Electrons are accelerated through a voltage difference of 175 kV inside a high v

Question

Electrons are accelerated through a voltage difference of 175 kV inside a high voltage accelerator tube.

What is the final kinetic energy of the electrons?

What is the speed of these electrons in terms of the speed of the light? (Remember that the electrons will be relativistic.)

Electrons are accelerated through a voltage difference of 175 kV inside a high voltage accelerator tube. What is the final kinetic energy of the electrons? Submit Answer Tries 0/20 What is the speed of these electrons in terms of the speed of the light? (Remember that the electrons will be relativistic.) Submit Answer Tries 0/20

Explanation / Answer

carge of electron e = 1.6*10^-19 C

V = 175 kV

from conservation foe energy

KE = PE

KE = eV

KE = 1.6*10^-19*175*1000

KE = 2.8*10^-14 J = 1.75*10^5 eV

(b) speed of light c = 3*10^8 m/s

from special thoery of relativity

E = moc^2 +(gamma -1) moc^2

rest mass energy of electron moc^2 = 0.511 MeV

E = 511000+175000 = 686000 eV

gamma = E/Eo = 686000/511000 = 1.3425

gamma = 1/(1-(v/c)^2)^0.5

1.3425 = 1/(1-(v/c)^2)^0.5

v = 0.667c

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