Rutherford's experiment established that

Options

A. inside the atom there are positive centres immersed in sea of electrons
B. nucleus contains protons, neutrons and mesons
C. most of the space in an atom is empty
D. All A, B and C

Explanation

### Step-by-Step Solution:

1. **Understanding Rutherford's Experiment**:
- Rutherford conducted an experiment using a thin gold foil and bombarded it with alpha particles. The alpha particles are positively charged and were expected to pass through the foil with minimal deflection if the atom was structured like the plum pudding model (which suggested a diffuse cloud of positive charge).

2. **Observations from the Experiment**:
- Most of the alpha particles passed straight through the gold foil, indicating that most of the atom is empty space.
- A small fraction of the alpha particles were deflected at small angles, and a very few were deflected back at angles close to 180 degrees.

3. **Conclusion from Observations**:
- The significant deflection of some alpha particles suggested that there is a dense, positively charged center within the atom, which we now know as the nucleus. This nucleus contains most of the atom's mass and is surrounded by electrons.

4. **Correct Answer**:
- Based on the observations and conclusions drawn from Rutherford's experiment, the correct statement is that "most of the space in the atom is empty, with a dense positive center (nucleus)".

5. **Evaluating the Options**:
- **Option 1**: Incorrect, as it suggests a 'sea of electrons' surrounding multiple positive centers.
- **Option 2**: Incorrect, as it mentions mesons which were not discovered at the time of Rutherford's experiment.
- **Option 3**: Correct, as it accurately describes the nucleus being a dense positive center with electrons surrounding it.
- **Option 4**: Incorrect, as it misrepresents the structure of the atom.

### Final Answer:
Rutherford's experiment established that most of the space in an atom is empty, with a dense positive center (nucleus).

---