# Charge to Mass Ratio (e/m ratio) of Cathode – Atomic Structure

## charge to mass ratio (e/m ratio) :

J.J.Thomson performed an experiment in 1897, to determine charge to mass ratio (e/m ratio) of cathode ray particle. For this purpose he used a discharge tube as shown in figure. In this tube electric field and magnetic field are applied to cathode rays which were perpendicular to each other as well as to the cathode rays. In absence of electric as well as magnetic field cathode rays fall on P1 but in presence of magnetic field of known strength ‘B’ they fall on P2. At this point magnetic force and centrifugal force balance each other, so

Bev      =          mv2/r

e/m      =          v2/rBv

e/m      =          v/Br ………………… (1)

But by applying electric field of variable strength cathode rays start coming back to point P1. Go on increasing strength of electric field and the strength when cathode rays again fall on P1 is noted as ‘E’. At this stage electric force and magnetic force balance each other, so

Bev      =          Ee

v          =          Ee/Be

v          =          E/B ……………….. (2)

Putting value of ‘v’ in equation-1

e/m      =          E/B.Br

e/m      =          E/B2r ……………… (3)

where e = Charge of cathode ray particle

m = mass of cathode ray particle

E = Strength of electric field

B = Strength of magnetic field

r = distance from P1 to P2

Thus by equation-3 we can determine charge to mass ratio of cathode ray particle, with out knowing charge as well as mass of the particle.

The e/m ratio of cathode ray particle was found to be 1.76 x 1011 C/kg.

It is further pointed out that e/m ratio of cathode ray particle is independent of nature of the gas used in the discharge tube as well as that of nature of cathode. It means cathode ray particle is a fundamental particle.

J.J.Thomson discovered this negative particle (having e/m ratio 1.76 x 1011 C/kg) in atom but the name electron is given to it by G.J.Stoney in 1891.

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