Problem 25 - Master Resource Book in JEE Main Physics

Question

In the photoelectric effect, the velocity of ejected electrons depends upon the nature of the target and (a) the frequency of the incident light (b) the polarisation of the incident light (c) the time for which the light has been incident (d) the intensity of the incident light

Step-by-Step Solution

Answer

The velocity of ejected electrons depends on the frequency of the incident light (option a).

Step 1: Understanding the Photoelectric Effect

The photoelectric effect refers to the ejection of electrons from a material's surface when light is shone upon it. The kinetic energy of these ejected electrons is dependent on certain factors.

Step 2: Identifying Factors Affecting Ejected Electrons

The energy and thus the velocity of the ejected electrons are influenced by the frequency of the incident light due to their relationship via Planck's equation in the context of the photoelectric effect.

Step 3: Analyzing Each Option

(a) Frequency affects electron velocity because higher frequency light provides more energy. (b) Polarisation does not directly affect electron velocity; it affects the direction. (c) The duration of light exposure does not affect electron velocity once emission starts. (d) Intensity relates to the number of photons, not energy per photon, hence not affecting velocity.

Step 4: Conclusion on Correct Option

Given that the energy (and thus velocity) of ejected electrons is tied to the frequency of the light used, the correct answer is that the velocity depends on the frequency of the incident light.

Key Concepts

electron velocity

Electron velocity in the photoelectric effect is a fascinating concept. When electrons are ejected from a material due to this effect, their velocity is a key focus. This velocity depends on the kinetic energy they acquire upon ejection. The kinetic energy is influenced by how much energy the incoming photons from the light possess.

Simply put, higher energy photons will result in ejected electrons achieving greater velocity. This relationship helps us understand why only certain frequencies of light can cause electrons to move with particular speeds. If the photon's energy is insufficient, the electron stays bound to the material's surface.

The electron's velocity helps in practical applications. For instance, it allows determination of the stopping potential needed to halt the ejected electrons in experimental setups.

incident light frequency

Incident light frequency plays a crucial role in the photoelectric effect by determining whether electrons can be ejected at all. When light hits a material, it is not just the intensity or amount of light that matters, but also the frequency.

Frequency refers to how fast the waves of light move up and down per second. Higher frequencies mean quicker oscillations and typically correspond to blue or ultraviolet light in the spectrum.

For the photoelectric effect, a light source must have a certain minimum frequency, known as the threshold frequency, to provide sufficient energy to eject electrons from the material's surface. If the frequency is below this threshold, electrons remain unaffected no matter how intense the light becomes.

Planck's equation

Planck's equation is a fundamental principle when exploring the photoelectric effect. It elegantly links the energy of photons to their frequency and can be expressed as:

• \( E = h u \)

Here, \( E \) represents the energy of the photons, \( h \) is Planck's constant, a universal figure, and \( u \) is the frequency of the incident light.

This equation implies that the energy of each photon is directly proportional to the frequency of the light. Therefore, as the frequency increases, the photon's energy increases, too.

Planck's equation is pivotal as it helps to understand why certain frequencies are necessary to achieve the photoelectric effect, providing the energy needed to release electrons from the material.

ejected electrons

Ejected electrons are at the heart of understanding the photoelectric effect. When light of a suitable frequency hits a material, electrons gain enough energy to break free from the atomic bind, resulting in what are known as ejected electrons.

Notably, the ejected electrons' kinetic energy depends on the energy they receive from the incoming photons. If the energy surpasses the work function, or the minimum required energy to liberate an electron, the surplus is converted into kinetic energy, enhancing their velocity.

Additionally, the concept of ejected electrons plays a role in modern devices. For example, solar panels utilize this principle to convert light energy into electrical energy by harnessing the movement of these electrons.