MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Electrons and Photons Page 1

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1. J. J. Thomson's Experiment on Cathode Rays

Sir J. J. Thomson performed a number of experiments to determine

 i) the velocity of the cathode particles and ii) the ratio of change to the mass of the cathode particles.

Determination of v: Electric and magnetic fields are applied simultaneously and so arranged that the forces exerted on the cathode particles by those fields are equal in magnitude and opposite in directions.
\
Force on cathode particles (electrons) due to electric field
= Force on cathode particles (electrons) due to magnetic field.
e E = e B v

 \ v = E B

 Where v = velocity of cathode rays. E = intensity of electric field. B = intensity of magnetic field.

If V is the potential difference applied between the plates C and D (see figure) and d is the distance between the plates

 E = V d

 \ v = V Bd

 Determination of :When only magnetic field is applied, cathode particles move along a circular path. The centripetal force is provided by the magnetic force.

.

 \ mv2 = Bev r

 \ e = n m Br

where v

= velocity of the particle

R

= radius of the circular path

B

= intensity of magnetic field

 e m

= change to mass ratio of cathode ray (electrons)

Remember

1. Work Function: The minimum energy which the incident radiation must possess to liberate photoelectrons from a photosensitive surface is known as the work function of that surface. It is denoted by the symbol W0 or Æ.
2. Stopping Potential: The potential difference necessary to bring the electrons of maximum K.E. to rest is called stopping potential. In other words, the retarding potential that stops the photoelectric current is called the stopping potential. If a negative potential difference of magnitude V0 is able to stop electrons of maximum K.E. m (Vmax)2, then     m(Vmax)2 = e V0
3. Threshold Frequency (n0) The threshold frequency for a given surface is defined as the minimum frequency of incident light below which no photoelectrons are emitted, however intense the incident light may be.

2. Photoelectric Effect

The phenomenon of emission of electrons by a metal surface when light is incident upon it is called photoelectric effect. The electrons emitted in the process are called photoelectrons.

Characteristics:

1. No photoelectric emission takes place when the frequency of the incident radiation (n) is below a certain minimum frequency called threshold frequency (n0), however high the intensity may be.
2. If frequency (n) of the incident radiation is kept constant at a value greater than (n0); photoelectric current is directly proportional to the intensity of incident radiation.
3. The maximum kinetic energy of photoelectron is independent of intensity but depends upon frequency of incident radiation.
4. The threshold frequency (n0) depends upon the material of the emitting surface.
5. The positive potential applied to the plate C is gradually reduced to zero. It is found that photoelectric current goes on decreasing. If potential difference is reversed, making the collector (C) negative with respect to the emitter and steadily increased, the photoelectric current stops at a certain potential which is known as the stopping potential (Vs). The maximum kinetic energy is related to the stopping potential Vs by the relation
m (Vmax)2= e Vs.
6. The emission of photoelectrons is instantaneous. Graphs showing the experimental results:

1. (a) Variation of photoelectric current with the collector potential for different frequencies greater than V0 [I = constant]
1. (b) Stopping potential vs is independent of the incident intensity I where V is constant.

 3. Einstein's Photoelectric Equation Einstein suggested that, Energy is radiated and also travels in form of bundles or quanta known as 'photons'. Each photon carries an energy hn. When a photon of incident radiation interacts with an electron inside an atom, the whole amount of energy is absorbed by the electron. The electron uses part of the energy (hn) gained to liberate itself and the rest is converted into kinetic energy. For each metal, a certain minimum amount of energy known as its work function (W0) is required to liberate an electron. The electrons which require minimum energy (W0) to liberate themselves, are the ones to emerge with maximum kinetic energy. \ hn - W0 = m (Vmax)2 \ hn = m(Vmax)2 + W0 … (1) But e Vs = m (Vmax)2, where Vs = stopping potential. \ hn = e Vs + W0 If frequency n is decreased, the maximum kinetic energy of photoelectron decreases till it becomes zero at n = n0 \ h n0 = 0 + W0 or hn0 = W0 … (2) Substituting (2) in (1), hn = m(Vmax)2 + hn0 \ m (Vmax)2 = hn - hn0 … (3) Explanation of Photoelectric Effect: All characteristics of photoelectric effect are explained by Einstein's photoelectric equation, whereas wave theory can explain only one: the increase in photoelectric current with intensity of incident radiation.

4. Photoelectric Cell and its Applications

A photoelectric cell works on the basis of the photoelectric effect-

(a)Symbol

(b) Photoelectric cell
A concave shaped cathode inside an evacuated glass bulb or tube emits photoelectrons. These are collected by an anode which is maintained at a positive potential with respect to cathode. When light is incident on the cathode of a photoelectric cell, photoelectrons are emitted and current flows. When light beam is cut off, current stops.

Applications of Photocell (Photoelectric Cell):

1. Exposure Meter: This is used by photographers to find the appropriate time of exposure required for taking good photographs.
2. Burglar Alarm: The photocell is connected to a relay and a bell so that bell starts ringing when an infra red beam is cut off by a burglar.
3. Reproducing Sound in Motion Pictures: When film is projected on a screen, a light beam passes through the sound track on the film moving in the projector. This light beam is made to fall on the cathode of a photocell to generate current varying according to the original sound track. A loudspeaker then converts this current into sound.
4. Automatic street light control, shutting and opening of doors, counting objects are also some applications where a photoelectric cell is used.
5. Lux Meter: This instrument is used to determine the intensity of light.

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