Consider the following radioactive decays
I. `""_(92)Uoverset(-alpha)to""_(90)`Th and
II . `""_(90)Thoverset(-alpha)to""_(88)Ra`
In which case group of parent and daughter elemets remains unchanged .

Options

A. In (I)
B. In (II)
C. Both in (I) and (II)
D. None of the above

Explanation

To solve the problem, we need to analyze the two radioactive decay processes given and determine in which case the group of parent and daughter elements remains unchanged.

### Step-by-Step Solution:

1. **Identify the Decay Processes**:
- **Decay I**: Uranium-92 (U) decays to Thorium-90 (Th).
- **Decay II**: Thorium-90 (Th) decays to Radium-88 (Ra).

2. **Determine the Atomic Numbers**:
- For Decay I:
- Parent: Uranium (U) has an atomic number of 92.
- Daughter: Thorium (Th) has an atomic number of 90.
- For Decay II:
- Parent: Thorium (Th) has an atomic number of 90.
- Daughter: Radium (Ra) has an atomic number of 88.

3. **Analyze the Groups in the Periodic Table**:
- **Group of Parent and Daughter in Decay I**:
- Uranium (U, atomic number 92) and Thorium (Th, atomic number 90) are both actinides and belong to the same group in the periodic table.
- **Group of Parent and Daughter in Decay II**:
- Thorium (Th, atomic number 90) and Radium (Ra, atomic number 88) belong to different groups. Thorium is an actinide, while Radium is an alkaline earth metal.

4. **Conclusion**:
- In Decay I, the parent (U) and daughter (Th) elements remain in the same group (actinides).
- In Decay II, the parent (Th) and daughter (Ra) do not remain in the same group.

Thus, the answer is that in **Decay I**, the group of parent and daughter elements remains unchanged.

### Final Answer:
**Decay I (Uranium-92 to Thorium-90) is the case where the group of parent and daughter elements remains unchanged.**

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