Class 12 Physics Electrons Notes

Class 12 Physics Electrons Notes



Unit – 5 
Modern Physics
Chapter – 20
Electrons


 


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Electron

The sub-atomic particle with a negative charge of about 1.6 x 10ˆ-19 C and having 9.1 x 10ˆ-31 kg is known as an electron.

Millikan’s oil drop Experiment

Millikan determines the value of the charge of an electron using an experiment known as Millikan’s oil drop experiment.

Principle

Millikan’s oil drop experiment is based on stoke’s law of viscosity. This law state, “When the sphere of radius ‘r’ falling through a viscous medium of co-efficient of viscosity (ղ) under the action of many forces. It attains steady velocity is called terminal velocity and force on Sphere ‘s’.

Construction 


Millikan's oil drop Experiment

Fig: Millikan’s oil drop Experiment

The experimental arrangement of this experiment Consists of the double-walled chamber having two windows W₁ and W₂ as shown in the fig above. The window W₁
is used to pass light in order to illuminate (shine).
The oil drop and window ‘ W₂’ is used to pass x-ray
In order to ionize the oil drop inside the double-walled
chamber, there are two metal plate A & B where
Plate A have a hole at its center. The upper plate
(A) is connected to a high-tension battery while the
lower plate is connected to the ground. Lock oil (a
non-volatile liquid ) can be sprayed into the hole at
Upper Plate ‘A’ with the help of an atomizer. The microscope
Is provided with a crosswire and micrometer scale.
So that the motion of the oil drop can be observed
and measured.

1. Motion of oil drop under gravity.


Motion of oil drop under gravity.

When an electric field is not applied, the oil drop fans
under gravity with increasing velocity. when the viscous
force act on oil drop, then its velocity becomes
Constant called terminal velocity.

where

r =radius of oil drop

ৎ =density of oil drop

σ = density of air

V₁ = terminal velocity

W = weight

F = viscus force

U = Upthrust

Now, 

Wight of oil drop (W1) = mass of oil drop x g

mg = v.ৎ.g

Again, 

Upthrust due to air (u) = weight of air displaced by oil drop 

Also, 

Viscus force (F) = σπηrV

When oil drops move with constant velocity,

F + u = W

equation (i) measures the radius of oil drop.

2. The motion of oil drop under electric field

When a strong field is applied between two plates, the negatively charged oil drops move in an upward direction and soon attain a terminal velocity (V2) in an upward direction. 

The motion of oil drop under electric field:

Also let ‘E’ be electric field intensity and ‘q’ be the charge, the electric force on oil drop in an upward direction be

fe = q.E 

Viscus force in a downward direction is 

F = σπηrV2

When the oil drop attains terminal velocity V2 then,

Class 12 Physics Electrons Notes

equation(ii) gives the charge of oil drop

3. When oil drop is at rest or stationary

Fe = W

qE = mg

where

q = ne   [∴ where n =no. of electron  ,e = charge of electron]

 where ,

v = Potential difference

d =  Separations between two plates

Class 12 Physics Electrons Notes

where,

v = volume of oil drop

r = radius of oil drop

p = density of oil

 Deflection of the electron inside the electric field

Fig: Motion of electron beam in electric field

Fig: Motion of electron beam in an electric field

Let us consider an electron of charge ‘e’ is inside the electric field of strength ‘E’ as shown in the figure. Then force experiment by an electron inside the electric field,

F = eE

Thus, The acceleration produced on this electron is, 

where m = mass of the electron.

If ‘y’ is the deflection in the vertical direction in time ‘t’, then;

If ‘x’ be the horizontal distance in time, ‘t’,

Class 12 Physics Electrons Notes

using equation (iii) in (ii),

Class 12 Physics Electrons Notes

If ‘V’ be the p.d between two plates of separation ‘d’ then the electric field is given by; 

E = V / d

Then, equation (iv) becomes; 

Class 12 Physics Electrons Notes

Equation (v) represent the equation of parabola hence the path of an electron field is parabolic in nature. 

When the electron just passes the plate x = D then equation (A) becomes.

Class 12 Physics Electrons Notes

Let, θ be the angle at which the beam emerged out from the field then,

Class 12 Physics Electrons Notes

The motion of electrons in a magnetic field

Motion of electron in a magnetic field 

Fig: Motion of electron in a magnetic field

Let us consider a beam of an electron moving with velocity ‘v’
horizontally entering inside uniform magnetic Field ‘B’ perpendicular to the direction of ‘V’
when it enters inside the magnetic field, a Lorentz force act on an electron
beam which is given by

Class 12 Physics Electrons Notes

This force is perpendicular to both B and V. Due to this
electron is deflected into a circular path as shown in the figure above

Let ‘m’ be the mass of the electron and ‘r’ be the radius of the circular path inside the magnetics field. Then,

Lorentz force provides the necessary centripetal force

Class 12 Physics Electrons Notes

This relation gives the radius of the circular path
Also,

Class 12 Physics Electrons Notes

So, the frequency of electron inside the magnetic field is given by,

Class 12 Physics Electrons Notes

And,
Time period of an electron inside a magnetic field is,

Class 12 Physics Electrons Notes

Where, 

E = V/d, Electric field intensity 

B = Magnetic field 

v = velocity, V = P.d. 

e = charge 

M = mass of electron

J.J Thomson Experiment

J.J Thomson discusses an experiment to determine the specific charge (e/m) of an electron which is known as J.J Thompson’s experiment.

Principle

When a beam of the electron is subjected to the uniform electric field and magnetic field acting perpendicular to each other in such a way that deflection is produced by another. Then the path of a beam of the electron remains undeflected.

Construction

Experimental Arrangement of J.J Thomson Experiment

 Fig: Experimental Arrangement of J.J Thomson Experiment

The experimental arrangement of J.J Thomson consists of cathode [c] and anode [A] which are enclosed in an evacuated discharge tube. When high voltage is applied between cathode and anode a fine beam of electrons emits from the cathode and through the hole of the anode they pass between two parallel plates p1 and p2

When an electric field is applied between two plates p1 and p2 then electron beams are deflected upward and appear at position ‘s1’. And when the magnetic field is applied the electron beam is deflected downward and appears at position ‘s2’. But, when both an electric field and a magnetic field are applied, then electron beams remain un-deflected and appear at position ‘s’.

 Theory 

When a potential difference (vo) is applied between cathode and anode, the beam of the electron is highly accelerated and gains a velocity ‘v’, whose K.E is given by ;

Class 12 Physics Electrons Notes

When both magnetic field and electric field are applied perpendicular to each other such that the beam of the electron does not bend. Then, the magnetic field force and electric force are equal;

i.e Magnetic force = Electric field 

Class 12 Physics Electrons Notes

Using equation (ii) in equation (i); 

Then;

Class 12 Physics Electrons Notes

If ‘V’ be the potential difference between two plates and ‘d’ be the separation between them.

Then,

Class 12 Physics Electrons Notes

using equation (iv) in (iii);

Class 12 Physics Electrons Notes

By knowing the value of V, B, d, and vo, we can find the value of e/m or a specific charge

Class 12 Physics Electrons Notes

By using J.J Thomson’s experiment and Millikan’s oil drop experiment we can calculate, 

Class 12 Physics Electrons Notes


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1 Comment

  1. Avishek DC

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