Photoelectric effect supports quantum nature of light because
(a) there is a minimum frequency of light below which no photoelectrons are emitted
(b) the maximum kinetic energy of photoelectrons depends only on the frequency of light and not onits intensity
(c ) even when the metal surface is faintly illuminated, the photoelectrons leave the surface immediately
(d) electric charge of the photoelectrons is quantised

Answer

To solve the question regarding the photoelectric effect and its support for the quantum nature of light, we will analyze each option provided and determine which one correctly supports the quantum theory.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect refers to the phenomenon where electrons are emitted from a material (usually a metal) when it is exposed to light of sufficient frequency. This effect cannot be explained by classical wave theory but can be explained by quantum theory.

2. **Evaluating Option (a)**:
- **Statement**: There is a minimum frequency of light below which no photoelectrons are emitted.
- **Analysis**: This is known as the threshold frequency. According to quantum theory, if the frequency of light is below this threshold, no electrons will be emitted regardless of the intensity of the light. This supports the idea that light has particle-like properties (photons) that must have a certain energy (related to frequency) to eject electrons.
- **Conclusion**: This option is correct.

3. **Evaluating Option (b)**:
- **Statement**: The maximum kinetic energy of photoelectrons depends only on the frequency of light and not on its intensity.
- **Analysis**: This is true; however, it does not directly support the quantum nature of light. While it indicates that energy is quantized, it does not explain why there is a threshold frequency.
- **Conclusion**: This option is partially correct but does not directly support the quantum nature as strongly as option (a).

4. **Evaluating Option (c)**:
- **Statement**: Even when the metal surface is faintly illuminated, the photoelectrons leave the surface immediately.
- **Analysis**: This statement is misleading. Photoelectrons will only be emitted if the light frequency is above the threshold frequency, regardless of how faint the illumination is. If the frequency is below the threshold, no electrons will be emitted, regardless of intensity.
- **Conclusion**: This option is incorrect.

5. **Evaluating Option (d)**:
- **Statement**: The electric charge of the photoelectrons is quantized.
- **Analysis**: While the charge of electrons is indeed quantized (as they are elementary particles), this statement does not specifically relate to the photoelectric effect or the quantum nature of light.
- **Conclusion**: This option is incorrect.

### Final Answer:
The correct answer is **(a)**: There is a minimum frequency of light below which no photoelectrons are emitted.