In a photoelectric experiment , the stopping potential `V_s` is plotted against the frequency v of the incident light . The resulting curve is a straight line which makes an angle `theta` with the v - axis. Then `tan theta` will be equal to (Here `E_0` = work function of the surface_

Options

A. `h/e`
B. `e/h`
C. `-phi/e`
D. `(eh)/phi`

Answer

To solve the problem, we need to analyze the relationship between the stopping potential \( V_s \) and the frequency \( \nu \) of the incident light in a photoelectric experiment.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect states that when light of a certain frequency shines on a metal surface, electrons are emitted. The energy of the incident photons is given by \( E = h\nu \), where \( h \) is Planck's constant and \( \nu \) is the frequency of the light.

2. **Energy Conservation**:
The energy of the incoming photon must overcome the work function \( E_0 \) of the material to release an electron. The excess energy is converted into kinetic energy of the emitted electrons. This can be expressed as:
\[ h\nu = E_0 + eV_s \]
where \( e \) is the charge of the electron and \( V_s \) is the stopping potential.

3. **Rearranging the Equation**:
Rearranging the above equation gives:
\[ V_s = \frac{h\nu}{e} - \frac{E_0}{e} \]

4. **Identifying the Linear Relationship**:
The equation \( V_s = \frac{h}{e}\nu - \frac{E_0}{e} \) is in the form of \( y = mx + c \), where:
- \( y \) is \( V_s \)
- \( x \) is \( \nu \)
- \( m \) (the slope) is \( \frac{h}{e} \)
- \( c \) (the y-intercept) is \( -\frac{E_0}{e} \)

5. **Finding the Slope**:
The slope \( m \) of the line is equal to \( \tan \theta \) where \( \theta \) is the angle the line makes with the frequency axis. Thus, we have:
\[ \tan \theta = \frac{h}{e} \]

6. **Conclusion**:
Therefore, the value of \( \tan \theta \) is:
\[ \tan \theta = \frac{h}{e} \]

### Final Answer:
\[ \tan \theta = \frac{h}{e} \]