An X-ray tube uses a 20,000 volt difference to accelerate electrons across a 3 c

Question

An X-ray tube uses a 20,000 volt difference to accelerate electrons across a 3 cm gap between the plates of a parallel plate capacitor. The electrons pass through a hole in the second plate and impact on a tungsten target to create the X-rays a) What is the electric field in the gap between the plates? b) What is the kinetic energy of the electrons in Joules when they impact the tungsten if they start from rest from the negative plate? The charge on an electron is -1.6x10-19 C. c) How fast are the electrons moving in m/s when they hit the tungsten? The mass of an electron is 9.31x10-31 kg.

Explanation / Answer

voltage diffrenece=20kV

distance =0.03

electric field between the gaps =E=-dV/dx=20kV/0.03=-666.67kN/C

b)kinetic energy of the electrons when starts from rest =qV=1.6*10^-19*20000=3.2*10^-15J

c)velocity where they hit=0.5mv^2=3.2*10^-15J

so v=sqrt(3.2*10^-15J*2/9.31*10^-31)=8.29*10^7m.s

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