Define –cut –off frequency work function an stopping potential with reference to photo electric effect.

The photoelectric effect is a fascinating phenomenon that illustrates the particle nature of light and its interaction with matter. To understand the concepts of cut-off frequency, work function, and stopping potential, let’s break them down one by one.

Cut-off Frequency

The cut-off frequency, often denoted as \( f_0 \), is the minimum frequency of incident light required to eject electrons from a material's surface. If the frequency of the incoming light is below this threshold, no electrons will be emitted, regardless of the light's intensity. This is a key aspect of the photoelectric effect, as it demonstrates that light behaves not just as a wave but also as a stream of particles called photons.

Understanding the Relationship

The cut-off frequency is directly related to the work function of the material, which we will discuss next. The relationship can be expressed mathematically using the equation:

• Energy of a photon: \( E = hf \)
• Work function: \( \phi = hf_0 \)

Here, \( h \) is Planck's constant, and \( E \) is the energy of the photon. When the frequency \( f \) of the incident light is equal to or greater than \( f_0 \), the energy of the photons is sufficient to overcome the work function, allowing electrons to be emitted.

Work Function

The work function, represented by \( \phi \), is the minimum energy required to remove an electron from the surface of a material. Each material has a unique work function, which determines its cut-off frequency. For example, if a metal has a work function of 4.5 eV, then the corresponding cut-off frequency can be calculated using the equation:

Cut-off frequency: \( f_0 = \frac{\phi}{h} \)

This means that if the energy of the incoming photons (calculated from their frequency) is less than the work function, no electrons will be emitted. This concept is crucial in understanding why different materials respond differently to light.

Stopping Potential

The stopping potential, denoted as \( V_s \), is the voltage needed to stop the most energetic photoelectrons emitted from a surface when exposed to light. When light of sufficient frequency strikes a material, it causes electrons to be emitted with varying kinetic energies. The stopping potential is a measure of the maximum kinetic energy of these emitted electrons, which can be expressed as:

Kinetic Energy: \( KE = eV_s \)

Where \( e \) is the charge of an electron. The stopping potential can be determined experimentally by applying a reverse voltage until the current of emitted electrons drops to zero. This gives us insight into the energy dynamics of the photoelectric effect.

Connecting the Concepts

To summarize, the cut-off frequency is the threshold frequency needed for electron emission, the work function is the energy barrier that must be overcome, and the stopping potential is the voltage required to halt the emitted electrons. Together, these concepts illustrate the intricate relationship between light and matter, showcasing the quantum nature of energy transfer.

Understanding these principles not only deepens your grasp of the photoelectric effect but also lays the groundwork for exploring more advanced topics in quantum mechanics and modern physics.