An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure (∼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. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method.) Determine e/m from the data.

Given:


Potential at collector, V = 100V


Magnetic field strength, B = 2.83 × 10-4 T


Radius of orbit traced by electron, r = 12.0 cm


Let specific charge (i.e. e/m) = K


Kinetic energy of an electron is given by:


KE = = eV


→ v = …(1)


Where,


M = mass of electron


v = velocity of electron


e = charge of electron


V = potential difference (accelerating potential)


We also know that the bending is caused by the magnetic field,


So we can write,


Magnetic force = centrifugal force


e × v × B =


→ e × B =


→ v = …(2)


Where,


e = Charge on electron


v = velocity of particle


B = magnetic field strength


m = mass of electron


r = radius of trajectory


By equating (1) and (2) we can write,


.


→


By putting the values in above equation we get,




Hence the specific charge is 1.7 × 10-11 C Kg-1.


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