The stopping potential necessary to reduce the phtoelectric current of zero-

Options

A. is directly proprotional to wavelength of incident light.
B. uniformly increases with the wavelength of incident light.
C. directly proportional to frequency of incident light.
D. uniformly increases with the frequnecy of incident light.

Explanation

To solve the problem regarding the stopping potential necessary to reduce the photoelectric current to zero, we can follow these steps:

### Step 1: Understand the Concept of Stopping Potential
The stopping potential (V₀) is the potential difference needed to stop the photoelectrons emitted from a material when light shines on it. It is the voltage required to reduce the photoelectric current to zero.

### Step 2: Relate Stopping Potential to Kinetic Energy
According to the photoelectric effect, the stopping potential is related to the kinetic energy (KE) of the emitted photoelectrons. The equation for kinetic energy in terms of stopping potential is:
\[ KE = eV₀ \]
where \( e \) is the charge of the electron.

### Step 3: Use Einstein's Photoelectric Equation
Einstein's photoelectric equation states:
\[ KE = h\nu - \phi \]
where:
- \( h \) is Planck's constant,
- \( \nu \) is the frequency of the incident light,
- \( \phi \) is the work function of the material.

### Step 4: Combine the Equations
From the two equations, we can equate the kinetic energy expressions:
\[ eV₀ = h\nu - \phi \]

### Step 5: Solve for Stopping Potential
Rearranging the equation to solve for the stopping potential gives:
\[ V₀ = \frac{h\nu - \phi}{e} \]

### Step 6: Analyze the Relationship with Frequency
From the equation \( V₀ = \frac{h\nu - \phi}{e} \), we can see that as the frequency \( \nu \) of the incident light increases, the stopping potential \( V₀ \) also increases linearly, provided that the work function \( \phi \) remains constant for a given material.

### Conclusion
Thus, the stopping potential necessary to reduce the photoelectric current to zero increases linearly with the frequency of the incident light.

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