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

The given assertion and reason require us to analyze the photoelectric effect and its explanation through the wave theory of light.

• Assertion (A): Photoelectric effect is a spontaneous phenomenon.
  • The photoelectric effect refers to the emission of electrons from a metal surface when it is exposed to light of a certain frequency or higher.
  • This effect is indeed spontaneous because electrons are emitted almost instantaneously as light of sufficient energy strikes the metal surface.
• 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.
  • The wave theory of light suggested that light energy is spread over the wavefront. Thus, it would require a prolonged exposure to accumulate enough energy to eject an electron, which contradicts the instantaneous nature of the observed photoelectric effect.
  • This discrepancy between wave theory and experimental observations led to the proposal of the quantum theory of light, where light comprises particles (photons) with energy directly proportional to their frequency.

Conclusion: Both Assertion (A) and Reason (R) are true. The assertion correctly states the spontaneous nature of the photoelectric effect, and the reason explains why the wave theory of light could not account for this phenomenon, leading to the development of quantum theory. Thus, Reason (R) is indeed the correct explanation of the Assertion (A).

Answer 2

Think about this from the perspective of what a wave picture of light predicts for energy delivery, then compare it with what is actually seen at a metal surface.

In the wave picture, the energy carried by light is spread evenly across the advancing wavefront, so an electron sitting on a metal surface receives only a small trickle of energy at a time. To be freed, it needs to build up enough energy to exceed the metal's work function.

Using typical laboratory light intensities and the tiny area over which a single electron can effectively collect energy, this trickle-based buildup works out to take an extremely long time, on the order of hours or even days, before a single electron would gather enough energy to escape.

Experimentally, though, electrons are seen leaving the metal surface as soon as light of sufficiently high frequency strikes it, with no measurable time lag. This is the spontaneous character referred to in the assertion.

Because the wave-theory time estimate is enormously longer than the observed near-zero delay, the wave picture cannot account for what is seen. The only way to explain a delay-free ejection is if the electron receives all the energy it needs in one go, from a single quantum of radiation, rather than gradually over time.

So both statements hold up: emission genuinely is spontaneous, and the wave-theory time-lag calculation genuinely is what fails to explain that spontaneity, which is precisely why the reason correctly explains the assertion.

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