In photoelectric effect experiment, the slope of the graph of the stopping potential versus frequency gives the value of :

Options

A. `(h)/(e )`
B. h
C. `(e )/(h)`
D. `(hc)/(e )`

Explanation

To solve the problem regarding the photoelectric effect experiment and the relationship between stopping potential and frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Photoelectric Effect Equation**:
The photoelectric effect can be described by the equation:
\[ E = \phi + KE \]
where \(E\) is the energy of the incident photons, \(\phi\) is the work function of the material, and \(KE\) is the kinetic energy of the emitted electrons.

2. **Relate Energy to Frequency**:
The energy of the photons can be expressed in terms of frequency (\(f\)) using the equation:
\[ E = hf \]
where \(h\) is Planck's constant.

3. **Express Stopping Potential**:
The stopping potential (\(V_0\)) is related to the kinetic energy of the emitted electrons. The kinetic energy can be expressed as:
\[ KE = eV_0 \]
where \(e\) is the charge of the electron.

4. **Combine the Equations**:
Substituting the expressions for energy and kinetic energy into the photoelectric effect equation gives:
\[ hf = \phi + eV_0 \]
Rearranging this equation, we find:
\[ eV_0 = hf - \phi \]
or
\[ V_0 = \frac{hf}{e} - \frac{\phi}{e} \]

5. **Identify the Linear Relationship**:
The equation \(V_0 = \frac{h}{e} f - \frac{\phi}{e}\) can be compared to the linear equation \(y = mx + c\), where:
- \(y\) is \(V_0\)
- \(x\) is \(f\)
- \(m\) (the slope) is \(\frac{h}{e}\)
- \(c\) (the y-intercept) is \(-\frac{\phi}{e}\)

6. **Conclusion**:
The slope of the graph of stopping potential (\(V_0\)) versus frequency (\(f\)) is given by:
\[ \text{slope} = \frac{h}{e} \]

### Final Answer:
The slope of the graph of the stopping potential versus frequency gives the value of \(\frac{h}{e}\), where \(h\) is Planck's constant and \(e\) is the charge of the electron.

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