(A) in the experiment of alpha particle scattering, extremely thin gold foils are preferred over other metals.
(R)gold is a ductile material.

Options

A. if both assertion and reason are true and reason is the correct explanation of assertion.
B. if both assertion and reason are true but reason is not the correct explanation of assertion.
C. if assertion is true but reason is false.
D. if both assertion and reason are false.

Explanation

To solve the question regarding the preference for extremely thin gold foils in the experiment of alpha particle scattering and the reasoning behind it, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding Alpha Particle Scattering**:
- Alpha particle scattering is an experiment that investigates the structure of the atom by firing alpha particles at a thin foil of metal. The way these particles scatter provides information about the atomic structure.

2. **Reason for Using Thin Foils**:
- Extremely thin foils are preferred because they allow alpha particles to pass through with minimal interactions, which is crucial for observing scattering events. Thicker materials would absorb or deflect too many particles, making it difficult to analyze the scattering.

3. **Properties of Gold**:
- Gold is chosen specifically because it is a ductile material, which means it can be hammered into very thin sheets without breaking. This property allows for the creation of extremely thin foils necessary for the experiment.

4. **Atomic Number of Gold**:
- Gold has a high atomic number (Z = 79), which means it has a large number of protons in its nucleus. This results in a strong positive charge in the nucleus.

5. **Electrostatic Repulsion**:
- When alpha particles, which are positively charged, approach the gold nucleus, they experience a significant electrostatic repulsion due to the high positive charge of the gold nucleus. This repulsion is stronger than it would be with metals of lower atomic numbers.

6. **Effect on Scattering Angles**:
- The strong repulsive force causes the alpha particles to scatter at larger angles. This is important for the experiment because it allows for the detection of the alpha particles at various angles, providing valuable data about the atomic structure.

7. **Conclusion**:
- While both statements in the question are true (gold is ductile, and thin foils are used), the reason provided (ductility) does not fully explain why gold is preferred. The key reason is its high atomic number, which leads to significant electrostatic repulsion and larger scattering angles.

### Final Answer:
(A) is true because extremely thin gold foils are preferred in alpha particle scattering experiments due to their ability to allow alpha particles to pass through with minimal interaction. (R) is also true, but it does not provide the correct reason for the assertion. The correct reason is that gold has a high atomic number, leading to strong electrostatic repulsion of the alpha particles.