Wave nature of light cannot explain photoelectric effect because in photoelectric effect , it is seen that

Options

A. For the frequency of light below a certain value , the photoelectric effect does not take place , irrespective of intensity
B. Maximum kinetic energy of ejected electrons of independent of intensity of radiation
C. There is no time lag between the incidence of radiation and emission of electrons
D. All of these

Answer

To solve the question regarding why the wave nature of light cannot explain the photoelectric effect, we can break down the explanation into several steps:

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect refers to the phenomenon where electrons are emitted from a metal surface when light (or electromagnetic radiation) of sufficient frequency strikes it.

2. **Key Parameters**:
- **Intensity (I)**: Refers to the power per unit area of the incident light.
- **Frequency (ν)**: The number of oscillations of the light wave per second.
- **Work Function (φ)**: The minimum energy required to remove an electron from the surface of the metal.
- **Threshold Frequency (ν₀)**: The minimum frequency of light required to emit electrons from the metal.

3. **Observations from the Photoelectric Effect**:
- **Dependence on Frequency**: Electrons are only emitted if the frequency of the incident light is above a certain threshold (ν₀). If the frequency is below this threshold, no electrons are emitted regardless of the intensity of the light.
- **Independence of Intensity**: The maximum kinetic energy of the emitted electrons is dependent only on the frequency of the incident light and not on its intensity. This is expressed in the equation:
\[ KE_{max} = hν - φ \]
where \( KE_{max} \) is the maximum kinetic energy of the emitted electrons, \( h \) is Planck's constant, and \( φ \) is the work function.

4. **Wave Nature vs. Particle Nature**:
- **Wave Nature**: According to the wave theory, increasing the intensity of light should increase the energy imparted to the electrons, leading to their emission regardless of frequency. However, this is not observed in the photoelectric effect.
- **Particle Nature**: The photoelectric effect supports the particle nature of light (photons), which states that light consists of discrete packets of energy. Each photon has energy proportional to its frequency (E = hν). If the photon energy is less than the work function, no electrons are emitted, regardless of intensity.

5. **Conclusion**:
The wave nature of light fails to explain the photoelectric effect because it cannot account for the threshold frequency requirement and the independence of the maximum kinetic energy of emitted electrons from the intensity of the light. The observations are consistent with the particle nature of light.

### Final Answer:
The wave nature of light cannot explain the photoelectric effect because:
- Electrons are emitted only if the frequency of light is above a certain threshold (ν₀), regardless of the intensity.
- The maximum kinetic energy of emitted electrons is independent of the intensity of the incident light, depending only on the frequency.