`._(90)Th^(232)` belongs to III group. It items an `alpha`-particle. The daughter element belongs to
a. I group b. II group
III. Group d. IV group

Options

A. a. I group
B. b. II group
C. c. III Group
D. d. IV group

Explanation

To solve the question, we need to analyze the decay of thorium-232 (\( _{90}^{232}Th \)) when it emits an alpha particle.

### Step-by-Step Solution:

1. **Identify the Alpha Particle**:
An alpha particle is represented as \( _{2}^{4}He \) or simply \( \alpha \). It consists of 2 protons and 2 neutrons.

2. **Write the Decay Equation**:
When thorium-232 undergoes alpha decay, it loses an alpha particle. The decay can be represented as:
\[ _{90}^{232}Th \rightarrow _{88}^{228}Ra + _{2}^{4}He \]
Here, \( _{88}^{228}Ra \) is the daughter element formed after the decay.

3. **Determine the Atomic Number and Mass Number of the Daughter Element**:
- The atomic number of thorium (Th) is 90. After losing 2 protons (from the alpha particle), the atomic number of the daughter element (radium, Ra) becomes:
\[ 90 - 2 = 88 \]
- The mass number of thorium is 232. After losing 4 (from the alpha particle), the mass number of the daughter element becomes:
\[ 232 - 4 = 228 \]

4. **Identify the Daughter Element**:
The daughter element is radium (\( _{88}^{228}Ra \)).

5. **Determine the Group of the Daughter Element**:
Radium (Ra) belongs to Group II of the periodic table, known as the alkaline earth metals.

### Conclusion:
The daughter element, radium, belongs to Group II.

### Final Answer:
The correct option is **b. II group**.

---