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Question -

An electron gun with its collector at apotential of 100 V fires out electrons in a spherical bulb containing hydrogengas at low pressure (тИ╝10тИТ2┬аmm of Hg). A magneticfield of 2.83 ├Ч 10тИТ4┬аT curves the path of the electrons in acircular orbit of radius 12.0 cm. (The path can be viewed because the gas ionsin the path focus the beam by attracting electrons, and emitting light byelectron capture; this method is known as the тАШfine beam tubeтАЩ method.Determine┬аe/m┬аfrom the data.



Answer -

Potential of an anode,┬аV┬а=100 V

Magnetic field experienced by the electrons,┬аB┬а=2.83 ├Ч 10тИТ4┬аT

Radius of the circular orbit┬аr┬а=12.0 cm = 12.0 ├Ч 10тИТ2┬аm

Mass of each electron =┬аm

Charge on each electron =┬аe

Velocity of each electron =┬аv

The energy of eachelectron is equal to its kinetic energy, i.e.,

It is the magnetic field, due to its bendingnature, that provides the centripetal force┬а┬аfor the beam. Hence,we can write:

Centripetal force =Magnetic force

Putting the value of┬аv┬аinequation (1), we get:

Therefore, the specific charge ratio (e/m)is

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