When light is incident an metallic surface, the maximum kinetic energy of emitted photo-electron depends on :

Question

Accepted Answer

The correct answer is Option 3: Frequency of incident light.

1. **Explanation for Option 3 (Correct Answer):**
   The maximum kinetic energy of emitted photo-electrons is determined by the frequency of the incident light due to the photoelectric effect. According to Einstein's photoelectric equation, the kinetic energy (K.E.) of the emitted photo-electrons is given by:

$$
   K.E. = h \nu - \phi
   $$

where $ h $ is Planck's constant, $ \nu $ is the frequency of the incident light, and $ \phi $ is the work function of the metal. This equation shows that the kinetic energy of the photo-electrons is directly proportional to the frequency of the incident light, minus the work function of the metal. Therefore, higher frequency light results in higher kinetic energy of the emitted electrons, assuming the frequency is above the threshold frequency for the metal.

2. **Explanation for why other options are incorrect:**

- **Option 1: Velocity of incident light**
     The velocity of light in a vacuum is a constant (approximately $ 3 \times 10^8 $ m/s) and does not vary with different light sources. Therefore, it does not affect the kinetic energy of the emitted photo-electrons. The photoelectric effect is dependent on the frequency of the light, not its velocity.

- **Option 2: Intensity of incident light**
     The intensity of light refers to the number of photons striking the surface per unit time. While increasing the intensity increases the number of emitted photo-electrons, it does not affect their maximum kinetic energy. The kinetic energy is solely dependent on the frequency of the light, not its intensity.

- **Option 4: The time interval for which light is incident on metal**
     The duration for which light is incident on the metal surface affects the total number of photo-electrons emitted but does not influence their maximum kinetic energy. The kinetic energy is determined by the frequency of the incident light, irrespective of how long the light is shone on the metal.

In conclusion, the maximum kinetic energy of emitted photo-electrons is dependent on the frequency of the incident light, making Option 3 the correct answer.