Which of the following statement about Rutherford's model of atom are correct?
(i) Considered the nucleus as positively charged.
(ii) Established that the `alpha`-particles are four times as heavy as a hydrogen atom.
(iii) Can be compared to solar system.
(iv) Was in agreement with Thomson's model.

Options

A. (i) and (iii)
B. (ii) and (iii)
C. (i) and (iv)
D. Only (i)

Explanation

To determine which statements about Rutherford's model of the atom are correct, let's analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement (i): Considered the nucleus as positively charged.**
- **Analysis:** Rutherford's model indeed proposed that the atom has a small, dense, positively charged nucleus at its center, around which electrons revolve. This statement is correct.
- **Conclusion:** This statement is **correct**.

2. **Statement (ii): Established that the alpha particles are four times as heavy as a hydrogen atom.**
- **Analysis:** Rutherford conducted the alpha scattering experiment, but he did not specifically establish a comparison stating that alpha particles are four times heavier than hydrogen atoms. This statement is misleading and incorrect.
- **Conclusion:** This statement is **incorrect**.

3. **Statement (iii): Can be compared to solar system.**
- **Analysis:** Rutherford's model can indeed be compared to a solar system, where the nucleus is like the sun and the electrons are like planets revolving around it. This analogy is commonly used to describe the structure of the atom in Rutherford's model.
- **Conclusion:** This statement is **correct**.

4. **Statement (iv): Was in agreement with Thomson's model.**
- **Analysis:** Rutherford's model contradicted Thomson's model. Thomson's model depicted the atom as a uniform sphere of positive charge with electrons embedded within it, while Rutherford's model introduced the concept of a nucleus. Therefore, these two models are not in agreement.
- **Conclusion:** This statement is **incorrect**.

### Final Conclusion:
The correct statements about Rutherford's model of the atom are:
- Statement (i) is correct.
- Statement (iii) is correct.

Thus, the correct options are **1 and 3**.