In the decay process:
`A overset(- alpha)rarr B overset(-beta)rarr C overset(-beta)rarr D` a)`A` and `B` are isodiaphers b)`A` and `C` are isotones c)`A` and `C` are isotopes d)`B, C` and `D` are isobars

Options

A. A and B are isobars
B. A and D are isotopes
C. B,C and D are isobars
D. A and C are isotones

Answer

To solve the problem, we need to analyze the decay process and the relationships between the elements involved. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Decay Process:**
- The decay process is given as:
\[ A \overset{-\alpha}{\rightarrow} B \overset{-\beta}{\rightarrow} C \overset{-\beta}{\rightarrow} D \]
- This means:
- Element A decays to element B by emitting an alpha particle.
- Element B decays to element C by emitting a beta particle.
- Element C decays to element D by emitting another beta particle.

2. **Determine the Changes in Atomic Number and Mass:**
- **Alpha Decay (A to B):**
- Atomic weight of A = A (mass number)
- Atomic number of A = Z
- After alpha decay, B will have:
- Atomic weight = A - 4
- Atomic number = Z - 2
- **Beta Decay (B to C):**
- Atomic weight of B = A - 4
- Atomic number of B = Z - 2
- After beta decay, C will have:
- Atomic weight = A - 4 (remains the same)
- Atomic number = Z - 1
- **Beta Decay (C to D):**
- Atomic weight of C = A - 4
- Atomic number of C = Z - 1
- After beta decay, D will have:
- Atomic weight = A - 4 (remains the same)
- Atomic number = Z (increased by 1)

3. **Analyze the Relationships:**
- **Isobars:** Same atomic weight but different atomic numbers.
- **Isotopes:** Same atomic number but different atomic weights.
- **Isotones:** Same number of neutrons but different atomic numbers and weights.

4. **Evaluate Each Statement:**
- **Statement a:** A and B are isodiaphers.
- **False.** A and B have different atomic weights (A vs. A-4).
- **Statement b:** A and C are isotones.
- **False.** A and C have different atomic numbers and weights.
- **Statement c:** A and C are isotopes.
- **False.** A and C have different atomic numbers (Z vs. Z-1).
- **Statement d:** B, C, and D are isobars.
- **True.** B, C, and D have the same atomic weight (A-4) but different atomic numbers.

5. **Conclusion:**
- The only correct statement is that B, C, and D are isobars.

### Final Answer:
The correct statement is:
**d) B, C, and D are isobars.**