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Physics-12 Complete Syllabus Course


Chapter 18 - Photon

Defination:

1. Photon: It is the type of elementary particle having zero rest mass and moving with the speed of light in vacuum.

2. Photoelectric effect: The emmission or rejection of electron from metallic surface when suitable frequency of incident light falls upon it, called photoelectric effect.
The electron which are emitted by this process is called photoelectron.
Some important terms related to photoelectric effect are:

i. Threshold frequency: The minimum frequency of incident radiation which is required to just emitt the electron from metallic surface is called threshold frequency. It is denoted by

ii. Threshold wavelength: The maximum wavelength of incident radiation which is required to just emitt the electron from metallic surface is called threshold wavelength. It is denoted by

iii. Work function: The minimum amount of energy which is required to just emitt the electron from metallic surface, is called work function. It is denoted by

It is given by, = h
where h= planck's constant = 6.62 x 10-34 Js
The value of work function is different for different material.

Quantum theory of Radiation

Statement: It states that,"The radiation emitted or absorbed by the body is not in continuous fashion but it is in the form of bundle or packet of energy". Each packet has definite amount of energy called photon.
If be the frequency of emitted radiation then energy of photon is givn by,
E = h
E = (h x c) /
where h= planck's constant
c= speed of light
= wavelength of emitted radiation

Experimental study of photoelectric effect


Figure shows the experimental setup for the study of photoelectric effect. It consist of an evacuated glass tube with two electrodes A and C called anode and cathode. A variable potential difference is applied across the two electrodes which is measured by voltmeter. The current which flows through the circuit is measured by milliammeter.

Working:

When the suitable frequency of light incident on a cathode through window W, the photoelectrons are emitted. The photoelectrons are accelerated and moves towards anode due to negative potential and flows through the external circuit. As a result, electric current is setup is called photoelectric current.

A) Keeping the potential difference remains constant between the electrodes as intensity of light increases, the photo electric current is also increases. The graph between intensity of light and photoelectric current is shown in figure graph:-
This graph shows that the strength of photoelectric current is directly proportional to intensity of light. It means number of electron emitted from metallic surface is depend on intensity of light.



B) As the polarity of battery in reverse i.e. cathode is at '+ve' potential whereas anode is in '-ve' potential. In this case, emitted photoelectrons are deaccelerated due to positive potential. As a result, few number of electrons are able to reach anode and finally few amount of current flows through the external circuit.
As the '-ve' potential at anode is further increased the photoelectric current decreases and finally becomes zero. Such negative potential at anode at which photoelectric current becomes zero is called stopping potential or cut-off potential.
If vmax be the maximum velocity acquired by photoelectrons then gain in potential energy at stopping potential is given by,
eV0= (1/2)mvmax <----- (i)

Einstein Photoelectric equation:


Statement:
According to Einstein, the light of frequency (υ) consist photon each of energy (hυ). When photon of light frequency is incident on a metallic surface than the energy is completely transferred to the free electrons in the metal. A part of energy is used to emitt the electron from the metallic surface and rest of it is used to utilize in kinetic energy to the emitted electron.
If Φ0 be the minimum energy spend in order to liberate the electron from the metallic surface and (1/2) mv2max be the maximum kinetic energy K.E. acquire by photoelectrons.
Therefore, Energy of photon= work function + K.E.
i.e. hυ = Φ0 (1/2) mv2max <----- (i)
If υ0 be the threshold frequency of given metal,
Φ0= hυ0 <------ (ii)
from equation (i) and equation (ii)
hυ = hυ0 + (1/2) mv2max <------ (iii)

Equation (iii) is the required Einstein photoelectric equation. The equation (iii) may also be written as,
(1/2) mv2max = h( υ - υ0) <------ (iv)

Special Cases:

i. If υ is less than υ0 then K.E. becomes negative which is impossible.
ii. If υ is equal to υ0 then K.E. becomes zero which is possible but no photoelectrons are emitted.
iii. If υ is greater than υ0 then K.E. becomes positive. In this condition, photoelectrons are emitted.

Millikan's experimental measurement of planck's constant:

Millikan's Experiment is used to verify Einstein photoelectric equation and to determine the value of planck's constant. It consist of metal drum 'D' with three cylindrical metal cap coated with alkali metal. The drum is kept at the centre evacuated glass bulb. K is the knife which is used to clean the metal cap time to time. 'W' is the window through which light is passed. The cathode (C) is connected to the negative potential through rheostate whereas positive potential is connected to the drum through Galvanometer.

Working:
When suitable frequency of incident radiation falls on a metal cap photoelectrons are emitted and moves towards cathode. As cathode is connected to negative potential so only few energetic electrons are able to reach the cathode as a result few amount of current flows through the circuit. As negative potential further the photoelectric current decreases and becomes zero and corresponding stopping potential is noted. If vmax be the maximum velocity acquired by photoelectrons, then gain in potential energy at stopping potential is,
hυ= hυ0 + (1/2)mv 2max <------- (ii)
from equation (i) and equation (ii)
hυ= hυ0 + eV0
eV0= hυ - hυ0
V0 = (hυ/e)-(hυ0/e)
V0 = (hυ/e)+(-hυ0/e) <------ (iii)
Equation (iii) is the equation of straight line between stopping potential and frequency of light having slope h/e and making and intercept (-hυ/e) on the stopping potential axis.
If the graph is plotted between frequency of light and stopping potential over wide range of frequency the graph was obtained as below,

Hence, experimental graph is an agreement with equation (iii). Hence Einstein photoelectric equation was verified.
To find the value of planck's constant, the slope is obtained from the graph between V0 and υ is (h/e). On multiplying it with charge of an electron i.e.
h= slope x charge of electron
(h/e) x e
6.62 x 10-34 Js


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