According to Einstein's photoelectric equation, the graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation is

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Explanation

To solve the problem regarding the graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation according to Einstein's photoelectric equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Einstein's Photoelectric Equation**:
The equation is given by:
\[ K_{\text{max}} = h\nu - \phi \]
where \( K_{\text{max}} \) is the maximum kinetic energy of the emitted photoelectrons, \( h \) is Planck's constant, \( \nu \) is the frequency of the incident radiation, and \( \phi \) is the work function of the material.

2. **Rearranging the Equation**:
We can rearrange the equation to express \( K_{\text{max}} \) in terms of frequency:
\[ K_{\text{max}} = h\nu - \phi \]
This shows that \( K_{\text{max}} \) is directly proportional to the frequency of the incident radiation.

3. **Identifying the Graph**:
In the equation \( K_{\text{max}} = h\nu - \phi \), we can interpret it as a linear equation of the form \( y = mx + c \), where:
- \( y \) is \( K_{\text{max}} \)
- \( x \) is \( \nu \)
- \( m \) (the slope) is \( h \)
- \( c \) (the y-intercept) is \(-\phi\)

4. **Slope and Intercept**:
- The slope \( m = h \) is positive since Planck's constant is a positive value.
- The y-intercept \( c = -\phi \) is negative because the work function \( \phi \) is a positive value representing the energy required to eject an electron.

5. **Graph Characteristics**:
- Since the slope is positive, the graph will be a straight line that rises as frequency increases.
- The line will intersect the y-axis below the origin due to the negative intercept.

6. **Conclusion**:
The graph of \( K_{\text{max}} \) versus \( \nu \) will be a straight line with a positive slope and a negative y-intercept. This indicates that as the frequency of the incident radiation increases, the kinetic energy of the emitted photoelectrons also increases linearly.

### Final Answer:
The graph between the kinetic energy of photoelectrons ejected and the frequency of incident radiation is a straight line with a positive slope and a negative y-intercept.

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