. `""_(29)^(65)Cu & ""_(30)^(65)Zn`

Explanation

To determine which pairs are isotones and isobars, we need to understand the definitions of these terms:

1. **Isotones**: Atoms that have the same number of neutrons but different numbers of protons (different atomic numbers).
2. **Isobars**: Atoms that have the same mass number (the sum of protons and neutrons) but different atomic numbers.

Now, let's analyze the given options step by step.

### Step 1: Analyze Option A - Calcium (Ca) and Potassium (K)

- **Calcium (Ca)**:
- Atomic number (Z) = 20
- Mass number (A) = 40 (20 protons + 20 neutrons)

- **Potassium (K)**:
- Atomic number (Z) = 19
- Mass number (A) = 39 (19 protons + 20 neutrons)

**Calculation of Neutrons**:
- Neutrons in Calcium = 40 - 20 = 20
- Neutrons in Potassium = 39 - 19 = 20

Since both have the same number of neutrons (20), **Calcium and Potassium are isotones**.

### Step 2: Analyze Option B - Carbon (C) and Oxygen (O)

- **Carbon (C)**:
- Atomic number (Z) = 6
- Mass number (A) = 12 (6 protons + 6 neutrons)

- **Oxygen (O)**:
- Atomic number (Z) = 8
- Mass number (A) = 16 (8 protons + 8 neutrons)

**Calculation of Neutrons**:
- Neutrons in Carbon = 12 - 6 = 6
- Neutrons in Oxygen = 16 - 8 = 8

Since the number of neutrons is different, **Carbon and Oxygen are neither isotones nor isobars**.

### Step 3: Analyze Option C - Calcium (Ca) and Argon (Ar)

- **Calcium (Ca)**:
- Atomic number (Z) = 20
- Mass number (A) = 40

- **Argon (Ar)**:
- Atomic number (Z) = 18
- Mass number (A) = 40

**Calculation of Neutrons**:
- Neutrons in Calcium = 40 - 20 = 20
- Neutrons in Argon = 40 - 18 = 22

Since both have the same mass number (40), **Calcium and Argon are isobars**.

### Step 4: Analyze Option D - Copper (Cu) and Zinc (Zn)

- **Copper (Cu)**:
- Atomic number (Z) = 29
- Mass number (A) = 65

- **Zinc (Zn)**:
- Atomic number (Z) = 30
- Mass number (A) = 65

**Calculation of Neutrons**:
- Neutrons in Copper = 65 - 29 = 36
- Neutrons in Zinc = 65 - 30 = 35

Since both have the same mass number (65), **Copper and Zinc are isobars**.

### Conclusion:

- **Isotones**: Calcium (Ca) and Potassium (K)
- **Isobars**: Calcium (Ca) and Argon (Ar), Copper (Cu) and Zinc (Zn)

Thus, the correct answers are:
- Option A (Isotones)
- Option C (Isobars)
- Option D (Isobars)