In photo electric effect, the slope of the straight line graph between stopping potential and frequency of the incident light gives the ratio of Planck's constant to

Options

A. charge of electron
B. work function
C. photo electric current
D. `K.E.` of electron

Answer

To solve the question regarding the photoelectric effect, we will derive the relationship between the stopping potential (V₀) and the frequency (ν) of the incident light, and determine what the slope of the graph represents.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect describes the phenomenon where electrons are emitted from a material (usually a metal) when it is exposed to light of sufficient frequency. The energy of the incident photons must be greater than the work function (φ) of the material for electrons to be emitted.

2. **Energy of Incident Photons**:
The energy (E) of a photon is given by the equation:
\[ E = h\nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the incident light.

3. **Work Function**:
The work function (φ) is the minimum energy required to remove an electron from the surface of the material.

4. **Kinetic Energy of Emitted Electrons**:
When a photon hits the material, the energy is used to overcome the work function and the remaining energy is converted into kinetic energy (K.E) of the emitted electron:
\[ K.E = h\nu - \phi \]

5. **Relation to Stopping Potential**:
The stopping potential (V₀) is the potential needed to stop the emitted electrons. The kinetic energy of the electrons can also be expressed in terms of stopping potential:
\[ K.E = eV₀ \]
where \( e \) is the charge of the electron.

6. **Setting the Equations Equal**:
By equating the two expressions for kinetic energy, we have:
\[ eV₀ = h\nu - \phi \]

7. **Rearranging the Equation**:
Rearranging gives:
\[ eV₀ = h\nu - \phi \implies eV₀ = h\nu - \phi \]
\[ eV₀ = h\nu - \phi \implies V₀ = \frac{h}{e}\nu - \frac{\phi}{e} \]

8. **Identifying the Slope**:
This equation is in the form of \( y = mx + c \) where:
- \( y = V₀ \)
- \( x = \nu \)
- \( m = \frac{h}{e} \) (the slope)
- \( c = -\frac{\phi}{e} \) (the y-intercept)

9. **Conclusion**:
The slope of the graph of stopping potential (V₀) versus frequency (ν) is given by:
\[ \text{slope} = \frac{h}{e} \]
Therefore, the slope gives the ratio of Planck's constant (h) to the charge of the electron (e).

### Final Answer:
The slope of the straight line graph between stopping potential and frequency of the incident light gives the ratio of Planck's constant (h) to the charge of the electron (e).