Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?

Options

A.
B.
C.
D.

Explanation

To solve the question about which graph does not represent the relationship between incident light and the electrons ejected from a metal surface, we need to analyze the principles of the photoelectric effect and the relationships involved.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
- According to Einstein's photoelectric equation, the energy of the incident photon (light) is given by \( E = h\nu \), where \( h \) is Planck's constant and \( \nu \) is the frequency of the light.
- The equation can be expressed as:
\[ h\nu = h\nu_0 + \frac{1}{2}mv^2 \]
where \( \nu_0 \) is the threshold frequency, \( m \) is the mass of the electron, and \( v \) is its velocity.

2. **Analyzing the Graphs**:
- **Graph A**: Represents the kinetic energy of the ejected electrons as a function of the frequency of the incident light. This is correct as per the photoelectric effect; kinetic energy increases with frequency above the threshold frequency.
- **Graph B**: Indicates that the kinetic energy of electrons is directly proportional to the energy of the light. This is also correct since energy is proportional to frequency.
- **Graph C**: Suggests that the number of electrons ejected per second depends on the intensity of light but is independent of frequency. This is true; however, the graph may incorrectly imply a relationship that doesn't exist.
- **Graph D**: Shows that the kinetic energy of electrons remains constant with changes in intensity. This is incorrect because the kinetic energy of ejected electrons depends on the frequency of the incident light, not its intensity.

3. **Conclusion**:
- The graph that does not correctly represent the relationship between incident light and the ejected electrons is **Graph D**. This is because it incorrectly suggests that the kinetic energy of the electrons is constant regardless of changes in intensity, which contradicts the principles of the photoelectric effect.

### Final Answer:
**Graph D does not represent the relationship between incident light and the electrons ejected from a metal surface.**