What is Stopping Potential and Its Formula?

The term “stopping potential” refers to the minimum electric potential that needs to be applied to a charged particle to completely halt its motion. In other words, it is the electric potential that can counteract the kinetic energy of the particle, bringing it to a complete stop.

For electrons, stopping potential helps us to understand the photoelectric effect, where light incident on a metal surface causes the emission of electrons.

The stopping potential formula (Vs) is given by:

Vs = (hf – ϕ) / e

where:

  • ( h ) is Planck’s constant (6.626 x 10-34 J·s)
  • (Vs) is the stopping potential,
  • ( f ) is the frequency of incident light (in Hz)
  • ( ϕ ) is the work function of the metal (in eV)
  • ( e ) is the elementary charge (1.602 x 10-19 C)

Additionally, the stopping potential in the context of the photoelectric effect is the voltage that needs to be applied to stop the emission of electrons from a metal surface when illuminated by light. The stopping potential (Vs) is related to the frequency of the incident light (f) and the work function of the metal (ϕ) by the equation:

This formula expresses the balance between the energy provided by the incident light (first term) and the energy needed to overcome the work function of the metal (second term). When the stopping potential is applied, it counteracts the kinetic energy of the emitted electrons, preventing them from reaching the collector plate in a photoelectric setup.

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Factors Affecting Stopping Potential

Several factors influence the value of stopping potential. Understanding these factors is crucial for studying various phenomena and practical applications. Let’s take a closer look at them:

1. Frequency of Incident Light

The frequency of the incident light has a direct impact on the energy carried by photons. Higher frequencies result in more energetic photons, which, in turn, possess greater kinetic energy. Consequently, higher-frequency light requires a higher stopping potential to halt the emitted electrons.

2. Work Function of the Metal

The work function (ϕ) of the metal refers to the minimum energy required to remove an electron from its surface. Metals with higher work functions demand greater stopping potentials to overcome the stronger binding forces holding the electrons within the material.

3. Charge of the Particle

The charge of the particle experiencing the electric field also influences the stopping potential. Heavier particles, such as ions, require different calculations than electrons due to their differing masses and charges.

4. Intensity of Incident Light

The intensity of the incident light affects the number of photons striking the metal surface. However, it does not directly impact the stopping potential, as it only alters the rate of electron emission, not the kinetic energy of individual electrons.

5. Nature of the Electric Field

The type of electric field used to stop the charged particles is a critical factor. Uniform electric fields are often utilized, but non-uniform fields can also play a role in certain experiments.

6. Temperature

At higher temperatures, the kinetic energy of the electrons within the metal also increases. As a result, the stopping potential must be adjusted accordingly.

The Photoelectric Effect: A Key Application of Stopping Potential

The photoelectric effect, first explained by Albert Einstein, is one of the fundamental phenomena that demonstrate the significance of stopping potential. The effect involves the emission of electrons from a metal surface when illuminated by light of sufficient frequency.

To better understand this concept, we will briefly see how the photoelectric effect works:

  1. Incident Light: When light of a specific frequency shines on a metal surface, it interacts with the electrons present in the metal.
  2. Emission of Electrons: If the frequency of the incident light is equal to or greater than the metal’s work function (ϕ), the electrons gain enough energy to break free from the metal’s surface.
  3. Formation of Photoelectrons: These released electrons are referred to as photoelectrons and carry the excess energy in the form of kinetic energy.
  4. Electric Field: An electric field opposes the motion of these photoelectrons and eventually brings them to a stop.
  5. Measuring Stopping Potential: By measuring the voltage required to bring the photoelectrons to a stop (stopping potential), scientists can calculate the kinetic energy of the emitted electrons.
  6. Einstein’s Explanation: Albert Einstein’s explanation of the photoelectric effect earned him the Nobel Prize in Physics in 1921. He proposed that light can be thought of as a stream of discrete particles, known as photons, each carrying a specific amount of energy.

Calculating Stopping Potential: Step-by-Step Guide

To calculate the stopping potential, follow these steps:

  1. Identify the Frequency: Determine the frequency (f) of the incident light by using appropriate instruments.
  2. Measure the Work Function: Find the work function (ϕ) of the metal from reliable sources or conduct experiments to determine it.
  3. Use the Formula: Plug the values of Planck’s constant (h), frequency (f), work function (ϕ), and elementary charge (e) into the stopping potential formula.
  4. Calculate Stopping Potential: Perform the calculations using the formula (Vs = (h.f – ϕ) / e) to obtain the stopping potential in volts (V).

FAQs

  1. Q: Can stopping potential be negative?
    A: Yes, stopping potential can be negative, especially when the kinetic energy of the emitted electrons exceeds the energy of the incident photons.
  2. Q: How does stopping potential affect the intensity of emitted electrons?
    A: Stopping potential does not affect the intensity of emitted electrons. It only determines the maximum kinetic energy they can possess.
  3. Q: What happens if the frequency of incident light is too low?
    A: If the frequency of incident light is below the threshold frequency, no electrons will be emitted, regardless of the intensity of the light.
  4. Q: Can different metals have the same stopping potential for the same incident light?
    A: No, different metals with varying work functions will require different stopping potentials for the same incident light.
  5. Q: How is stopping potential used practically?
    A: Stopping potential finds applications in various fields, including photodetectors, solar panels, and electronic sensors.
  6. Q: What units are used for stopping potential?
    A: Stopping potential is typically measured in volts (V).

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