For photoelectric effect with incident photon wavelength `lamda`, the stopping potential is `V_0` Select the correct graph.

Options

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Answer

To solve the problem regarding the photoelectric effect and the stopping potential \( V_0 \) as a function of the incident photon wavelength \( \lambda \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Photoelectric Effect**:
The photoelectric effect occurs when light (photons) hits a material and causes the emission of electrons. The energy of the incident photons is given by the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the incident light.

2. **Energy Considerations**:
For an electron to be emitted, the energy of the photon must be greater than the work function \( \phi \) of the material. The kinetic energy \( K \) of the emitted electrons can be expressed as:
\[ K = E - \phi = \frac{hc}{\lambda} - \phi \]

3. **Relate Kinetic Energy to Stopping Potential**:
The kinetic energy of the emitted electrons can also be related to the stopping potential \( V_0 \) by the equation:
\[ K = eV_0 \]
where \( e \) is the charge of the electron. Therefore, we can equate the two expressions for kinetic energy:
\[ eV_0 = \frac{hc}{\lambda} - \phi \]

4. **Rearranging the Equation**:
Rearranging the equation gives us:
\[ V_0 = \frac{hc}{e} \cdot \frac{1}{\lambda} - \frac{\phi}{e} \]
This equation is in the form of a linear equation \( y = mx - c \), where:
- \( y = V_0 \)
- \( x = \frac{1}{\lambda} \)
- \( m = \frac{hc}{e} \) (slope)
- \( c = \frac{\phi}{e} \) (y-intercept)

5. **Graph Interpretation**:
From the equation \( V_0 = \frac{hc}{e} \cdot \frac{1}{\lambda} - \frac{\phi}{e} \), we can see that the graph of \( V_0 \) versus \( \frac{1}{\lambda} \) will be a straight line with a positive slope. The x-intercept occurs when \( V_0 = 0 \), which gives us the threshold wavelength where photoemission starts.

6. **Select the Correct Graph**:
Based on the linear relationship derived, we can identify that the correct graph will show a straight line with \( V_0 \) on the y-axis and \( \frac{1}{\lambda} \) on the x-axis. The line will intersect the x-axis at the point corresponding to the threshold wavelength.

### Final Answer:
The correct graph is the one that depicts a straight line with \( V_0 \) on the y-axis and \( \frac{1}{\lambda} \) on the x-axis, indicating a linear relationship.