Question

An electron gun with its collector at a potential of 100 V fires outelectrons in a spherical bulb containing hydrogen gas at lowpressure (∼10–2 mm of Hg). A magnetic field of 2.83 × 10–4 T curves the path of the electrons in a circular orbit of radius 12.0 cm. (Thepath can be viewed because the gas ions in the path focus the beamby attracting electrons, and emitting light by electron capture; thismethod is known as the ‘fine beam tube’ method.) Determinee/m from the data.

Answer 1

It is given that the potential of an anode, V=100 V, the magnetic field experienced by the electrons, B=2⋅83× 10 −4  Tand the radius of the circular orbit, r=12⋅0 cm.

The energy of each electron is equal to its kinetic energy.

1 2 m v 2 =eV v 2 = 2eV m (1)

From the formula of centripetal force,

F= m ν 2 r

The centripetal force will be equal to magnetic force and it can be written as,

m v 2 r =evΒ v= eΒr m (2)

Substitute the value of vin equation (1).

2eV m = ( eΒr m ) 2 e m = 2V Β 2 r 2

Substitute the values in above expression.

e m = 2×100 ( 2⋅83× 10 −4 ) 2 × ( 12× 10 −2 ) 2 =1⋅73× 10 13   Ckg −1

Hence, the specific charge ratio ( e m ) is 1⋅73× 10 13   Ckg −1 .