Question

Assertion : Photoelectric effect is a spontaneous phenomenon. Reason (R): According to the wave picture of radiation, an electron would take hours/days to absorb sufficient energy to overcome the work function and come out from a metal surface.

• 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:

Key photoelectric observations:

Instant emission (no time lag)
Threshold frequency exists
Supports photon (quantum) theory of light

Answer 1

The Correct Option is A

Concept: The photoelectric effect demonstrates the particle nature of light:

Emission of electrons occurs instantly when light of sufficient frequency falls on a metal
No measurable time delay

Step 1: Analyze Assertion (A). Photoelectric emission occurs immediately once light of frequency above threshold strikes the surface. Hence, it is considered a spontaneous (instantaneous) phenomenon. Assertion is true.
Step 2: Analyze Reason (R). According to classical wave theory:

Energy is delivered continuously
Electron should accumulate energy gradually
This would cause a measurable time delay
But experiments show no delay. Thus, the reason correctly describes the classical prediction.
Step 3: Link between A and R. The absence of time lag (spontaneity) contradicts classical wave theory and supports photon theory. Hence, the reason explains why the effect is spontaneous. Conclusion: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Answer 2

This assertion-reason question is about why the photoelectric effect appears instantaneous. Let's approach it by outlining what classical wave theory actually predicts for the time delay and comparing that prediction with what is observed, checking each option against this comparison.

1. Option A (Both true, R is the correct explanation): Classical wave theory pictures light energy as spread continuously and uniformly over the wavefront. On this picture, a bound electron on a metal surface would absorb energy gradually as the wave washes over it, and standard order-of-magnitude estimates using typical light intensities show it would take on the order of hours, sometimes even days, for a single electron to accumulate enough energy to escape. Yet experiments show electrons are ejected essentially at once when light of sufficiently high frequency strikes the surface, with no measurable time lag. This gap between the very slow classical prediction and the essentially instantaneous observed emission is exactly what led to the idea that light delivers energy in discrete packets, each capable of ejecting an electron in one absorption event. So the reason correctly describes the classical wave-theory time-lag prediction, and it directly explains why the assertion, spontaneity, is significant: it highlights that the observed behavior cannot come from the wave picture. This makes the assertion true and the reason both true and explanatory.
2. Option B (Both true, R not the explanation): This would apply if R were true but unrelated to why A holds. But R's calculation of the expected wave-theory delay is precisely the fact used to justify why instantaneous emission is remarkable and points toward a photon picture, so R does explain A. Ruled out.
3. Option C (A true, R false): This would require the wave-theory delay estimate itself to be wrong. It isn't; it is the standard calculation showing classical theory badly fails to predict instantaneous photoemission. Ruled out.
4. Option D (Both false): This would require photoemission to not actually be instantaneous, which contradicts well-established experimental observation. Ruled out.

Only option A fits: both statements are true, and the large mismatch between the wave-theory time estimate and the observed instantaneous emission is exactly why the effect is called spontaneous.

Therefore, the correct answer is Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).