Question

Electrons accelerate at a high rate from the negative to the positive electrode of an x-ray tube, and emit x-rays when they slam into a metallic target. If the potential difference between the electrodes is 125,000 V, then (a) how much work is done by the field on each electron? (b) What is the kinetic energy of an electron when it reaches the positive electrode?

Answer 1

formula used :

work done on a charge Q coulomb when it moves from one point to other, and the points have potential difference of V volts=-QV joules    ….(1)

for electron

Charge = Q = -1.6 X10^-19C

(a)

potential difference is given to be=V=125,000 Volts

so using (1) we get work done on each electron =-QV=-(-1.6 X10^-19C X 125,000 Volts) = 2 X 10^-14 joules ……(2)

(b) according to conservation of energy ,sum of kinetic energy and potential energy always remain constant

since initially kinetic as well as potential energy was zero

therfore after reaching positive electrode

kinetic energy + potential energy = 0 …..(3)

since we know that potential energy = - work done

therefore from (2) potential energy = -2 X 10^-14 joules

putting this in equation (3) we get

kinetic energy - 2 X 10^-14 joules=0

hence

kinetic energy =2 X 10^-14 joules