Photoelectric effect in detail

Photoelectric effect

 It is the phenomena of emission of electron from a metal surface when the radiation of suitable frequency fall on them. The emitted electron are called Photo electron . And the current so produced is called Photoelectric effect.
For example:- alkali metal EMIT the photoelectron when visible light fall on them. while other metal like zinc, emit Photon electrons, when ultraviolet radiation fall on them.

Work function:- It is minimum amount of energy required by an  electron to just escape from the metal surface.
Its value depend upon 1. nature of metal  2. condition of its surface generally is measured in electron volt.

Laws of Photoelectric effect

1:- For a given metal &  frequency of incident radiation, the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
2:- For a given metal, if the frequency of incident radiation is less than a particular frequency then no photoelectrons emitted this frequency is called Threshold frequency. for a given metal, its value is constant but for different metal its value is different.
3:- Above the threshold frequency. Then maximum kinetic energy of emitted photoelectrons depend upon frequency of incident radiation it does not depend upon their intensity.
4:- It is an instantaneous process. the time lag between incidence of radiation and emission of photoelectron is very small and less than 10 raise to power -9.

Einstein equation of Photoelectric effect

 when a photon of energy fall on a metal surface, its energy is absorbed by free electron of the metal surface one part of this energy is used in liberting the electron from metal surface which is equal to the work function of the metal and remaining part of the energy appear in the form of kinetic energy of photoelectrons. thus
 energy of photon = work function + kinetic energy of photoelectron.
Where m and v be the  mass and velocity of the photo electron.
 Now we consider a photon of frequency v*. Where v* = threshold frequency. this photon can only eject the photoelectron.
                  hv-hv*=1/2mv2
       or h(v-v*)=1/2mv2

Explanation of laws of photoelectric emission 

1:- When a photon fall on a metal surface, energy is absorbed by the free electron of metal surface. one part of this energy is used in librating the electron from the metal surface and remaining part appear in the form of kinetic energy of photoelectron. Thus as the number of a photon or intensity of incident radiation increases, the number of a photoelectron emitted per second also increase.

2:- If v<v* then kinetic energy of photoelectron become negative. which is not possible no photo electron is emitted. In this way if the frequency of incident radiation is less than threshold frequency. then no photoelectrons emitted.
3:- As h is  constant. for a given metal v* is constant. So maximum kinetic energy of photoelectron depend upon frequency of incident radiation.
 As the intensity of incident radiation increase the number of incident Photon falling per second increases. but the energy hv of the a photon remains same, so the kinetic energy of photoelectron remain same.
4:-  As the photoelectron are emitted due to the collision between photon and electron so it is an instantaneous process.

Experimental study of Photoelectric effect-

 The experiment arrangement of to study the laws of photo electric effect is shown in figure. It consists of a glass tube in which vacuum is created. A quartz window is fitted with it. Two electrodes C and A are sealed in it. C is a photo sensitive cathode and A is a collecting anode. the anode A can be kept at desired positive or negative potential with respect to cathode. the current is measured by milliameter and potential difference is measured by voltmeter.

                Circuit of photoelectric effect

1:-Effect of intensity

 The anode A is kept at positive potential with respect to cathode. now that radiation of  fixed frequency (greater than threshold frequency) are allowed to fall on the cathode. The cathode emitts the electron which reach at anode and current start to flow. we increase the intensity of incident radiation in steps and corresponding current is noted. A graph is plotted between intensity and current as shown in figure. from figure it is clear that the current is directly proportional to intensity of the incident radiation or we can say that the number of photoelectron emitted per second is directly proportional to the intensity.

2:- Effect of potential of anode on photoelectric current

 We allowed to fall the radiation of constant frequency and intensity on the cathode the positive potential of anode is increased in steps and not the corresponding current. Initially the current increase and finally become maximum called the saturation current. At this state all photoelectron emitted by cathode reach at anode directly. if the anode potential is further increase the value of a current remains same is maximum
 Now we give negative potential to the anode we see that the value of a photoelectric current  decrease because the photoelectron emitted by cathode are repelled by anode and only energetic photoelectrons reach at anode. As we increase the negative potential of anode the value of a current is decreases. at a certain negative potential it becomes zero. This potential is called stopping potential or cutoff potential. It is defined as the minimum negative potential given to anode with respect to the cathode at which photoelectric current becomes zero is called stopping potential.
 It is clear that ev*=half mVsquaremax the Vmax =maximum velocity of electron.
Now we allowed the fall the radiation of a high intensity i1 and i3 but same frequency v. we see that the saturation current is more and more but stopping potential is same. Thus it is clear that
1:- All photoelectrons does not have same kinetic energy.
2:-  For a given frequency the stopping potential for maximum kinetic energy of photoelectron does not depend upon the intensity of incident radiation.

Effect of frequency of incident radiations

 Now we allowed to fall the radiation intensity and frequency. we see that the saturation current is same for stopping potential are more negative. It is clear that the saturation current does not depend upon the frequency, while stopping potential depend upon the frequency of incident radiation as stopping potential is the measurement of a maximum kinetic energy of photoelectron.so maximum Kinetic energy of photoelectron depend upon frequency of incident radiation.
 If we draw a graph between frequency of incident radiation and stopping potential we get a straight line it is clear that for a particular frequency , the stopping potential is zero or we can say that the kinetic energy of photoelectron is zero. the frequency is called Threshold frequency.
If the frequency of incident radiation is less than a particular frequency then no photoelectrons emitted.
 From Einstein equation Photoelectric effect