Unit - 5 Modern PhysicsChapter - 20Electrons
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 (Õ²) under the action of many forces. It attains steady velocity is called terminal velocity and force on Sphere 's'.
Construction
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.
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.
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,
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
where,
v = volume of oil drop
r = radius of oil drop
p = density of oil
Deflection of the electron inside the 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',
using equation (iii) in (ii),
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;
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.
Let, θ be the angle at which the beam emerged out from the field then,
The motion of electrons 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
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
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This relation gives the radius of the circular path Also,
So, the frequency of electron inside the magnetic field is given by,
And, Time period of an electron inside a magnetic field is,
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
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 ;
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
Using equation (ii) in equation (i);
Then;
If 'V' be the potential difference between two plates and 'd' be the separation between them.
Then,
using equation (iv) in (iii);
By knowing the value of V, B, d, and vo, we can find the value of e/m or a specific charge
By using J.J Thomson's experiment and Millikan's oil drop experiment we can calculate,
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