Question

Assertion (A) : On increasing the intensity of incident light of frequency $\nu$ ($> \nu_0$) on a photosensitive surface, the photocurrent increases.
Reason (R) : The stopping potential for a photosensitive surface increases with increase of frequency $\nu$ ($> \nu_0$) of incident light.

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

Hint:

Keep these rules permanently separated in your mind: Intensity controls only the number (current), while Frequency controls only the energy (stopping potential).

Answer 1

The Correct Option is B

Concept:
• The photoelectric effect firmly relies on the quantum particle nature of light, where light comprises discrete energy packets called photons.

• The optical intensity of a light beam physically corresponds directly to the sheer number of photons striking a specific target area per second. Increasing intensity vigorously increases the photon count, not their individual energy.

• Assuming the constant frequency is safely above the threshold ($\nu > \nu_0$), more bombarding photons will cleanly eject more photoelectrons, directly and linearly increasing the total measured saturation photocurrent.

• The stopping potential, conversely, depends strictly and only on the maximum kinetic energy of the ejected electrons, which is dictated exclusively by the incident photon frequency (energy), completely independent of intensity.

Step 1: Evaluate the Assertion (A)
The assertion states that increasing the intensity of valid incident light ($\nu > \nu_0$) directly causes the resulting photocurrent to increase.
According to established quantum principles, higher light intensity essentially means a significantly larger number of photons are aggressively hitting the metal surface every second.
Since one incoming photon generally ejects exactly one electron, more impacting photons will invariably result in a higher number of emitted photoelectrons per second.
More moving electrons directly constitute a higher electrical current.
Therefore, the Assertion (A) is a scientifically true statement.

Step 2: Evaluate the Reason (R)
The reason states that the stopping potential required for a given photosensitive surface physically increases when the frequency of the incident light is actively increased.
Einstein's robust photoelectric equation is elegantly stated as $eV_0 = h\nu - \Phi$.
It is mathematically obvious from this linear equation that if the incident frequency $\nu$ increases, the corresponding stopping potential $V_0$ must also simultaneously and linearly increase.
Therefore, the Reason (R) is also a completely scientifically true statement.

Step 3: Determine if the Reason correctly explains the Assertion
The Assertion thoroughly discusses how changing light intensity directly manipulates the sheer number of flowing electrons (photocurrent).
The Reason, however, discusses an entirely separate phenomenon: how changing light frequency manipulates the maximum energy of those electrons (stopping potential).
While both physics statements are undeniably factual within the realm of the photoelectric effect, they are addressing two fundamentally completely unlinked parameters.
The reason spectacularly fails to provide any logical explanation whatsoever for why intensity impacts current.

Step 4: Conclusion
Both statements are individually perfectly true, but the reason is entirely disconnected from explaining the assertion. Thus, the correct choice is definitely option (B).