Short Answer
Stopping potential is the minimum negative potential applied to the collector (or anode) in a photoelectric experiment to stop the fastest photoelectrons from reaching it. When this potential is applied, the photocurrent becomes zero because even the most energetic electrons cannot reach the anode.
Stopping potential helps measure the maximum kinetic energy of emitted electrons. It depends only on the frequency of the incident light and not on its intensity. This makes it a key concept in understanding the photoelectric effect and verifying Einstein’s photoelectric equation.
Detailed Explanation :
Stopping potential
Stopping potential is an important concept used in the study of the photoelectric effect. In a typical photoelectric experiment, light of a certain frequency is allowed to fall on a metal surface, causing electrons to be emitted. These emitted electrons travel toward a collector plate (anode), creating a current known as photocurrent. However, not all emitted electrons have the same energy. Some electrons are slow, some are medium-speed, and some are very fast. The fastest electrons carry the maximum kinetic energy.
To measure this maximum kinetic energy, a negative potential is applied to the anode. This negative potential creates an electric field that opposes the motion of the electrons trying to reach the anode. As the negative potential is gradually increased, fewer and fewer electrons are able to reach the anode, causing the photocurrent to decrease.
At a certain value of negative potential, even the fastest electrons cannot reach the anode. At this point, the photocurrent drops to zero. This minimum negative potential required to stop the most energetic electrons is called the stopping potential.
Stopping potential is usually denoted by V₀ and measured in volts. It provides a direct way to calculate the maximum kinetic energy of emitted electrons using the relation:
K.E.ₘₐₓ = eV₀
where e is the charge of an electron.
Meaning and significance of stopping potential
Stopping potential helps scientists understand the behaviour of photoelectrons and the nature of light. It gives direct evidence that the kinetic energy of electrons depends only on the frequency of incident light and not on its brightness or intensity. This was one of the key findings that classical physics could not explain.
Classical wave theory claimed that increasing the intensity of light should increase the energy of electrons. According to that theory, brighter light should produce faster electrons. But experiments using stopping potential showed the opposite. Increasing intensity only increases the number of emitted electrons, not their maximum kinetic energy. The kinetic energy remains the same for a given frequency of light.
This behaviour clearly supports Einstein’s theory that each electron absorbs energy from a single photon. The energy of each photon depends on the frequency of light, not on intensity. If a photon has energy hν, and the metal’s work function is W₀, then the maximum kinetic energy is:
K.E.ₘₐₓ = hν – W₀
To stop electrons with this kinetic energy, a stopping potential V₀ is needed such that:
eV₀ = hν – W₀
This relation perfectly matches experiments and proves the quantum nature of light.
Factors affecting stopping potential
Stopping potential depends mainly on the frequency of the incident light. Higher-frequency light (such as ultraviolet) provides more energy to electrons, which increases their maximum kinetic energy. As a result, a higher stopping potential is needed to stop them.
On the other hand, lower-frequency light (such as red or infrared) provides less energy. The electrons emitted are slower, so a smaller stopping potential is enough to stop them. If the frequency of light is below the threshold frequency for that metal, no electrons are emitted, and the stopping potential becomes zero.
Another important point is that stopping potential does not depend on the intensity of light. Whether the light is dim or bright, the stopping potential remains the same for a given frequency. This confirms that photoelectric emission depends on photon energy, not on the number of photons.
The nature of the metal also influences stopping potential because different metals have different work functions. Metals with higher work functions produce electrons with lower kinetic energy for the same frequency, resulting in lower stopping potentials.
Applications of stopping potential
Stopping potential is used for accurate measurement of the maximum kinetic energy of photoelectrons. This helps in verifying Einstein’s photoelectric equation and determining the value of Planck’s constant experimentally.
It is also used in studying the energy levels of metals, comparing different materials, and designing sensitive light-detection devices such as phototubes, photomultiplier tubes, and light sensors. In scientific research, stopping potential helps understand the interaction of electromagnetic radiation with matter and the energy distribution of emitted electrons.
Stopping potential also finds use in spectroscopy, where the energies of electrons ejected by ultraviolet or X-ray radiation are studied. This information helps in determining atomic structure and chemical composition.
Conclusion
Stopping potential is the minimum negative voltage required to stop the fastest photoelectrons from reaching the anode in a photoelectric experiment. It provides a direct measure of the maximum kinetic energy of emitted electrons and depends only on the frequency of the incident light. This concept played a major role in establishing the quantum theory of light and continues to be important in modern physics and technology.