# Photoelectric effect

### Emission of electrons

At room temperature the free electrons move randomly within the conductor, but they don’t leave the surface of the conductor due to attraction of positive charges. Some external energy is required to emit electrons from a metal surface.The minimum energy required to emit the electrons which are just on the surface of the conductor is called the work function.The work function(W) is the property of the metallic surface.
The energy required to liberate an electron from metal surface may arise from various source such as light,heat, electric field etc. Depending on the nature of source of energy, the following emissions are possible.
 1 Thermionic emission When a metal is heated,the free electrons in the metal absorb the heat energy and can overcome the surface barrier.Consequently,the free electrons are emitted from the metal surface.This process is known as thermionic emission.The electrons so emitted are known as thermions. 2 Field emission When a conductor is put under strong electric field the free electrons on it experience an electric force in the opposite direction of field. Beyond a certain limit electrons start coming out of the metal surface. Emission from a metal surface by this method is called the field emission. 3 Secondary emission The emission of electrons from a metal surface by the bombardment of high speed electrons or other particle is known as secondary emission. 4 Photoelectric emission The emission of free electrons from a metal surface by falling light which has an energy greater than the work function of the metal is called photoelectric emission. The electrons emitted so are called photoelectrons.

### Photoelectric effect

• The phenomenon of emission of the electrons from metal surface exposed to light energy of suitable frequency is called as Photoelectric Effect.
• The electrons emitted by the metal surface are called as photoelectrons.
• The current constituted by photoelectrons is known as photoelectric current.
• For photoemission to take place, energy of incident light photons should be greater than or equal to the work function of the metal.
E ≥ W
hν ≥ W
Where,
E = energy of incident light photons
ν = frequency of incident light photons
W =  work function of the metal
h is plank’s constant

### Study of photoelectric effect

The given setup (as shown in figure 1) is used to study the photoelectric effect experimentally.
figure 1
In an evacuated glass tube, two zinc plates A and C are enclosed. Plates A acts asanode and C acts as cathode. Two plates are connected to a battery B and ammeter (μA). If the radiation is incident on the plate C through a quartz window W, electrons are emitted out of plate and current flows in the circuit. The plate A can be maintained at desired potential (+ve or -ve) with respect to plate C.

• When light of suitable frequency falls on the Cathode, photoelectrons are emitted. These electrons get accelerated towards the anode which is at positive potential w.r.t. the cathode and constitute the current called photoelectric current.
• For fixed frequency and intensity of incident light,this photoelectric current increases with the increase in applied positive potential of anode.
• When all the photoelectrons emitted by cathode reach the anode, the photoelectric current attains maximum value known as saturation current.
• This saturation current will not increase with the increase in positive potential of anode.
• Now the potential of anode is decreased such that it attains negative potential with reference to cathode.
• The negative potential applied to anode is increased to a certain value Vo, for which no photoelectrons reach the anode. That is,at this potential ,photoelectric current is zero.
• The minimum negative potential Vo, applied to anode for which photoelectric current becomes zero is called cut off potential or stopping potential.
• At this stage,the maximum kinetic energy (1/2mv2max) of photoelectron must be equal to eVo
i.e.
• The variation of photoelectric current with varying potential of anode in shown in figure 2.
figure 2

### 2. Effect of Intensity of incident light on Photoelectric Current

• Let a constant potential difference be applied across the anode and the cathode.
• When ultraviolet light is incident on the cathode C, photoelectrons are emitted which are collected by anode. The photoelectric current (Ip) constituted by these photoelectrons is measured with the micro-ammeter (µA).
• As the intensity of the incident light increases (keeping the frequency constant),more and more photoelectrons are emitted by the cathode and hence photoelectric current increases linearly i.e. Ip ∝ Ith , where Ith is the threshold current.The variation of photoelectric current with the intensity of incident light is shown in Figure 3.
• figure 3
• If the intensity of the incident light is increased (say from I1 to I2) and frequency is kept same then the variation of the photo-electric current with the potential of the anode is shown in Figure 4.
• figure 4
Thus, we find that intensity of incident light does not effect the stopping potential.

### 3. Effect of frequency of incident light on stopping potential

• The intensity of incident light is kept constant but the frequency is changed so that in each case the saturation current is exactly the same.
• Now for a given frequency (ν1) of the incident light, the positive potential at anode is decreased to zero. It is found that the photoelectric current decreases.
• Now, the anode is given negative potential which is increased till the photoelectric current becomes zero. Let this value of negative potential be V01.
• The experiment is repeated with the incident light of frequency ν2 > ν1. It is found that now the stopping potential is higher than V01 as shown in figure 5. Let it be V02 .
• It is found that the value of stopping potential depends upon the frequency of the incident light.
figure 5
Threshold frequency(νo)
• The minimum frequency below which photoelectric emission is not possible is called threshold frequency or cutoff frequency.
• The value of threshold frequency depends upon the nature of the substance emitting the photo-electrons.
Laws of Photoelectric Emission
1. For a given material, there is a certain minimum (energy) frequency, called threshold frequency, below which the emission of photoelectrons stops completely, no matter how high is the intensity of incident light.
2. The photoemission is an instantaneous process. After the radiation strikes the metal surface, it just takes 10-9 s for the ejection of photoelectrons.
3. The maximum kinetic energy of the photo-electrons is found to increase with increase in the frequency of incident light, provided the frequency exceeds the threshold limit. The maximum kinetic energy is independent of the intensity of light.
4. For a light of any given frequency, photoelectric current is directly proportional to the intensity of light, provided the frequency is above the threshold frequency.

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