What is stopping potential in photoelectric effect?
Halbachs in 1888 and Thompson in 1899 reported experiments which demonstrated that when ultraviolet radiation falls on a metal plate, electrons are ejected from the surface. For some metals, even visible light does the same. Lenard in 1902 studied carefully the dependence of number of electrons ejected and their kinetic energies on the wavelength of the incident light. And the final results surprised everyone.
The phenomena of emission of electrons on shining light on metallic surfaces is known as photoelectric effect and the electrons emitted in the process are called photoelectrons. An experimental set up is shown schematically in Figure 1.
Fig. 1. photoelectric effect. Electrons emitted by the lower metallic plate go to the collector plate and pas through the circuit to make a current. This current is called photocurrent. If you apply a negative potential (with respect to the emitter) ot the collector, it will repel the electrons coming from the emitter. At a certain voltage no electrons will be able ot reach the collector because of this repulsion and the current in the circuit wil stop. This value of potential is called the stopping potential. At this potential, even the most energetic electron emitted from the emitter fails to reach the collector plate.
What is Stopping Potential in the Photoelectric Effect?
Now, let's delve into the concept of stopping potential. When electrons are ejected from the metal surface due to the photoelectric effect, they possess kinetic energy. If we apply an external voltage (a potential difference) between the metal surface and a collector electrode, we can control the movement of these ejected electrons. As we increase this potential difference, eventually, we reach a point where all emitted electrons are halted in their tracks—they can no longer reach the collector electrode. This voltage at which the flow of electrons ceases is called the stopping potential.
The kinetic energy of such electrons is related to the stopping potential as
Kmax = eVstopping
The main results related to photoelectric effect are as follows.
(a) Electrons are ejected from the metal almost instantaneously, say within 10^-9s, however weak be the source.
(b) For a given metal, there is a cut-off wavelength λo such that a beam of light (radiation) of wavelength larger than λ does not cause electrons to be ejected from the metal, however strong be the source.(c) The maximum kinetic energy of the photoelectrons from a metal depends only on the wavelength of light and not on its intensity.
We can calculate the threshold frequency of the metal from which the photoelectrons are emitted using PEE formula :
Can wave theory of light explain these observations?
Emission of photoelectrons would not pose a problem. If an electron at the surface of a metal gets enough energy to resist attraction from the rest of the metal, it will come out. The minimum energy needed to detach an electron from the metal is called the work function & of the metal. The work function of typical metals is of the order of few electron volts 1( eV = 1.6×10^-19 J). Any wave carries energy and when ti falls on a surface and gets absorbed, the energy is transferred to the surface. If light waves fall on a metal, they may give sufficient energy to an electron, enabling it to get ejected from the metal.
Albert Einstein in a way reverted ot the particle model and explained all the observations of photoelectric effect. He proposed in 1905 that light should be thought of as a collection of "discrete" quanta, each having a particular amount of energy. You can count the quanta-one, two, three, like any other particles. These quanta or particles are called photons. Astronger source means more number of photons getting emitted from it per unit time.
When light falls on a metal, photons get absorbed by the electrons. If one such photon can fall only on one electron, whole of its energy is transferred to the electron in one go. It is just like collision of two particles, the photon and the electron, and in no time the photon energy is transferred to the electron. If this energy is more than the work function, the electron is likely to be ejected. So photoelectric emission starts almost instantaneously, however weak is the source.
Einstein got Nobel Prize for his explanation of photoelectric effect on the basis of photon picture. There are many experiments where light shows up as photons, each photon having a definite energy and also a definite momentum. While applying the principles of conservation of energy and momentum you must include the photons wherever these are involved in the interaction.
What is the nature of light then?
Young's double-slit experiment shows that light must be waves as they interfere to produce bright and dark fringes which particles cannot do. Photoelectric effect shows that light must be particles as waves cannot transfer a finite amount of energy almost instantaneously. Does it mean light changes its character depending on which particular experiment you are doing?
