Photoelectric Effect

The stopping potential of photoelectrons is potential needed to stop the electrons from reaching the collector depends only on the frequency of incident radiation. It is directly proportional to it. This is because, more the frequency of incident light, more will be the energy of the photons incident photons. Thus, more will be the energy (kinetic) acquired the electrons.
More the kinetic energy of emitted electrons, higher is the potential needed to stop them (stopping potential).

Step 1: Understanding the photoelectric effect.
According to the photoelectric effect, the maximum kinetic energy of the photoelectron is given by , where is the maximum velocity of the photoelectron. The work function of the metal is related to the stopping potential by , where is the charge of the electron.

Step 2: Using the energy conservation principle.
The energy imparted to the photoelectron is used in two ways: to overcome the work function and to provide kinetic energy. Thus, Solving for , we get:
Step 3: Conclusion.
The stopping potential is , which is option (D).

Step 1: Write photoelectric equation.
Step 2: Write equations for given wavelengths.
For wavelength : For wavelength : Step 3: Subtract the equations.
Step 4: Find .
Step 5: Substitute back to find threshold wavelength.
From second equation:

Step 1: Meaning of reverse bias.
In reverse bias, p-side is connected to the negative terminal and n-side to the positive terminal of the battery.
Step 2: Effect on depletion layer.
The applied electric field adds to the junction field, pulling majority carriers away from the junction.
Step 3: Resulting effect.
This increases the width of the depletion layer and raises the potential barrier.
Step 4: Conclusion.
Hence, the width of the depletion layer increases.

Step 1: Using definition of critical angle.
For light going from glass to air,

Step 2: Applying Snell’s law for air to glass.

Step 3: Substituting angle of incidence.
Here , so

Step 4: Solving for angle of refraction.

Step 5: Conclusion.

Step 1: Use of the photoelectric equation.
The photoelectric equation is given by: where is Planck's constant, is the speed of light, is the wavelength, is the work function, and is the stopping potential.
Step 2: Solving for the wavelength.
Rearranging the equation to solve for , we get: Step 3: Conclusion.
Thus, the wavelength of the incident radiation is , corresponding to option (B).

Step 1: Understanding the photoelectric effect.
The stopping potential is related to the energy of the incident photons. The energy of a photon is given by: where is Planck's constant and is the speed of light. The stopping potential depends on the energy of the incident photons compared to the work function of the material. The equation for the stopping potential is: Step 2: Using the given conditions.
From the problem, we know: For , the stopping potential is : For , the stopping potential is : Step 3: Solving the equations.
By solving the equations, we find that the threshold wavelength is .
Step 4: Conclusion.
Thus, the threshold wavelength for the metallic surface is , corresponding to option (A).

Step 1: Einstein’s photoelectric equation.
where is the work function of the metal.

Step 2: Effect of increasing work function.
For a given frequency , if increases, the term decreases.

Step 3: Conclusion.
Hence, the maximum kinetic energy of emitted photoelectrons decreases.

Step 1: Use Einstein’s photoelectric equation.
Since work function is negligible, the entire photon energy converts into kinetic energy of photoelectrons:


Step 2: Express momentum using de-Broglie wavelength.


Step 3: Rearrangement.


Step 4: Conclusion.
The wavelength of the incident radiation is proportional to the square of the de-Broglie wavelength of the photoelectrons.

Step 1: Use the photoelectric equation.
The photoelectric equation is given by: where is the charge of the electron, is the stopping potential, is Planck’s constant, is the frequency of the light, and is the work function of the material. The frequency is related to the wavelength by: where is the speed of light. Step 2: Calculate the change in stopping potential.
For the light of wavelength , the stopping potential is . For light of wavelength , the stopping potential is . Using the photoelectric equation, we get: By solving these two equations, we can find that the threshold wavelength is . Step 3: Conclusion.
Thus, the threshold wavelength for the surface is , which corresponds to option (A).

Step 1: Understanding photoelectric emission.
In the photoelectric effect, the stopping potential is the minimum voltage needed to stop the most energetic photoelectrons emitted by a material when illuminated by light. The stopping potential depends on the frequency of the incident light and not on its intensity. Step 2: Effect of intensity.
The intensity of the incident light affects the number of photoelectrons emitted but does not change the maximum kinetic energy of the emitted electrons. Since the stopping potential depends on the kinetic energy of the electrons (which is related to frequency), it remains unaffected by changes in light intensity. Step 3: Conclusion.
Thus, the correct answer is (B), the stopping potential remains the same.

Step 1: Understanding the photoelectric effect.
In the photoelectric effect, the stopping potential is the potential required to stop the most energetic photoelectrons emitted from the photocell. The stopping potential depends on the frequency of the incident light but not on the intensity of the light.
Step 2: Effect of intensity.
Increasing the intensity of the incident radiation increases the number of photoelectrons emitted but does not affect their maximum kinetic energy. Since the stopping potential is determined by the maximum kinetic energy of the photoelectrons, it remains unchanged with increasing intensity.
Step 3: Conclusion.
Thus, the stopping potential remains unchanged when the intensity of incident radiation is increased, which corresponds to option (B).

Step 1: Relation between kinetic energy and frequency
The photoelectric equation is given by: where is Planck's constant, is the frequency of incident light, and is the work function of the material. Step 2: Frequency and wavelength relation
The frequency is related to the wavelength by: where is the speed of light. Step 3: Substituting in the equation
Substituting into the photoelectric equation: Thus, the maximum kinetic energy of the photoelectrons is inversely proportional to the wavelength .

Concept: Energy of a photon is given by: To calculate energy in electron volts (eV), we use the convenient relation:
Step 1: {Write the given wavelength.}
Step 2: {Use the standard formula.}
Step 3: {Compute the value.}
Step 4: {Verification using SI units (optional).} Convert to eV: