Question

In photoelectric effect, the photoelectric current is independent of

• A. intensity of incident light
• B. potential difference applied between two electrodes
• C. the nature of emitter material
• D. frequency of incident light

Hint:

To easily remember the relationships in the photoelectric effect: \begin{itemize} \item \textbf{Intensity} \(\rightarrow\) \textbf{Number of electrons} \(\rightarrow\) \textbf{Photoelectric Current}. \item \textbf{Frequency} \(\rightarrow\) \textbf{Energy of electrons} \(\rightarrow\) \textbf{Kinetic Energy / Stopping Potential}. \end{itemize} This helps distinguish between what affects the current and what affects the energy of the electrons.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Photoelectric current is the flow of these emitted electrons (photoelectrons). The question asks which factor does not affect the magnitude of this current.
Step 2: Detailed Explanation:
Let's analyze the relationship between photoelectric current and the given options:
(A) Intensity of incident light: Photoelectric current is directly proportional to the intensity of the incident light (provided the frequency is above the threshold frequency). Higher intensity means more photons are striking the surface per unit time, which in turn ejects more electrons, leading to a larger current. So, the current is dependent on intensity.
(B) Potential difference applied between two electrodes: The potential difference can either accelerate or decelerate the photoelectrons. An accelerating potential helps more electrons reach the collector, increasing the current up to a saturation point. A retarding (negative) potential opposes the flow, decreasing the current. Thus, the current is dependent on the potential difference.
(C) The nature of emitter material: The material's nature determines its work function (\(\phi_0\)), which is the minimum energy required to eject an electron. This defines the threshold frequency (\(f_0\)). If the incident light's frequency is below \(f_0\), no current flows. So, the existence of the current depends on the material.
(D) Frequency of incident light: According to Einstein's photoelectric equation (\(K_{max} = hf - \phi_0\)), the frequency of the incident light determines the maximum kinetic energy of the emitted photoelectrons, not their number. As long as the frequency is above the threshold frequency (\(f>f_0\)), changing the frequency (while keeping the intensity constant) will change the speed of the electrons, but not the number of electrons emitted per second. Since the photoelectric current depends on the number of electrons emitted per second, it is independent of the frequency of the incident light.
Step 3: Final Answer:
The photoelectric current is independent of the frequency of the incident light (assuming the frequency is above the threshold). Therefore, option (D) is the correct answer.