A : The resolving power of an electron microscope is higher than that of an optical microscope.
R : The wavelength of electron is less than the wavelength of visible light.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of A
C. A is true and R is false
D. Both A and R are false

Answer

To analyze the statements provided in the question, we will break down the concepts of resolving power and wavelength, and how they relate to electron microscopes and optical microscopes.

### Step-by-Step Solution:

1. **Understanding Resolving Power**:
- Resolving power is the ability of an optical instrument to distinguish between two closely spaced objects. It is defined as the minimum distance between two points that can still be distinguished as separate entities.
- Mathematically, resolving power (RP) is inversely proportional to the wavelength (λ) of the light or particles used in the microscope. This means that as the wavelength decreases, the resolving power increases.

**Hint**: Remember that resolving power is inversely related to wavelength.

2. **Wavelength of Visible Light**:
- The wavelength of visible light ranges from approximately 400 nm (violet) to 700 nm (red). This range is relatively large compared to the wavelengths associated with electrons.

**Hint**: Recall the typical range of wavelengths for visible light.

3. **Wavelength of Electrons**:
- According to de Broglie's hypothesis, particles such as electrons have an associated wavelength given by the formula:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant and \(p\) is the momentum of the electron. Since electrons can be accelerated to high speeds, their momentum can be quite large, resulting in a much smaller wavelength compared to visible light.

**Hint**: Use de Broglie's equation to understand how the wavelength of electrons is calculated.

4. **Comparison of Wavelengths**:
- Since the wavelength of electrons is significantly smaller than that of visible light, we can conclude that the resolving power of an electron microscope, which uses electrons, is much higher than that of an optical microscope, which uses visible light.

**Hint**: Compare the wavelengths to see why the resolving power differs.

5. **Conclusion**:
- Therefore, both statements A and R are true. Statement R correctly explains statement A because the higher resolving power of the electron microscope is indeed due to the smaller wavelength of electrons compared to visible light.

**Hint**: Ensure you understand the relationship between resolving power and wavelength to conclude effectively.

### Final Answer:
Both A and R are true, and R is the correct explanation of A. Thus, the correct option is option one.