In interperting Rutherford's experiments on the scattering of alpha particle by thin foils, one must examine what were known factors, and what the experiment settle. Which of the following are true in this context?

Options

A. The number of electrons in the target atoms `(i.e. Z)` was settled by these experiments.
B. The validity of Coulomb's law for distance as small as `10^(-13)` was known before these experiments.
C. The experiment settled that size of the nucleus could not be larger than a certain value.
D. The experiment also settled that size of the nucleus could not be smaller than a certain value.

Explanation

To solve the question regarding Rutherford's experiment on the scattering of alpha particles by thin foils, we will analyze the known factors and conclusions drawn from the experiment step by step.

### Step-by-Step Solution:

1. **Understanding Rutherford's Experiment**:
- Rutherford conducted an experiment where alpha particles were directed at a thin gold foil. The scattering of these particles provided insights into the structure of the atom.

2. **Known Factors Before the Experiment**:
- It was known that atoms were composed of electrons and some positively charged component. However, the exact nature and structure of the nucleus were not well understood before this experiment.

3. **Key Findings of the Experiment**:
- The experiment demonstrated that most alpha particles passed through the foil with little deflection, indicating that atoms are mostly empty space.
- A small fraction of alpha particles were deflected at large angles, suggesting the presence of a dense, positively charged center – which Rutherford termed the nucleus.

4. **Conclusions Drawn from the Experiment**:
- The experiment established that there is a positively charged mass at the center of the atom (the nucleus).
- It helped in determining the approximate size of the nucleus, suggesting that the radius of the nucleus could not be larger than a certain value.

5. **Evaluating the Statements**:
- **Statement about the number of electrons (Z)**: This was not settled by the experiment. Therefore, this statement is false.
- **Validity of Coulomb's law**: The experiment did not confirm the validity of Coulomb's law for distances as small as \(10^{-13}\) m. Hence, this statement is also false.
- **Size of the nucleus**: The experiment determined that the size of the nucleus could not exceed a certain value, making this statement true.
- **Minimum size of the nucleus**: The experiment did not determine a minimum size for the nucleus. Thus, this statement is false.

6. **Final Conclusion**:
- Based on the analysis, the only true statement in the context of Rutherford's experiment is that it established that the size of the nucleus could not be larger than a certain value.

### Answer:
The correct answer is that the experiment settled that the size of the nucleus could not be larger than a certain value.

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