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To understand the effect of frequency on the photoelectric effect, we need to revise some basic related terminology. These are:

  1. Threshold frequency- It is the minimum frequency required to remove an electron from the surface of the metal. [V0]
  2. Work function /potential- the minimum energy required to emit an electron on the surface of a metal. [W]
  3. Cut off potential/Stopping Potential-It is the potential required for stooping electrons from leaving the surface when the work potential of the metal is lower than the incident light.
  4. Kinetic energy- the energy that a particle has owing to its state of motion [KE]

Another important equation to remember is E= hv, where E stands for the energy of a photon, h is Planck’s constant, and v is the frequency. This equation was given by Max Planck.

Effect of Frequency on Photoelectric Effect

If we take a constant intensity of incident light and make variations in the frequency of incident light, we observe that it has a linear effect on the cut-off potential/stopping potential of a given metal. The result is that the frequency of incident light is linearly /directly proportional to the stopping potential of the metal. Another effect is that the kinetic energy of electrons is also linearly proportional to the incident light Incident frequency should be higher than the threshold frequency of the metal for the photoelectric effect to happen. Upon increasing the frequency of incident light frequency, electrons will be ejected with higher kinetic energy. If the frequency of incident light is lower than the threshold frequency of the metal photoelectric effect will not take place.

Photoelectric Equation by Einstein

According to Einstein, the inelastic collision of a photon with electrons results in the absorption of a photon by an electron completely or partially. The resulting energy is used in the following ways:

  1. To free the electron from the surface of the metal.
  2. To provide kinetic energy for ejected photoelectrons.

Einstein explained the photoelectric effect based upon Planck’s equation E=hv. Electrons that are emitted from underneath the metal lose some amount of kinetic energy in the collision process, however surface electrons contain all kinetic energy from the photon. This can be represented through the following equations;

   

                                  E =KE+ W

                          

                                  hv=KE+W

                           

                                  KE =hv-W

The threshold frequency is the point wherein V0 electrons have started getting ejected and have no considerable Kinetic Energy. There is no photoelectric effect below threshold frequency therefore the energy of the photon would be equal to the fork function at threshold frequency. This is represented by;

                                     

                              W= hvo

                 

                 KE = ½ Mv^2= hV – hV0= h[V-VO]

Then stopping potential becomes =½ mv^2. This shows that Einstein has used the particle nature of light to explain the photoelectric effect.

Characteristics of Photoelectric Effect

The photoelectric effect is an immediate process, that is there is no time lag between the higher frequency light striking the metal and electrons being emitted from it. The effect can take place only if the incident light has a frequency higher than the threshold frequency of the metal on which the light is striking. The intensity of the radiation of incident light does not affect the kinetic energy at the surface on which the light strikes.

Practical Applications of Photoelectric effect

The photoelectric effect has many applications in day-to-day life. Earlier televisions used the effect in video camera tubes. Devices that enable night vision are based on this principle. The burglar alarms and light sensors are also based on this principle. One of the most important applications is solar panels that convert light energy into electricity. Recently nuclear processes are also being studied based on the photoelectric effect.

Conclusion

Experimentation has repeatedly proven that the photoelectric effect and the frequency of fixed intensity of incident light variation have a linear variation effect. This means that the photoelectric effect of a metal increases with an increase in the frequency of incident light. Einstein worked on the E=hv equation given by Planck and proved this linear effect using mathematical equations. This helped in proving that light has a particle nature and small packers of energy called quantum. The various practical applications of this effect include night vision devices, burglar alarms, solar panels, light sensors, etc.