Which is correct graph for photoelectric effect.

Options

A.
B.
C.
D.

Answer

To determine the correct graph for the photoelectric effect, we need to analyze the relationship between the kinetic energy of photoelectrons and the frequency of incident light, as well as the intensity of light.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect describes how electrons are emitted from a material when it is exposed to light of sufficient frequency. The energy of the incoming photons is given by the equation:
\[ E = h \nu \]
where \(E\) is the energy of the photon, \(h\) is Planck's constant, and \(\nu\) is the frequency of the light.

2. **Kinetic Energy Equation**:
The kinetic energy (\(KE_{max}\)) of the emitted photoelectrons can be expressed as:
\[ KE_{max} = h \nu - \phi \]
where \(\phi\) is the work function of the material. Rearranging gives:
\[ KE_{max} = h \nu - \phi \]

3. **Graphing the Relationship**:
If we plot the kinetic energy of the photoelectrons (\(KE_{max}\)) on the y-axis and the frequency (\(\nu\)) on the x-axis, the equation resembles the linear equation of a straight line:
\[ y = mx - c \]
Here, \(m\) (the slope) is equal to \(h\) and \(c\) (the y-intercept) is equal to \(-\phi\).

4. **Analyzing Graph Options**:
- **First Graph**: This graph shows kinetic energy remaining constant regardless of frequency. This is incorrect because kinetic energy should increase with frequency.
- **Second Graph**: This graph shows a straight line with a positive slope and a negative y-intercept. This is correct as it represents the relationship \(KE_{max} = h \nu - \phi\).
- **Third Graph**: This graph shows kinetic energy plotted against light intensity. Since intensity affects the number of emitted electrons but not their kinetic energy, this graph is also correct in the context of showing that kinetic energy remains constant regardless of intensity.
- **Fourth Graph**: This graph shows kinetic energy plotted against wavelength (\(\lambda\)). Since \(E\) is inversely proportional to \(\lambda\), as \(\lambda\) increases, \(KE_{max}\) should decrease. This graph incorrectly shows kinetic energy as constant with increasing wavelength, which is incorrect.

5. **Conclusion**:
The correct graphs for the photoelectric effect are:
- **Option 2**: Kinetic energy vs. frequency (linear relationship).
- **Option 3**: Kinetic energy vs. intensity (constant kinetic energy).