The slope of frequency of incident light and stopping potential for a given surface will be

Options

A. `h`
B. `h//e`
C. `eh`
D. `e`

Answer

To find the slope of the graph of frequency of incident light versus stopping potential for a given surface, we can use Einstein's photoelectric equation. Let's derive the relationship step by step.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect occurs when light of sufficient frequency strikes a material and causes the ejection of electrons. The energy of the incident photons must be greater than the work function of the material for electrons to be emitted.

2. **Einstein's Photoelectric Equation**:
The equation is given by:
\[ E \cdot V_0 = h \nu - \phi_0 \]
where:
- \(E\) is the charge of the electron,
- \(V_0\) is the stopping potential,
- \(h\) is Planck's constant,
- \(\nu\) is the frequency of the incident light,
- \(\phi_0\) is the work function of the material.

3. **Rearranging the Equation**:
We can rearrange the equation to express \(V_0\) in terms of \(\nu\):
\[ E \cdot V_0 = h \nu - \phi_0 \]
Dividing through by \(E\):
\[ V_0 = \frac{h}{E} \nu - \frac{\phi_0}{E} \]

4. **Identifying the Linear Relationship**:
The equation \(V_0 = \frac{h}{E} \nu - \frac{\phi_0}{E}\) is in the form of \(y = mx + c\), where:
- \(y\) is the stopping potential \(V_0\),
- \(x\) is the frequency \(\nu\),
- \(m\) (the slope) is \(\frac{h}{E}\),
- \(c\) (the y-intercept) is \(-\frac{\phi_0}{E}\).

5. **Conclusion**:
The slope of the graph of frequency of incident light versus stopping potential is:
\[ \text{slope} = \frac{h}{E} \]

### Final Answer:
The slope of the frequency of incident light and stopping potential for a given surface will be \(\frac{h}{E}\).