Question Analysis: Assertion (A) and Reason (R) type question.
Step 1 (Conceptual Analysis of Assertion): [0.25 Mark]
The photoelectric effect is an instantaneous process. Once the incident light frequency $\nu$ exceeds the threshold frequency $\nu_0$, the emission of photoelectrons occurs without any time lag (typically $\approx 10^{-9} \text{ s}$). Therefore, the statement that it is a "spontaneous" (in the sense of time-independent/instantaneous) phenomenon is correct in the context of experimental observation.
Step 2 (Conceptual Analysis of Reason): [0.5 Mark]
According to the classical wave theory, energy is distributed continuously over the wavefront. The energy absorbed by an electron per unit time is given by:
$$P = I \cdot A$$Where $I$ is intensity and $A$ is the effective cross-sectional area of the atom. Calculations based on classical wave theory show that for low-intensity light, an electron would require a significant duration (hours or days) to accumulate energy equal to the work function $\Phi_0$:
$$\Phi_0 = h\nu_0$$Since the wave theory fails to explain the instantaneous nature observed experimentally, the Reason (R) correctly describes the prediction of the wave picture.
Step 3 (Final Concluded Answer): [0.25 Mark]
Correct Option: (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true because the photoelectric effect is instantaneous.
- Reason (R) is true because it correctly identifies the failure of the wave theory to explain the time-lag (or lack thereof).
- However, (R) does not explain why the effect is spontaneous; rather, it explains why the wave theory is inconsistent with the observed spontaneity.
💡 EL10 Concept Insight: Imagine trying to fill a bucket with water using a tiny dropper from far away; the wave theory says it would take forever to fill, but in reality, the photoelectric effect is like a "magic" switch that turns on instantly the moment the light hits, proving that light acts like a stream of individual energy bullets (photons) rather than a continuous wave.