an increase in intensity of the incident light does not change the maximum velocity of the emitted photo-electron. why?

The phenomenon you're referring to is rooted in the principles of the photoelectric effect, which was famously explained by Albert Einstein. To understand why an increase in the intensity of incident light does not affect the maximum velocity of emitted photoelectrons, we need to delve into the relationship between light, energy, and electrons.

The Basics of the Photoelectric Effect

In the photoelectric effect, when light shines on a metal surface, it can cause electrons to be emitted from that surface. However, not all light can achieve this; it must have a certain minimum frequency, known as the threshold frequency, to provide enough energy to overcome the work function of the metal—the energy required to release an electron from the surface.

Energy of Photons

Light can be thought of as being made up of particles called photons. Each photon carries a specific amount of energy, which is determined by its frequency (or wavelength) according to the equation:

E = hf

Here, E is the energy of the photon, h is Planck's constant, and f is the frequency of the light. When light of sufficient frequency strikes the metal, photons transfer their energy to electrons.

Intensity vs. Maximum Velocity

Now, let’s clarify the role of intensity. The intensity of light is related to the number of photons hitting a surface per unit time. So, increasing the intensity means more photons are striking the surface, but it does not change the energy of each individual photon. Therefore, while more electrons can be emitted with higher intensity (because more photons are available to interact with electrons), the maximum kinetic energy of the emitted electrons remains unchanged.

The maximum kinetic energy of the emitted photoelectrons can be expressed by the equation:

K.E. = hf - φ

In this equation, K.E. is the maximum kinetic energy of the emitted electrons, hf is the energy of the incoming photons, and φ is the work function of the metal. As you can see, the maximum kinetic energy depends solely on the frequency of the incident light and the work function, not on the intensity.

Illustrative Example

Imagine you’re throwing balls at a target. If you throw one ball with a lot of force (high frequency), it can break through a barrier (the work function) and hit the target with great speed (high kinetic energy). If you throw many balls (increased intensity) but they are soft and light (low frequency), they might not break through the barrier at all, or if they do, they won’t hit the target with much speed. The energy of each ball (photon) is what determines how fast it can go, not how many you throw.

Summarizing Key Points

• The energy of a photon is determined by its frequency, not its intensity.
• Intensity increases the number of emitted electrons but does not affect their maximum kinetic energy.
• The maximum velocity of photoelectrons is dictated by the energy of the individual photons and the work function of the material.

In essence, while increasing the intensity of light can lead to more electrons being emitted, it does not influence the maximum speed at which any individual electron can be emitted. This is a fundamental aspect of the photoelectric effect and highlights the distinct roles of energy and intensity in photon interactions with matter.