Einstein’s Photo Electric Equation and Applications

Einstein’s photo electric equation explains photo electric effect and its further properties successfully. Wave theory of light has failed to explain concept of photo electric effect. Hence plank’s quantum concept is taken into consideration to explain this property. According to this property light is emitted by a source not continuously but discreetly in the form of wave packets called quanta.

When the light strikes a surface, number of photons are striking the surface. More the intensity, more the number of photons. Each photon will have certain energy, basing on the frequency of incident light. Each photon will pass all its energy to a electron on the surface of the metal. They electron is associated with the metal and it needs some energy to release itself from the valency orbit.

When the energy given by the photon is sufficient to release the electron from the metal surface, the electrons are emitted from the metal surface. The number of the electrons emitted from the metal surface depends on the number of the photons that are striking the metal surface. If the intensity of the light is more, there is availability of more number of photons and hence more photo electric current is emitted. That is the reason why intensity and the photo electric current are proportional to each other.

The electrons in the valency orbit need a minimum energy to get released itself from the metal surface. The incident frequency shall be able to give at least this much of energy to release the electron. This minimum frequency is called threshold frequency. This minimum required energy for the release of the electron is called work function. The energy given by the photon is first used to release the electron from the metal surface. If there is any further energy that is given by the photon, the electron uses that energy and moves with the kinetic energy.

According to photo electric equation, the entire energy supplied by the photon is used first to release the electron from the metal surface and then to move the electron from the cathode towards the anode. First the energy has to be supplied to release the electron from the metal surface and only when there is an extra energy it can be used to move the electron. Supplying of energy equal to work function is the precondition for the emission of photo electrons.

We can derive the equation for the maximum kinetic energy of by a electron as shown below.

If intensity of light is more, more photons are available and each photon will go and give its energy to the electrons. And hence there is more electrons emitted and hence there will be more photo electric current. The number of the electrons emitted is independent of frequency. But whether the current is able to be emitted are not is a dependent of frequency. The incident frequency and its corresponding energy shall be sufficient to release the electron from the metal surface. That is the energy of the frequency shall be more than the work function for the photo electric effect to happen.

Application

A monochromatic radiation incident on a metal surface of work function W, maximum kinetic energy of the emitted electrons is K. If the frequency of the incident radiation is n times the initial frequency and then how its kinetic energy will be affected?

We can write photo electric equation to solve this problem. We know that the total energy of the photon is equal to the sum of work function and the kinetic energy of the electron. Basing on that, we can write the equation for the kinetic energy in both the cases with their respective frequencies as shown below. Simply buy solving this to equations we can get the answer.