Assign groups to the elements `A, B, C, D` and `E` starting from element `X("group" 2^(nd))`
`underset((II A))(X)overset(-alpha)(rarr)Aoverset(-beta)(rarr)Boverset(-beta)(rarr)Coverset(-alpha)(rarr)D`
What is relation between `A` and `D`?

Answer

To solve the problem, we need to assign groups to the elements A, B, C, D, and E based on the transformations starting from element X, which is in group 2. We will analyze each transformation step by step.

### Step 1: Identify the group of element A
- **Starting Element (X)**: Group 2
- **Transformation**: X → A (emission of an alpha particle)
- **Effect of Alpha Emission**:
- Mass decreases by 4 (M - 4)
- Atomic number decreases by 2 (Z - 2)
- **New Group for A**: Since X is in group 2 and the atomic number decreases by 2, A will be in group 18 (2 - 2 = 0, which wraps around to group 18).

### Step 2: Identify the group of element B
- **Transformation**: A → B (emission of a beta particle)
- **Effect of Beta Emission**:
- Mass remains the same (M - 4)
- Atomic number increases by 1 (Z - 2 + 1 = Z - 1)
- **New Group for B**: Since A is in group 18 and the atomic number increases by 1, B will be in group 1 (18 + 1 = 19, which wraps around to group 1).

### Step 3: Identify the group of element C
- **Transformation**: B → C (emission of another beta particle)
- **Effect of Beta Emission**:
- Mass remains the same (M - 4)
- Atomic number increases by 1 (Z - 1 + 1 = Z)
- **New Group for C**: Since B is in group 1 and the atomic number increases by 1, C will be in group 2 (1 + 1 = 2).

### Step 4: Identify the group of element D
- **Transformation**: C → D (emission of an alpha particle)
- **Effect of Alpha Emission**:
- Mass decreases by 4 (M - 8)
- Atomic number decreases by 2 (Z)
- **New Group for D**: Since C is in group 2 and the atomic number decreases by 2, D will again be in group 18 (2 - 2 = 0, which wraps around to group 18).

### Summary of Groups
- **X**: Group 2
- **A**: Group 18
- **B**: Group 1
- **C**: Group 2
- **D**: Group 18

### Step 5: Determine the relation between A and D
- **Atomic Number**: Both A and D have the same atomic number (Z - 2).
- **Mass Number**: A has mass M - 4, and D has mass M - 8.
- **Conclusion**: A and D have the same atomic number but different mass numbers, which means they are isotopes of each other.

### Final Answer
The relation between A and D is that they are isotopes.

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