Question

Photoelectric effect is the phenomenon in which (1) Photons come out of the metal when it is hit by a beam of electrons. (2) Photons come out of the nucleus of an atom under the action of an electric field. (3) Electrons come out of the metal with a constant velocity which depends on the frequency and intensity of incident light wave. (4) Electrons come out of a metal with different velocities not greater than a certain value which depends only on the frequency of the incident light wave and not on its intensity.

Short answer

Option (4) is correct because the emission of electrons depends on the frequency of the incident light and not on its intensity.

Step-by-step solution

- Understanding the Photoelectric Effect

The photoelectric effect refers to the emission of electrons from a material when light shines on it. This phenomenon is crucial in understanding the quantum nature of light and the energy it can transfer to electrons.

- Analyzing Each Option

We need to evaluate each given option to find the correct statement.

- Evaluating Option 1

Option (1) states that photons come out of the metal when it is hit by a beam of electrons. This is incorrect because the photoelectric effect specifically refers to the ejection of electrons, not photons.

- Evaluating Option 2

Option (2) says photons come out of the nucleus of an atom under the action of an electric field. This is not related to the photoelectric effect, which deals with electrons being emitted from metals when exposed to light.

- Evaluating Option 3

Option (3) states that electrons come out of the metal with a constant velocity depending on the frequency and intensity of the incident light wave. This is incorrect because the velocity of the electrons depends on the frequency of the incident light but not on its intensity.

- Evaluating Option 4

Option (4) indicates that electrons come out of a metal with different velocities not greater than a certain value which depends only on the frequency of the incident light wave and not on its intensity. This is the correct description of the photoelectric effect. The maximum kinetic energy of the emitted electrons is dependent on the frequency of the incident light and is independent of its intensity.

Key concepts

Quantum nature of light

The quantum nature of light is fundamental to understanding how the photoelectric effect works. Light, in this context, behaves both as a wave and a particle.
That means it has properties of both forms. Albert Einstein first introduced the idea that light can be considered as particles called photons.
Each photon has a specific energy related to its frequency, established by the Planck relation: \(E = h u\) where \(E\) is the energy, \(h\) is Planck's constant, and \(u\) (nu) is the frequency.

This concept helps explain why shining light on a metal surface can cause the emission of electrons (photoelectric effect).
The electrons absorb the energy of the photons, which can be enough to overcome the binding energy holding them in the metal.
Overall, the quantum nature of light allows us to explore and explain phenomena that classical wave theories of light fail to address.

Emission of electrons

The emission of electrons in the context of the photoelectric effect occurs when light hits a metal surface.
Photons in the light provide their energy to the electrons in the metal.
If a photon has enough energy, which primarily depends on its frequency, it can knock an electron out of the material.

There are a few key points to consider:

• **Threshold Frequency:** Only light with a frequency beyond a certain minimum (threshold frequency) can emit electrons.
• **Instantaneous Emission:** The emission happens as soon as the light is incident on the metal, showing an immediate effect.
• **Electron Energy:** The emitted electrons have a range of kinetic energies, with the maximum determined by the light's frequency. The relationship is given by \( K_{max} = hu - \phi \), where \(K_{max}\) is the maximum kinetic energy, \(hu\) is the energy of the photon, and \(\phi\) is the work function of the metal.

Frequency of incident light

The frequency of the incident light is a crucial factor in the photoelectric effect.
The light’s frequency must be above a certain threshold for electrons to be ejected from the metal.
This threshold frequency varies depending on the type of metal used.

Here's why frequency matters:

• **Energy Transfer:** The energy of each photon is directly tied to its frequency, as given by \(E = h u\).
• **Threshold Concept:** If the photon's energy (frequency) is below the threshold, no electrons will be emitted regardless of the light's intensity.
• **Kinetic Energy of Electrons:** Above the threshold frequency, the excess energy transferred to the electrons becomes their kinetic energy, according to \( K_{max} = hu - \phi \). Hence, with higher frequencies, the emitted electrons move faster.

The threshold frequency phenomenon underscores why blue or ultraviolet light is effective in causing the photoelectric effect, but not red light.

Intensity of light

While the frequency of light is crucial in determining whether electrons are emitted, the intensity of light impacts the number of electrons emitted.
Intensity refers to the amount of light energy hitting a surface per unit area per second.

Key points to note:

• **Photon Count:** The intensity of light is related to the number of photons hitting the surface. Higher intensity means more photons available to kick electrons out.
• **No Effect on Energy:** Although intensity increases the number of emitted electrons, it does not change the energy of individual electrons. Their maximum kinetic energy still depends on the light’s frequency.
• **Practical Implication:** In experiments, increasing light intensity leads to a higher current in photoelectric experiments while the stopping potential remains the same.

Therefore, the photoelectric effect shows a dependency on light frequency for the electron's kinetic energy and on light intensity for the electron emission rate.