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INTRODUCTION
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| J.J Thomson was the first scientist who measured charge to mass ratio (e/m) of an electron. | |||
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PRINCIPLE
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| 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. | |||
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APPARATUS
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| 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. | |||
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THEORY
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| 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 | |||
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Fm
= evB--------(1)
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| For latest information , free computer courses and high impact notes visit : www.citycollegiate.com | |||
| This magnetic field provides necessary centripetal force to electron so that it follows a circular path. | |||
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i.e. Fm = Fc evB = mv2/r eB = mv/r e/m = v/Br -----(2) |
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| By knowing the values of v, B and r, value of e/m can be determined. | |||
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RADIUS
OF CURVATURE
OF PATH |
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| 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: | |||
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AD x OD = BD x DO (2r-a)(a) = b.b 2ra-a2 = b |
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| Since ‘a’ is very small as compared to ‘2r’, so we neglect ‘a2’. | |||
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2ra = b2 r = b2/2a |
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DETERMINATION
OF THE VELOCITY (FIRST METHOD)
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| The electrons are first accelerated by applying a potential (V) b/w discs A and B before entering the magnetic field. | |||
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K.E = V.e Or 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 |
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PARTICLES SELECTOR METHOD
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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 |
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Fe = Ee Force
on electron by magnetic field |
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Since both forces balance each other Fm = Fe Bev = Ee |
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V
= E/B
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| Putting the value in eq. (2) | |||
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e/m = v/Br e/m = E/B/Br e/m = E/B2r |
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NUMERICAL VALUE OF e/m
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After substituting the values we get e/m = 1.75888x1011 C/Kg |
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| For latest information , free computer courses and high impact notes visit : www.citycollegiate.com | |||