DETERMINATION OF e/m OF AN ELECTRON
INTRODUCTION
    J.J Thomson was the first scientist who measured charge to mass ratio (e/m) of an electron.
PRINCIPLE
 
    When a narrow beam of charged particles are projected at constant speed (v) across a magnetic         field in a direction perpendicular to the field, the beam of particles experiences a force, which makes     them move in a circular path.
APPARATUS
 
    It consists of a highly evacuated glass tube, fitted with electrodes. Electrons are produced by     heating a tungsten filament electrically. Electrons are made to accelerate and form a beam by     passing through discs A and B. They are passed through electric and magnetic field. Finally they fall     on zinc sulphide screen.
THEORY
 
    Actually electrons moving side ways are also directed towards the screen by applying a –ve potential     on a hollow cylinder (c) open on both sides surrounding the filament. Electrons are accelerated by     applying a potential difference of above 1000 V between the filament and disc A. A further potential     difference of 500 V is applied between the discs A and B. The arrangement focuses the beam to the     hole of the disc B from where it is further proceeds to a straight line. When beam of electrons enters     a magnetic field it moves in a circular track. The force experienced by the electron is
Fm = evB--------(1)
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    This magnetic field provides necessary centripetal force to electron so that it follows a circular path.

i.e. Fm = Fc

evB = mv2/r

eB = mv/r

e/m = v/Br -----(2)

    By knowing the values of v, B and r, value of e/m can be determined.
RADIUS OF CURVATURE
OF PATH
    If r is the radius of curvature of circular path, ‘a’ is the distance b/w ‘O’ and ‘O/’, and ‘b’ is the     distance b/w electron gun and screen then by using the property of chord:

AD x OD = BD x DO

(2r-a)(a) = b.b

2ra-a2 = b

    Since ‘a’ is very small as compared to ‘2r’, so we neglect ‘a2’.

2ra = b2

r = b2/2a

DETERMINATION OF THE VELOCITY (FIRST METHOD)
 
    The electrons are first accelerated by applying a potential (V) b/w discs A and B before entering the     magnetic field.

K.E = V.e

Or
1/2mv2 = Ve

v = (2Ve/m)1/2

Putting the value of v in eq. (2)

e/m = v/Br

e/m = (2Ve/m)1/2/Br

Squaring on both sides

e2/m2 = 2Ve/m/B2r2

or
e/m = 2Ve/B2r2

PARTICLES SELECTOR METHOD
 

    This is a more accurate method as compared to the above method. In this method, the beam is     passed through crossed electric and magnetic field. The electric field is so adjusted that the light     spot comes back to ‘O’ from ‘O/’. i.e. electron beam passes and straight without deflection.

Force on electron by electric field

Fe = Ee

Force on electron by magnetic field
Fm = Bev

    Since both forces balance each other

Fm = Fe

Bev = Ee

V = E/B
    Putting the value in eq. (2)

e/m = v/Br

e/m = E/B/Br

e/m = E/B2r

NUMERICAL VALUE OF e/m
 

    After substituting the values we get

e/m = 1.75888x1011 C/Kg

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