Question

An X-ray tube operates at `20k V`. Find the maximum speed of the electron strinking the anode , given the charge of electron is `1.6 xx 10^(-19)` coulomb and mass of electron is `9 xx 10^(-31) kg`.

Answer 1

When an electron of charge `e` is accelerated through a potential different `V`, it acquired energy `e V`. If `m` be the mass of the electron and `v_(max)` the maximum speed of electron , then
`(1)/(2) m v_(max)^(2) = e V` or `v_(max) = sqrt(((2 e V)/(m)))`
Subsitituting the given value , we get
`v_(max) = sqrt(((2 xx (1.6 xx 10^(-19)) xx 20.000)/(9 xx 10^(-31))))`
`= 8.4 xx 10^(7) ms^(-1)`