Which of the following conclusions couldnot be derived from Rutehrford's `alpha`-particle scattering experiment?

Options

A. Most of the space in the atom is empty
B. The radius of the atom is about `10^(-10)` m while that of nucleus is `10^(-15)` m
C. Electrons move in a circular path of fixed energy called orbits.
D. Electrons and the nucleus are held together by electrostatic forces of attraction

Explanation

To determine which conclusion could not be derived from Rutherford's alpha-particle scattering experiment, we need to analyze the key findings of the experiment and the conclusions drawn from them.

### Step-by-Step Solution:

1. **Understanding Rutherford's Experiment**:
- Rutherford conducted an experiment where he bombarded a thin gold foil with alpha particles.
- He observed that most of the alpha particles passed straight through the foil, while a small number were deflected at various angles, and a few were reflected back.

**Hint**: Remember the setup of the experiment and the behavior of alpha particles as they interacted with the gold foil.

2. **Conclusions from the Experiment**:
- **Conclusion 1**: Most of the space in the atom is empty.
- This conclusion was drawn because most alpha particles passed through without any deflection.

**Hint**: Consider what the passage of particles without deflection implies about the structure of the atom.

3. **Conclusion 2**: The radius of the atom is about \(10^{-10}\) meters, while that of the nucleus is \(10^{-15}\) meters.
- This conclusion is consistent with the observations, as the nucleus is very small compared to the overall size of the atom.

**Hint**: Think about the relative sizes of the nucleus and the atom based on the scattering results.

4. **Conclusion 3**: Electrons move in a circular path of fixed energy called orbits.
- This conclusion is not something that Rutherford could derive from his experiment. While he proposed that electrons surround the nucleus, he did not provide evidence for their specific paths or energies.

**Hint**: Reflect on the limitations of Rutherford's model regarding electron behavior.

5. **Conclusion 4**: Electrons and nucleons are held together by electrostatic force of attraction.
- This conclusion is valid and aligns with the observations, as the positive charge of the nucleus would attract the negatively charged electrons.

**Hint**: Consider the forces acting between charged particles in the atom.

6. **Identifying the Incorrect Conclusion**:
- From the analysis, the only conclusion that could not be derived from Rutherford's experiment is that electrons move in a circular path of fixed energy called orbits.

### Final Answer:
The conclusion that could not be derived from Rutherford's alpha-particle scattering experiment is: **Electrons move in a circular path of fixed energy called orbits**.