With reference to the observations in photo-electric effect, identify the correct statements from below :
(A) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light.
(B) The value of saturation current increases on moving the source of light away from the metal surface.
(C) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light.
(D) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves.
(E) Existence of threshold wavelength can not be explained by wave nature of light/ electromagnetic waves.
Choose the correct answer from the options given below :

Solution

Physics sir · 2 steps

Frequency decides how fast each electron leaves, intensity decides how many leave. Test every line with that.

1. Einstein's equation. One photon gives all its energy hν to one electron. The electron spends the work function φ₀ to escape, and the rest becomes kinetic energy.

   1/2mvₘₐₓ² = hν - φ₀ ⇒ vₘₐₓ² = 2h/m ν - 2φ₀/m

   Statement	What really happens	Verdict
   (A)	vₘₐₓ² against ν is a straight line with slope 2h/m. It is linear, though not proportional.	Correct
   (B)	Moving the source away lowers the intensity, so fewer photons arrive per second. Saturation current decreases.	Wrong
   (C)	Lower LED power means fewer photons of the same frequency. Kₘₐₓ depends only on ν, so it stays the same.	Wrong
   (D)	One photon hits one electron and gives its energy at once. That is exactly how the particle picture explains instant emission.	Wrong
   (E)	In the wave picture, any wavelength could build up enough energy given enough time. So it cannot explain a threshold.	Correct

2. So. Only (A) and (E) are correct, which is option (b).

The idea to keep. In photoelectric questions, frequency controls the energy per electron (Kₘₐₓ, stopping potential). Intensity or power controls the number of electrons (the current). The particle picture explains every observation.

Answer from the NTA final answer key. Solution by PrepWiser.