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

Options

A. there is minimum frequency of light below which no photoelectrons are emitted
B. the maximum kinetic enetgy of photoelectrons dep ends only on the frequency of light and not on its intensity
C. enven when the metal surface enetgy is fainithly illuminated (with frequency more than the thresholdn frequency ) the photoelectrons leave the surfce immeidaltely
D. electric charg of the photoelectrons is quantize

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 of light.

### 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 demonstrates that light has particle-like properties.

2. **Analyzing Each Option**:
- **Option (a)**: "There is a minimum frequency of light below which no photoelectrons are emitted."
- This statement is true. It indicates that there is a threshold frequency (or threshold wavelength) below which no electrons are emitted, regardless of the intensity of the light. This supports the quantum nature of light because it suggests that light must have a minimum energy (related to frequency) to eject electrons.

- **Option (b)**: "The maximum kinetic energy of photoelectrons depends only on the frequency of light and not on its intensity."
- This statement is also true. According to Einstein's photoelectric equation, the kinetic energy of emitted electrons is directly proportional to the frequency of the incident light, not its intensity. However, this option does not directly address the quantum nature of light as clearly as option (a).

- **Option (c)**: "Even when the metal surface is faintly illuminated, the photoelectrons leave the surface immediately."
- This statement is misleading. While photoelectrons can be emitted immediately if the light frequency is above the threshold, the term "faintly illuminated" suggests low intensity, which can affect the number of emitted electrons but not their immediate emission if the frequency condition is met.

- **Option (d)**: "Electric charge of the photoelectrons is quantized."
- This statement is incorrect. The charge of an electron is a fundamental constant and is not quantized in the context of the photoelectric effect. This option does not support the quantum nature of light.

3. **Conclusion**:
The best option that supports the quantum nature of light is **(a)**: "There is a minimum frequency of light below which no photoelectrons are emitted." This reflects the particle-like behavior of light, where energy is quantized in the form of photons.

### Final Answer:
The correct option is **(a)**.

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