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Question: How to derive the equation for stopping voltage of a photoelectron, i.e, \(K{E_{\max }} = |e{V_0}|\)...

How to derive the equation for stopping voltage of a photoelectron, i.e, KEmax⁡=∣eV0∣K{E_{\max }} = |e{V_0}|

Explanation

Solution

The stopping voltage (or stopping potential) alludes to the voltage distinction needed to prevent electrons from moving among plates and making a flow in the photoelectric analysis. Review that in the photoelectric test, light is coordinated onto a metal plate and if the recurrence of light is sufficiently high, electrons are launched out from the surface.

Complete answer:
These electrons at that point travel to a subsequent metal plate discovered straightforwardly across. The base measure of energy that is needed to discharge an electron from the metal surface is known as the work. The greatest active energy that the shot out electron has is given by deducting the work from the energy found in one photon.
We realize that Stopping potential is that benefit of impeding potential distinction should be applied between two plates which are only adequate to end the fiercest photograph electrons produced from the photoelectric material.
We need to compare the most extreme motor energy Kmax⁡{K_{\max }}of the photograph electron (having charge e) to the halting likely V0{V_0}.
We realize that
Electric potential energy=Potential Difference×Charge{\text{Electric potential energy}} = {\text{Potential Difference}} \times Charge
⇒U=V0×Q\Rightarrow U = {V_0} \times Q
To stop the most vigorous photo-electron
⇒U=Kmax⁡\Rightarrow U = {K_{\max }}
∴∣V0×e∣=Kmax⁡\therefore \left| {{V_0} \times e} \right| = {K_{\max }}
⇒Kmax⁡=∣eV0∣\Rightarrow {K_{\max }} = \left| {e{V_0}} \right|
Indication of extent is utilized as kinetic energy and electric potential energy are equivalent and inverse.
At the point when charge e is expressed in coulomb, the energy is determined in joules. At the point when the charge is given as rudimentary charges, the energy will be determined in electron volts eV.eV.

Note: Under the correct conditions light can be utilized to push electrons, liberating them from the outside of a strong. This cycle is known as the photoelectric effect (or photoelectric emission or photoemission), a material that can show these marvels is supposed to be photoemissive, and the launched out electrons are called photoelectrons; however, there isn't anything that would recognize them from different electrons. All electrons are indistinguishable from each other in mass, charge, spin, and magnetic moment.