High intensity discharge lamps (HID) are used for stadium lighting and in the he

Question

High intensity discharge lamps (HID) are used for stadium lighting and in the headlights of some luxury vehicles. A particular HID has electrodes separated by 10 cm, at a potential difference 75 V. Since the lamps are full of pressurized gas, the electrons often collide with the gas atoms, transferring their kinetic energy to the gas. The average distance between collisions, d, is 0.15 cm. What is the average kinetic energy (in eV) an electron gains between collisions? Assume the electric field is uniform and constant. What is the magnitude of the electric field described in question (1)? Please show your work including every step in the calculation (i.e. pulling constants out of derivatives or integrals, dot products, etc).

Explanation / Answer

electric field=potential difference/distance

=75 /0.1=750 V/m

between collision , electron travels 0.15 cm

potential difference between these two points

=electric field*distance

=750*0.15*0.01=1.125 volts

so kinetic energy transferred to the gas=potential difference*charge

=1.125 eV

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