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 xx 10^(-4)` curves the path of the electrons in a circular orbit of radius 12.0 cm . (The path can be viewe because the gas ions in the path focus the beam by attracting electrons and emitting light by electron capture , the method is known as the 'fine beam tube ' method ) Determine e/m from the data .

Explanation

Given , V = 100 V, B = `2.83 xx 10^(-4) T , m_(e) = 9.1 xx 10^(-31) kg , e = 1.6 xx 10^(-19) C , `
r = 12 cm = 0.12 m , KE `=1/2 " mv"^(2) = eV rArr 1/2 xx 9.1 xx 10^(-31) xx v^(2) = 1.6 xx 10^(-19) xx 100`
` v^(2) = (2 xx 1.6 xx 10^(-17))/(9.1xx 10^(-31)) = 3.516 xx 10^(13) :. v = sqrt(2.516 xx 10^(13)) = 5.93 xx 10^(6) ` m/s
Specific charge of electron , `e/m = v/(rB) [ :' (mv^(2))/r = Bev ] = ( 5.93 xx 10^(6))/(2.83 xx 10^(-4) xx 0.12 )`
` :. e/m - 1.74 xx10^(11) ` C/kg