Question

The figure shows a photo cell circuit. The cathode of the photo cell is illuminated by a monochromatic light. If the intensity is kept constant and the frequency of the incident light is increased, then the

• A. photo electric current in the circuit increases
• B. photo electric current in the circuit decreases
• C. maximum kinetic energy of the photo electrons increases
• D. photo electric current in the circuit can be reduced to zero, when the polarity of the terminals is reversed

Answer 1

Answer: (C)

C

Answer 2

The question asks what happens in a photocell circuit when the intensity of monochromatic light is kept constant and its frequency is increased.

Let's analyze the principles of the photoelectric effect:

1. Photoelectric Current and Intensity: The photoelectric current is directly proportional to the number of photoelectrons emitted per second. The number of photoelectrons emitted per second is directly proportional to the intensity of the incident light (provided the frequency is above the threshold frequency). Since the intensity of the incident light is kept constant, the number of photons striking the cathode per unit time remains constant. Consequently, the number of photoelectrons emitted per second will remain constant, and thus the photoelectric current will remain constant.

2. Maximum Kinetic Energy and Frequency: According to Einstein's photoelectric equation: $K_{max} = h\nu - \phi_0$ where:

   • $K_{max}$ is the maximum kinetic energy of the emitted photoelectrons.
   • $h$ is Planck's constant.
   • $\nu$ is the frequency of the incident light.
   • $\phi_0$ is the work function of the material (a constant for a given cathode material).

   From this equation, if the frequency ($\nu$) of the incident light increases, and the work function ($\phi_0$) is constant, then the maximum kinetic energy ($K_{max}$) of the photoelectrons will increase linearly with frequency.

Let's evaluate the given options:

• (A) photo electric current in the circuit increases: Incorrect. The photoelectric current depends on the intensity of light, not its frequency (assuming frequency is above the threshold). Since intensity is constant, the current remains constant.
• (B) photo electric current in the circuit decreases: Incorrect. For the same reason as (A), the current remains constant.
• (C) maximum kinetic energy of the photo electrons increases: Correct. As per Einstein's photoelectric equation, an increase in the frequency of incident light directly leads to an increase in the maximum kinetic energy of the emitted photoelectrons.
• (D) photo electric current in the circuit can be reduced to zero, when the polarity of the terminals is reversed: This statement is a general characteristic of the photoelectric effect (by applying a stopping potential). However, it does not describe a change that occurs due to increasing frequency under constant intensity. In fact, if the frequency increases, the magnitude of the stopping potential required to reduce the current to zero (which is $V_0 = K_{max}/e$) will increase. So, while the current can be reduced to zero, this option doesn't highlight the specific effect of increasing frequency as effectively as option (C).

Therefore, the most accurate statement describing the consequence of increasing the frequency of incident light while keeping intensity constant is that the maximum kinetic energy of the photoelectrons increases.