Correct Option: (C) Assertion (A) is true, but Reason (R) is false.
Step 1 (Governing Law & Principle): [0.25 Mark]
The photoelectric effect is governed by Einstein's Photoelectric Equation:
$$K_{max} = h\nu - \Phi_0$$Where $K_{max}$ is the maximum kinetic energy, $h\nu$ is the energy of the incident photon, and $\Phi_0$ is the work function of the metal surface.
Step 2 (Step-by-Step Logical Analysis): [0.50 Mark]
- Analysis of Assertion (A): Even with monochromatic light (constant $\nu$), electrons are emitted from different depths within the metal. Electrons escaping from the surface require only the work function $\Phi_0$ to be overcome, while electrons from deeper layers lose additional energy due to collisions before reaching the surface. Thus, the kinetic energy $K$ ranges from $0$ to $K_{max}$. Therefore, Assertion (A) is true.
- Analysis of Reason (R): The Assertion specifically states the process uses monochromatic light. The Reason discusses a scenario involving "different wavelengths," which contradicts the premise of the Assertion. Furthermore, the Reason implies that the variation in kinetic energy is solely due to different wavelengths, which is physically incorrect for the given context. Therefore, Reason (R) is false.
Step 3 (Final Concluded Answer): [0.25 Mark]
Since the Assertion is a correct statement based on the physics of electron collisions within the metal, and the Reason provides an incorrect explanation (as it contradicts the monochromatic condition), the correct choice is (C).
💡 EL10 Concept Insight: Think of the metal like a crowded room; even if everyone gets the same amount of "energy" (light) to leave, the people standing right by the door get out easily, while those stuck in the back lose energy bumping into others, so they all exit at different speeds.