Question

Assertion (A) : Photoelectric current depends upon the intensity of the incident radiation.
Reason (R) : Stopping potential is independent of the intensity of the incident radiation.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

To remember photoelectric dependencies: - Intensity controls the quantity of electrons (and hence the photoelectric current). - Frequency controls the energy of electrons (and hence the stopping potential).

Answer 1

The Correct Option is B

Concept: The photoelectric effect is the emission of electrons when light shines on a metal surface. According to the photon theory of light:
• Intensity: The intensity of a light beam of a given frequency is proportional to the number of photons hitting a unit area per second.
• Photon-Electron Interaction: One incident photon interacts with exactly one electron inside the metal lattice.
• Stopping Potential (\(V_0\)): The stopping potential is the negative voltage required to stop the fastest photoelectrons from reaching the anode. It depends on the maximum kinetic energy (\(K_{\max}\)) of the emitted electrons: \[ eV_0 = K_{\max} = h\nu - \phi_0 \]

Step 1: Verifying the accuracy of Assertion (A).
Increasing the intensity of the incident light source (while keeping the frequency constant) increases the number of photons hitting the metal surface per second. Since each photon can eject an electron, more photons result in more photoelectrons emitted per second. This directly increases the photoelectric current (\(I \propto \text{Intensity}\)). Thus, the Assertion statement is true.

Step 2: Verifying the accuracy of Reason (R).
The stopping potential is determined by Einstein's equation: \[ V_0 = \frac{h\nu - \phi_0}{e} \] This equation shows that the stopping potential depends solely on the frequency (\(\nu\)) of the incoming light and the work function (\(\phi_0\)) of the metal surface. Changing the intensity changes the number of photons, but does not alter the energy of individual photons (\(E = h\nu\)). Therefore, the maximum kinetic energy of the escaping electrons remains unchanged, meaning the stopping potential is independent of intensity. Thus, the Reason statement is independently true.

Step 3: Evaluating the causal relationship.
While both statements are factually true, the Reason does not explain the Assertion. The Assertion states that the photoelectric current increases with intensity because a higher intensity means more photons are available to eject more electrons per second. The Reason simply states an independent fact about the stopping potential. Since the Reason is not the correct explanation of the Assertion, the correct option is (B).